Hossam El-Asrag

Massachusetts Institute of Technology, Cambridge, Massachusetts

Anthony C. Iannetti

Glenn Research Center, Cleveland, Ohio 

Radiation-Spray Coupling for Realistic Flow

Confi gurations

NASA/TM—2011-217111

October 2011
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Hossam El-Asrag

Massachusetts Institute of Technology, Cambridge, Massachusetts

Anthony C. Iannetti

Glenn Research Center, Cleveland, Ohio 

Radiation-Spray Coupling for Realistic Flow

Confi gurations

NASA/TM—2011-217111

October 2011

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
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Level of Review: This material has been technically reviewed by technical management. 

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subject to revision as analysis proceeds.
Abstract

Three Large Eddy Simulations (LES) for a lean-direct injection (LDI) combustor

are performed and compared. In addition to the cold flow simulation, the effect of

radiation coupling with the multi-physics reactive flow is analyzed. The flamelet

progress variable approach is used as a subgrid combustion model combined with

a stochastic subgrid model for spray atomization and an optically thin radiation

model. For accurate chemistry modeling, a detailed Jet-A surrogate mechanism is

utilized. To achieve realistic inflow, a simple recycling technique is performed at the

inflow section upstream of the swirler. Good comparison is shown with the experimental data mean and root mean square profiles. The effect of combustion is found

to change the shape and size of the central recirculation zone . Radiation is found

to change the spray dynamics and atomization by changing the heat release distribution and the local temperature values impacting the evaporation process. The

simulation with radiation modeling shows wider range of droplet size distribution by

altering the evaporation rate. The current study proves the importance of radiation

modeling for accurate prediction in realistic spray combustion configurations, even

for low pressure systems.

NASA/TM—2011-217111 1

Radiation-Spray Coupling for Realistic Flow Configurations 

Hossam El-Asrag 

Massachusetts Institute of Technology 

Cambridge, Massachusetts 02139 

Anthony C. Iannetti 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 
1 Introduction

All modern combustors must balance the need for stability and performance

with the goals of efficiency and emissions reduction. The emissions from stationary as well as non-stationary gas turbines have a profound effect on the

environment and the balance of the eco-system [1]. For example, green house

gases like Carbon dioxide CO2, water vapor H2O, and methane CH4 are primary by-products from the burning of fossil fuels in internal combustion and

gas turbine engines. These gases contribute to the global warming effect by

absorbing the sun infrared rays. Other important pollutants are CO and NOx.

While CO has known hazardous health effects, NO causes acid rain and depletes the ultra-violet protective layer known as the ozone layer [2]. Finally,

hydrocarbon fuels under rich conditions generate soot, which is known for its

carcinogenic precursors and associated organics [3,4]. A common technique to

reduce emissions of NOx, CO, soot, and unburned hydrocarbons is to operate

at lean premixed conditions, which in return leads to stability problems [5–

7]. For aircraft engines, this poses a safety concern and is therefore typically

avoided. Modern engines for next generation supersonic transportation aircraft, however, face even more stringent emissions regulations. Because of

the high cruise altitude of these aircrafts in the lower stratosphere, engine

emissions contribute directly to depleting the ozone layer [8]. To meet this

challenge, several techniques have been proposed that are based on essentially

premixed combustion. Among these are lean- premixed-prevaporized combustion (LPP) and lean direct injection combustion (LDI [9]). The latter is the

focus of the present study.

NASA/TM—2011-217111 2
challenges [10,11]. Gas turbine engines operate under turbulent conditions using complex fossil fuels [12] that introduce a wide range of length and time

scales [13]. The resolution of these scales usually require fine mesh [14], which

can lead to costly computation. In addition, the production of pollutants usually involves a large number of chemical reactions that expands the numerical

effort. Furthermore, the complexity of the system is exacerbated as most of

gas turbine engines fuels are injected in the liquid phase. The breakup of the

spray droplets and their subsequent evaporation is another complex process

that is not well understood yet [15,16] and which might be inherently coupled

with the formation of pollutant and other physical process such as radiation [17]. Therefore, efficient numerical tools are needed to simulate reactive

multiphase flow in complex geometries under high Reynolds number turbulent

conditions [18–20].

In the past decade, large eddy simulation (LES), has proved to be a promising

tool for turbulent reactive flow simulations [20] using both structured [21–26]

and unstructured meshes [27–30]. In the current work, the full single element

Lean Direct Injection (LDI) combustor is simulated in the LES framework.

The Lean Direct Injection configuration is a good candidate for low emissions

gas turbine requirements, where the combined geometry of a swirler and a

Venturi nozzle results in stable combustion with potentially ultra-low NOx and

soot emissions. Air is injected in a swirler and it mixes with the fuel droplets to

atomize, break up aerodynamically and partially premix in the Venturi before

entering the combustor. The combination of the swirler and the Venturi has

proven to maximize the atomization performance and minimize pressure drop

across the injector [31]. The Venturi nozzle also provides sufficient residence

time for the fuel droplets to vaporize and mix uniformly with the swirled air

The numerical prediction of the emissions in each system is faced by many

droplets in a lean mixture.

NASA/TM—2011-217111 3
Here, non-reactive and reactive multi-physics simulations will be shown for an

LDI system [32–34]. The current paper presents simulations that couple the

interaction of turbulence with the important physical processes such as spray

dynamics, chemistry, and radiation in a realistic configuration. The combustor

emission characteristics, radiation coupling, flow/flame interaction, as well as

the spray characteristics will be shown and compared with experimental data.

A description of the modeling approach is outlined in the next section.

For accurate chemistry modeling, a detailed Jet-A surrogate mechanism is

utilized [35]. The number of species and reactions considered are 122 and 900,

respectively. Jet-A is known to be a common fuel for gas turbine engines. In

the context of LES, the detailed Jet-A surrogate mechanism will be introduced

in the frame work of the flamelet approach [36].

2 Combustion and radiation modeling

The combustion model used is the flamelet/progress-variable (FPV) approach [37,38].

The FPV approach is based on the flamelet concept, which relates the species

mass fractions and energy to the mixture fraction through the flamelet equations

ρ

∂Φ

∂t − ρ

χ

2

∂

2Φ

∂Z2

=  ̇ω , (1)

where Z is the mixture fraction, ρ is the density, Φ = (T, yi)

T

is a vector

that contains the species mass fractions yi and the temperature T.  ̇ω is the

source-term vector and χ is the scalar dissipation rate, which represents the

NASA/TM—2011-217111 4
local rate of molecular mixing and which is strongly impacted by the large

scale turbulent mixing process. The steady laminar flamelet model (SLFM)

tabulates the solution of Eq. (1) (without the unsteady term) as a function of

the mixture fraction and the stoichiometric scalar dissipation rate χst. Hence

an equation of state (EOS) relating reactive scalars to the mixture fraction

and its dissipation rate is written as

Φ = Fχ,Φ (Z, χst) . (2)

The solutions to the flamelet equations are characterized by the non-linear interaction between chemistry and transport. For increasing dissipation rate, the

flame temperature decreases, which ultimately leads to extinction. In SLFM,

only non-extinguished solutions of the flamelet equations are considered, which

limits the applicability of the model. It was shown by Pierce and Moin [37],

for example, that SLFM predicts too much heat release in the essentially

non-reactive regions close to the nozzle for a flame that is aerodynamically

stabilized by a recirculation region. To overcome this limitation, Pierce and

Moin [37] proposed a tabulation based on a reaction progress parameter λ

instead of the scalar dissipation rate, which leads to the Flamelet/Progress

Variable (FPV) formulation of the steady flamelet model.

As a result, the new state vector is given as Ψ = Fλ,Ψ (Z, λ). The reaction

progress parameter λ is defined according to Ihme et al. [38] through a reaction

progress variable C such that it is independent of the mixture fractionZ.

The progress variable C can be a combination of certain species representing

combustion products, temperature or sensible enthalpy. The progress variable

here is the sum of the mass fractions of CO2, CO, H2O, and H2. The reaction

progress parameter λ is then defined for each flamelet as the stoichiometric

NASA/TM—2011-217111 5
value of the reaction progress variable. Hence, the reaction progress parameter

an be obtained from an inversion of the flamelet library.

C = FC (Z, λ) , (3)

assuming that inversion is unique, which puts a restriction on the definition

of the reaction progress variable.

The state vector Φ = Fλ,Φ (Z, λ) is obtained by the solution of Eq. (1), which

includes all possible steady state solutions. Then, a joint probability density

function (PDF) needs to be evaluated to obtain the Favre filtered (e) values

of the state vector. Since Z and λ are defined to be independent variables, by

using Bayes′theorem, the joint PDF at a certain time and position in space

is given as

P ̃ (Z, λ; x, t) = P ̃ (λ|Z; x, t) P ̃ (Z; x, t) , (4)

where marginal PDF of the mixture fraction P ̃ (Z) is assumed to be a beta

distribution [37], and the conditional reaction progress parameter PDF is a

delta function. Since the β-distribution is characterized by the scalar mean Ze

and the scalar variance Zg′′2, and the delta-function by the mean eλ the flamelet

tabulation can be written in the form:

Φ =e Fλ,fΦ



Z, e Zg′′2,

eλ



. (5)

With Eq. 5 and

Ce = Fλ,fΦ



Z, e Zg′′2,

eλ



, (6)

NASA/TM—2011-217111 6
the mean reaction progress parameter as an independent parameter in the

tabulation can be replaced by Ce, which is readily available in a simulation

through the solution of a filtered transport equation for Ce. As previously

mentioned, for accurate temperature predictions, radiation might have to be

considered. Ihme and Pitsch [39] have extended the above FPV approach to

account for radiation as an unsteady process. In this model, the unsteady

flamelet equations are solved considering radiative heat losses. The unsteady

solution starts from the steady adiabatic solution and proceeds until a new

steady state is found. The time can be replaced by the enthalpy, which is

defined to include the heats of formation, and which therefore appears as a

new parameter in the tabulation. Consequently, the extended FPV EOS can

be written as

Ω =e FΩe



Z, e Zg′′2, C, e Hf



. (7)

As a result, four parameters have to be computed as part of the LES solution, namely the filtered mixture fraction Ze, the subfilter scalar variance

Zg′′2, the filtered progress variable Ce, and the filtered enthalpy Hf. Here, the

scalar variance Zg′′2is evaluated using an algebraic model [37], which assumes

homogeneity and local equilibrium for the subgrid scales and is given by

ρ ̄Zg′′2 = CZ∆

2

ρ ̄|∇Ze|

2

, (8)

where the mixture fraction coefficient CZ is computed dynamically and  ̄ρ is

the filtered density. Finally, three additional transport equations are solved

for Ze, Hf and Ce as follows:

∂ρ ̄Ze

∂t + ∇ · 

ρ ̄ue

eZ



= ∇ · ρ ̄Df∇Ze



+ ∇ · τe

res

z

, (9)

NASA/TM—2011-217111 7
∂ρ ̄Ce

∂t + ∇ · 

ρ ̄uCf



= ∇ · ρ ̄Df∇Ce



+ ∇ · τe

res

c +  ̄ρ

eω ̇ C , (10)

∂ρ ̄Hf

∂t + ∇ · 

ρ ̄uHf



= ∇ · ρ ̄Df∇Hf



− eq ̇r, (11)

where Df is the filtered molecular diffusivity, assuming equal species diffusivities and unity Lewis numbers, and eω ̇ C is the filtered chemical source term of

the progress variable, which is tabulated in the flamelet library. In the above

equations, the residual stresses τe

res are modeled by a dynamic approach [37].

For an optically thin radiation model [40], the filtered radiation source term

is

qer = 4σ



Tf4 − eT

4

∞

X(pgiai), (12)

where pi and ai are the partial pressure and Planck mean absorption coefficient of species i, respectively, σ is the Stefan Boltzmann constant, and eT

4

∞

is the ambient reference temperature at one atmosphere. To account for the

unsteadiness of NOx production, the filtered mass fraction of NO, eYNO is computed by solving a transport equation rather than extracting the values from

the flamelet tables [39]. The filtered LES equation can then be written as

∂ρ ̄

eYNO

∂t + ∇ · 

ρ ̄uYfNO= ∇ · ρ ̄Df∇ eYNO+  ̄ρ

eω ̇ NO , (13)

where the filtered production rate eω ̇ NO is closed according to the model by

Ihme and Pitsch [39]. More details about the FPV and the radiation model

can be found in [39].

NASA/TM—2011-217111 8
3 Secondary breakup spray model

Jet-A fuel spray droplets are injected from the centerline simplex atomizer,

with a specified drop-size distribution. The hollow cone spray has a total angle

of 90◦. The spray models employed have been described in detail by Apte et

al. [41,28,42]. Here, we summarize the most important features.

A stochastic subgrid model for spray atomization is used here. The initial

liquid film is approximated by a droplet of size equal to the nozzle diameter.

The model views the subsequent particle breakup of the injection of a specified drop-size as a discrete random process, where droplet size is treated as

a time-dependent stochastic variable. The temporal and spatial evolution of

the particle size distribution is then governed by the Fokker-Plank differential

equation. This evolution leads to the formation of new droplets and destruction of the parent ones. The new droplets position and velocity vectors are

tracked by a Lagrangian algorithm in the physical space. Two-way coupling

between the gas phase and the liquid droplets is achieved by the source terms

in the gas-phase equations, which represent the mutual effect of mixing and

momentum/energy transport. These effects are induced by droplet breakup,

evaporation, and convection by the flow-field. Simultaneously with the process

of secondary droplet breakup and mixing with the gas phase, the liquid phase

evaporates under the appropriate conditions. The evaporation model solves

a set of ordinary differential equations (ODEs) that describe the variation

of the droplet mass and temperature due to evaporation and assumes that

non-equilibrium effects inside the droplet volume are neglected. A third-order

Runge-Kutta scheme is used to integrate the set of ODEs with the minimum

physical drop time scale. The mathematical formulation of the above scheme

is omitted here for brevity and can be found elsewhere [42].

NASA/TM—2011-217111 9
4 Numerical setup

The simulation is performed by the unstructured LES code CDP. CDP is

a set of massively parallel unstructured finite-volume flow solvers developed

specifically for large eddy simulation. The solver used to perform the reactive

simulations reported in this work is a node-based low-Mach number solver [43].

A the fully incompressible solver is used for the non-reactive case for computational efficiency. The LES governing equations and the sub-grid momentum

closures are omitted here for brevity.

The experimental setup and data are provided by Farhad et al. [44]. The geometry of the single-element combustor is shown in Fig. 1a with the inflow

pipe upstream of the swirler. Liquid fuel is injected through the center (closed

for the non-reactive case), while air is injected through a swirler with vane angles of 60◦

. The global swirl number is 1. The swirler is composed of six helical

vanes with an effective area of 870 mm2. The fuel droplets from the centerline

and the swirled air are mixed in a converging-diverging Venturi nozzle. The

helical air swirler has an inside diameter of 9.3 mm and an outside diameter of

22.1 mm. The combustor has a square cross-sectional area of 50.8 x 50.8 mm.

The mesh uses 1,072,640 hexahedral elements, which is slightly above the

861, 823 element mesh used in the RANS calculations [44,45] and about half

the LES structured mesh used by Patel and Menon [22]. The unstructured

mesh is shown in Fig. 1. The mesh distribution along the z = 0 plane and

in the vanes is shown in Fig. 1b, while the y − z plane grid distribution

NASA/TM—2011-217111 10
is presented in Fig. 1c. The mesh cells are clustered toward the centerline

and toward the walls of the combustor. Here, we extend the original RANS

mesh [44] to account for more realistic inflow.

An inflow bulk velocity of 20.14 m/s is provided through a tube upstream of

the swirl injector. The inflow air is at temperature To = 294 K and pressure

of 1 atm, while the global equivalence ratio is 0.75. The fuel spray has an

inflow mass flow rate of 4.15.10−04 kg/s and an initial velocity of 20 m/s.

The droplets are injected with a Rosin-Rammler distribution

Fm(D) = 1 − exp −

D

δ

n

!

, (14)

where Fm(D) is the cumulative distribution function of the droplet diameter

D, and the parameters n = 1.34 and δ = 24 μ m are chosen to curve-fit

the distribution of the experimental data at the first measured location (x =

3mm). An inflow recycling technique is used [46] to achieve realistic inflow

turbulence. The recycling is done until the inflow profile of the upstream pipe

recovers a realistic inflow turbulent boundary layer. The boundary conditions

used are inflow/outflow in the x -direction and adiabatic walls in the y and z

directions.

Statistics are collected over a physical time of 0.032 seconds after the initial

transient for the reactive flow cases and over 0.167 seconds for the cold-flow

case. Based on the bulk inflow velocity and the full length of the combustor,

this represents two complete flow-through times for the reactive cases and

about seven flow-through times for the non-reactive case. The simulation was

performed on a Linux cluster at Stanford University with infiniband interconnection and dual Intel Clovertown (Quad Core) 2.33 GHz processors with 8 GB

NASA/TM—2011-217111 11
RAM per node. With the current mesh resolution the code scaling was found

to level off at 96 processors for the spray-combustion case. The computational

time per flow through time was 900 CPU hours for the reactive case.

5 Results and discussion

In this section, two LES simulations are compared to the experimental data.

The statistics for the two simulations, with and without radiation, are collected

over the same total run time. Unless mentioned otherwise, only the case with

radiation is considered for the comparison with the radial experimental profiles. Almost all available experimental data are used in the comparison and

selected non-reactive flow data are included to show the effect of heat release.

First, the time-averaged flow features of the reactive flow will be shown and

compared with the non-reactive case with an emphasis on the radiation effect.

Subsequently, the mean and root mean squared (rms) values of the gas flowfield, the scalars, and the spray characteristics will be compared with the

experimental data.

Due to the swirling flow, an adverse pressure gradient is generated in the

axial direction and a vortex breakdown bubble (VBB) is established. The

LDI is characterized by a central recirculation zone (CRZ) in addition to

recirculation zones (RZs) at the corner of the dump plane. Three RZs had

been observed previously in the non-reactive case [46,47,45]. Figures 2a and 2b

show isosurfaces of mean axial velocity for hUi = 0 m/s for both the reactive

and non-reactive cases, where the brackets denote a time average. The length

of the CRZ in the non-reactive case is approximately twice as that in the

NASA/TM—2011-217111 12
reactive one. However, the reactive CRZ has a larger effective bulk diameter.

Also, a small toroidal RZ close to the divergent part of the Venturi exists in

the reactive flow case as shown by the side view in Fig. 3, which is caused

by flow separation. A more compact and stronger reactive CRZ is due to the

expansion of the flowfield by heat release effects as shown later.

Figure 4 shows vector plots for the time-averaged total velocity magnitude for

the reactive flow case with radition. Only the projections in the y = 0 plane

are shown here for clarity. Figure 4a shows that the CRZ starts early inside

the divergent part of the Venturi nozzle, in addition to a small RZ observed

just downstream of the injector exit. These two small RZs inside the Venturi

enhance mixing and atomization of the spray with the swirling air. However, at

the injector exit, the droplets and the spray sheet have enough momentum to

penetrate this RZ toward the Venturi exit as shown in Fig. 4b. This observation

will be confirmed later by the axial and radial velocity profiles. Figure 4c shows

the velocity magnitude vector plot downstream of the dump. The CRZ has

an azimuthal vortex at the location x = 17 mm downstream of the dump

plane. Figure 4c also shows an additional annular vortex at the burner corners

where the second RZ is located. Corner vortices are found to extend along the

combustor wall corners up to the exit plane in the y − z plane (not shown

here), which will affect the spray distribution as shown later.

An instantaneous temperature distribution is shown in Fig. 5. Figure 5a shows

a snapshot of the y = 0 plane. Figures 5b-d show three consecutive snapshots

at the location x = 11 mm. Figures 5a and 5d are at the same instant in time.

The temperature shows high gradients at the shear layer location and around

the CRZ, which leads to strong mixing. At the edge of the CRZ, fresh cold

gases (dark areas) are engulfed into the CRZ. Inside the core of the RZ, the

NASA/TM—2011-217111 13
temperature shows nearly uniform distribution due to the strong mixing the

fluid undergoes before entering the CRZ.

A comparison of the heat release distribution is shown in Fig. 6. The flame

without radiation shows locally lower mean values than the case with radiation, for which the heat release is more distributed. The reason is that radiation

causes the temperatures to be locally lower, which leads to smaller evaporation rates of the liquid fuel and consequently a lower fuel vapor mass fraction

as observed in Fig. 7.

Two snapshots of the spray distribution from the two simulations are shown

in Fig. 8. The spray exhibits a 90ocone angle. Some of the spray droplets

are trapped inside the corner vortex, which results in an increase in the mean

droplet diameter close to the walls. The simulation with radiation shows a

wider range of droplet sizes. For the shown instantaneous snapshots with radiation, droplet size ranges between 0.5 μm and 50 μm, while without radiation

the range is between 0.7 μm and 40 μm. This is attributed to a higher evaporation rate when radiation is not included. Since no primary breakup model is

employed here, the spray spectrum shows an intermediate regime, where the

spray injected from the nozzle undergoes secondary breakup, followed by a dilute regime where the droplets evaporate. The intermediate regime is mainly

inside the Venturi, while the dilute regime extends until all the droplets are

evaporated.

The steady state droplet and parcel-size histograms for the whole combustor

volume for both cases are shown in Fig. 9. In general, the case without radiation has a lower number density of droplets over the whole spectrum. This

will subsequently affect the flow dynamics and the flame structure (as shown

NASA/TM—2011-217111 14
earlier). The radiation effect on droplet evaporation can be assessed in Fig. 10.

This figure shows the time-averaged rate of droplet mass evaporation at the

plane y = 0. This value represents the time average of the source term of the

droplet mass variation. The case without radiation shows higher evaporation

rates in the vicinity of the injector and in the flame surface surrounding area

due to the reasons discussed earlier.

The LES simulation with radiation modeling is compared with the experimental data next. Figures 11a and 11b show spray droplet mean diameter D10 and

Sauter mean diameter D32. Overall good agreement is observed. At the first

three axial locations a peak value is shown that starts at a radial distance of

8 mm from the centerline (for x = 3 mm) and then spreads radially towards

the wall (for x > 3 mm). This location is an indication of the spray sheet

cone angle. Since the spray droplets directly emitted from the injector have

a large droplet size, the profiles show peak values at these radial locations.

Downstream of x = 15 mm some droplets are trapped in the wall-corner vortex. It is interesting to note that the value of the mean diameter is increasing

downstream due to evaporation of the smaller diameter droplets (larger than

the cut-off value of the experimental measurements). This is consistent with

the experimental data.

The spray droplets′ mean axial velocity distribution is shown in Fig. 12. Good

agreement is observed for all locations. Consistent with Fig. 11, the LES shows

over-predicted droplet mean axial velocity at the locations of over-prediction

in the droplet size. Again, over-prediction is expected at the first few locations,

where the small-size droplets are not considered in the experiment.

NASA/TM—2011-217111 15
radiation on the flow features, the centerline mean axial velocity profiles are

shown in Fig. 13. Reactive and non-reactive data from experiments are compared with the LES results with and without radiation. The figure shows that

the non-reactive RZ extends to about 100 mm downstream of the dump, while

the reactive RZ is stronger and more compact (about 50 mm in length). The

expansion of the flow by heat release changes the local velocity and pressure

distribution. This local expansion (in the flame region) increases the pressure

gradient and leads to faster flow deceleration. This results in a shorter but

wider RZ. The CRZ without radiation is over-predicted by about 5 mm due

to the change in the flame structure and the spray distribution as shown in

Fig. 6.

As discussed below, the LES simulation shows that inside the divergent section

of the Venturi a small RZ is established, followed by an increase in the velocity

due to a sudden expansion after the dump. This is followed by a steep reduction

inside the RZ due to the adverse pressure gradient. There are no experimental

data inside the Venturi, but the profile captures the initial peak after the dump

accurately, which confirms the foregoing physical conclusions. Note that the

current simulation captures the centerline profile initial peak. The deviations

near the injector will be discussed later.

The mean and rms axial velocities are shown in Figs. 14 and 15. The first

three locations (x = 3 mm, x = 5 mm and x = 9 mm) are found to be the

most difficult to match with the experiment. These locations exhibit high unsteadiness and high measurement errors. The experimental measurements [34]

use a Phase Doppler Particle Analyzer (PDPA). A problem usually related to

the measurements is how to distinguish between the seed particles to measure

the gas phase velocity and the spray droplets. In the LDI experimental meaTo show the extent of the centerline RZ and the effect of heat release and

NASA/TM—2011-217111 16
surements [34] the nominal diameter of the seed particles used was 1 μm. To

distinguish between the spray and the seed particles, all particles smaller than

4 μm were used to represent the gas-phase velocity. However, inside the CRZ

the small spray droplets just ejected from the nozzle still have high momentum in the positive direction. As a result, the experimental velocity profiles

near the exit (i.e., x = 3 mm, x= 5 mm and x = 9 mm) are all positive despite

the existence of the CRZ. Therefore, at these locations we expect to underpredict the experimental data. A previous RANS simulation [45] shows also

higher deviation at x = 3 mm, and comparable results at x = 9 mm. The LES

simulation by Patel and Menon [22] also shows lower velocity at the location

x = 5 mm. Starting from the x = 15 mm location, the current LES simulation shows good results compared with the experimental data. The CRZ

extends to approximately 50 mm downstream of the dump. At the x = 92 mm

location, the profile shows a nearly uniform velocity that recovers the inflow

mass flow rate at the exit cross-sectional area. This uniformity is important

in gas turbine engines to minimize the thermal stresses on the turbine blades.

A slight deviation is found towards the walls. This can be attributed to the

fact that the CRZ in the current simulation is wider than in the experiment.

As a result, the flow is more compressed between the CRZ and the walls and

the velocity is higher.

The rms axial velocity profile is shown in Fig. 16. The rms peaks close to

the dump plane at the onset of the shear layer and then decays axially as

the shear layer decays downstream. The predicted and experimental axial rms

profiles show good agreement. The high rms values at the first three locations

confirm the high unsteadiness of the shear layer. For example, at x = 5 mm

the rms value is around 100% of the corresponding mean value. At the first

NASA/TM—2011-217111 17
three locations, over-prediction is noticed at the y = 15 mm radial location.

The discrepancy with the experimental data at the first three locations is due

to the reasons mentioned in the previous paragraph. The LES data predict

two rms peaks that start at the radial location y = 9 mm at the first axial

location. These two peaks spread downstream with the spread of the shear

layer. Downstream of x = 20 mm, the peaks start to move again toward the

centerline following the CRZ surface. After reaching the x = 46 mm location,

the peaks are completely merged. After this location, no reverse flow exists

and the shear layer is completely diffused. Similar observations apply to Fig.

17, where the radial profiles of the turbulent shear stress are plotted. The

shear stress shows antisymmetric radial profiles. Good agrement is shown, with

deviations at the first two locations. The zero shear stress at the centerline

indicates flow symmetry around the centerline.

Figure 18 shows the mean velocity component in the y-direction at different

axial locations. The flow is rotating in the clockwise direction (CCW) viewed

from the outflow cross-section. The global swirl number is of the order of 1. In

contrast to other velocity components, the results show good agreement with

the first location at x = 3 mm. The flow shows solid body rotation around the

centerline downstream of the location x = 29 mm. Upstream of this location

the flow is rotating around the central RZ.

The focus of the following discussion are the LDI emission characteristics. For

supersonic vehicles, the NO emissions directly deplete the stratospheric ozone

layer. Therefore, accurate models are required to predict gas turbine emissions.

As discussed earlier, NO production is a slow process and it is coupled with

other processes that have long characteristic time scales such as radiation.

Radiation affects NO in an indirect way through the change in temperature,

NASA/TM—2011-217111 18
which then changes the production rate. As a result, the first step is to predict

temperature accurately. Figure 19 shows the centerline mean temperature with

and without radiation modeling. This figure shows that without radiation the

temperature is over-predicted. This is consistent with earlier observations.

The radiation model employed here is an optically thin model [39]. The model

assumes that the medium is non-absorbing and neglects the heat lost or gained

by wall absorption and reflection. Figure 20 shows radial temperature profiles

at the locations where experimental data are available. The temperature is

under-predicted at the centerline. This may suggest a need for a more accurate radiation model that accounts for the absorption within the flame, the

scattering by the media (although might be negligible in this case), and the

wall effect.

Figure 21 shows the centerline species distribution for CO and NO. The CO

level along the centerline is captured reasonably well. An initial peak is observed in the rich combustion region followed by a decay in the CO level as it

is oxidized to produce CO2. The centerline NO profile also shows good results.

The effect of radiation generally improves the results.

6 Conclusions

Large eddy simulations for a liquid fuel injection LDI are performed. The

simulations show that LDI is a good candidate for low emissions, yet stable,

gas turbine engines. Radiation modeling is found to be essential for accurate

NO and temperature predictions. By changing the heat release distribution,

radiation alters the spray dynamics and the droplets size distribution. Thus,

NASA/TM—2011-217111 19
radiation can be important even for low pressure systems where radiation

from flame region is relatively small, but effect of radiation on spray dynamics

significantly affects temperature distribution. The simulations show the current ability of LES as a numerical tool to simulate multi-physics problems in

complex geometries using realistic chemistry models.

7 Acknowledgements

This work is funded by NASA Glenn Research Center. The authors thanks

Nan-Suey Liu for providing advice, grid and experimental data for comparison.

Many thanks to Heinz Pitch for his continuous support and revision for this

manuscript and for his helpful discussions and technical advice. The authors

also acknowledge Frank Ham from Stanford for his valuable support with the

CDP code and Jeffrey P. Moder from GRC for reviewing the final version of

the manuscript.

NASA/TM—2011-217111 20
(a) LDI geometry (b) The vanes and the y-x mesh

plane

(c) y-z mesh plane

Fig. 1. The LDI single element geometry and unstructured hexahedral mesh.

NASA/TM—2011-217111 21
(a) Reactive (b) Non-reactive

Fig. 2. Iso-surface of the time-averaged axial velocity (hUi = 0 m/s).

NASA/TM—2011-217111 22
Fig. 3. Side view (y = 0 plane) to the CRZ for the reactive flow case.

NASA/TM—2011-217111 23
Y X

Z

(a) Zoom of the injector area (b) Zoom of droplet distribution in the

injector area

(c) The vortices around the CRZ and at

the corners.

Fig. 4. Vector plots of the mean velocity magnitude projected in the y = 0 plane

for the reactive flow case with radiation.

NASA/TM—2011-217111 24
(a) y = 0 plane (b) z -y plane

(c) z -y plane (d) z -y plane

Fig. 5. Instantaneous temperature distribution for the case with radiation. (a) for

the z -x plane, (b), (c) and (d) for the z -y plane at three consecutive time snapshots

at x = 11 mm.

NASA/TM—2011-217111 25
(a) With radiation (b) No radiation

Fig. 6. Distribution of the time averaged heat release hQHri.

(a) With radiation (b) No radiation

Fig. 7. Cross sectional view through the swirler at y = 0 plane for distribution

of the time-averaged gas-phase fuel mass fraction h Y F i combined with the RMS

temperature contours (Trms).

NASA/TM—2011-217111 26
(a) With radiation (b) No radiation

Fig. 8. Instantaneous droplet distribution sized by droplet mass combined with the

instantaneous temperature distribution at the y = 0 plane.

NASA/TM—2011-217111 27
1e-07 1e-06 1e-05

log(Dp)μm

0

5000

10000

15000

Number of droplets

Fig. 9. Radiation effect on the droplet parcel histogram. (With radiation − · − · −,

without radiation −)

NASA/TM—2011-217111 28
(a) With radiation (b) No radiation

Fig. 10. Time-averaged droplet mass evaporation rate in (kg/s) at the central y = 0

plane.

NASA/TM—2011-217111 29
0

25

50

0

25

50

-30 -20 -10 0 10 20 30 0

100

200

0

100

200

0

100

200

-30 -20 -10 0 10 20 30 0

100

200

X = 3 mm

X = 5 mm

X = 15 mm

X = 20 mm

X = 36 mm

X = 46 mm

(a) Arithmetic mean droplet diameter

(D10)

0

100

200

0

100

200

0

150

300

0

150

300

0

100

200

-30 -20 -10 0 10 20 30 0

100

200

X = 3 mm

X = 5 mm

X = 15 mm

X = 20 mm

X = 36 mm

X = 46 mm

(b) Sauter mean diameter (SMD)

(D32)

Fig. 11. Radial profiles of droplet arithmetic mean and Sauter mean diameters

(Experiment data ◦, computation −)

NASA/TM—2011-217111 30
0

15

30

0

10

20

0

10

20

-30 -20 -10 0 10 20 30

Radial distance (mm)

-1.5

0

1.5

3

X = 3 mm

X = 5 mm

X = 9 mm

X = 15 mm

(a) x = 3 mm-x = 15 mm

0

20

40

0

20

40

0

20

40

-30 -20 -10 0 10 20 30

Radial distance (mm)

0

20

40

X = 20 mm

X = 29 mm

X = 36 mm

X = 46 mm

(b) x = 20 mm-x = 46 mm

Fig. 12. Radial profiles of mean droplet axial velocity (Experiment data ◦, computation −)

NASA/TM—2011-217111 31
0 50 100

Axial distance X (mm)

-20

-10

0

10

20

<U> (m/sec)

Fig. 13. Comparison of time-averaged centerline axial velocity hUi. Non-reactive

flow (Experiment ✷, computation −), reactive flow (Experiment ◦, computation

with radiation − · −, computation with no radiation · · ·).

NASA/TM—2011-217111 32
-25

0

25

-25

0

25

-20

0

20

-25

0

25

-30 -20 -10 0 10 20 30

 Radial distance (mm)

-25

0

25

X=3mm

X=5mm

X=9mm

X=15mm

X=20mm

(a) x = 3 mm - x = 20 mm

-25

0

25

-25

0

25

-25

0

25

-25

0

25

-30 -20 -10 0 10 20 30

Radial Distance (mm)

-25

0

25

X=29mm

X=38mm

X=46mm

X=61mm

X=92mm

(b) x = 29 mm - x = 92 mm

Fig. 14. Mean axial velocity hUi at different axial locations (Experiment data ◦,

computation −).

NASA/TM—2011-217111 33
0

15

30

0

10

20

30

0

10

20

0

10

20

-30 -20 -10 0 10 20 30

Radial Distance (mm)

0

10

20

X=3mm

X=5mm

X=9mm

X=15mm

X=20mm

(a) x = 3 mm-x = 20 mm

0

10

20

0

10

20

0

10

20

0

10

20

0

10

20

-30 -20 -10 0 10 20 30

Radial distance (mm)

0

10

20

X=29mm

X=38mm

X=46mm

X=61mm

X=76mm

X=92mm

(b) x = 29 mm-x = 92 mm

Fig. 15. RMS axial velocity Urms at different axial locations (Experiment data ◦,

computation −).

NASA/TM—2011-217111 34
0 20 40 60 80 100

Axial distance (mm)

0

10

20

U

rms(m/sec)

Fig. 16. RMS axial velocity along the centerline (Experiment data ◦, computation −).

NASA/TM—2011-217111 35
-50

-25

0

25

50

-25

0

25

-25

0

25

50

-30 -20 -10 0 10 20 30

Radial distance (mm)

0

25

50

X = 5 mm

X = 9 mm

X = 46 mm

X = 76 mm

Fig. 17. Radial profiles of the shear stress ug′v

′

NASA/TM—2011-217111 36
-20

0

20

-20

0

20

-20

0

20

-20

0

20

-30 -20 -10 0 10 20 30

Radial Distance (mm)

-40

-20

0

20

X=3mm

X=5mm

X=9mm

X=15mm

X=20mm

(a) x = 3 mm-x = 20 mm

-20

0

20

-20

0

20

-20

0

20

-20

0

20

-20

0

20

-30 -20 -10 0 10 20 30

Radial distance (mm)

-20

0

20

X = 29mm

X=38mm

X=46 mm

X=61mm

X=72mm

X=92mm

(b) x = 29 mm-x = 92 mm

Fig. 18. Mean velocity component in the y direction h UY i (Experiment data ◦,

computation −)

NASA/TM—2011-217111 37
0 50 100 150 200

Axial distance (mm)

0

500

1000

1500

2000

2500

3000

T (K)

Fig. 19. Comparison of the centerline mean temperature hTi. (Experiment ◦, computation without radiation (−) and with radiation (· − ·).

NASA/TM—2011-217111 38
800

1200

1600

2000

800

1200

1600

2000

800

1200

1600

2000

-30 -20 -10 0 10 20 30

Radial distance (mm)

800

1200

1600

2000

X=5mm

X = 10 mm

X = 20 mm

X = 40 mm

(a) x = 5 mm-x = 40 mm

800

1200

1600

2000

800

1200

1600

2000

800

1200

1600

2000

-30 -20 -10 0 10 20 30

Radial distance (mm)

1200

1600

2000

X = 60 mm

X = 67 mm

X = 110 mm

X = 130 mm

(b) x = 60 mm-x = 130 mm

Fig. 20. Mean radial temperature profiles h T i (Experiment ◦, computation −)

NASA/TM—2011-217111 39
50 100 150 200 250 300

100 

1 k

10 k

<CO (ppm)>

0 100 200 300

Axial distance (mm)

1

10

100

<NO(ppm)>

Fig. 21. Time averaged centerline species mass fractions profiles in ppm (hY COi and

hY NOi) without radiation (−) and with radiation (· − ·).

NASA/TM—2011-217111 40
References

[1] A. H. Lefebvre, Gas Turbine Combustion, 2nd Edition, Taylor & Francis,

London, UK, 1999.

[2] G. M. Faeth, G. Roth, M. Gundersen, Combustion emission and control., in:

G. Roy (Ed.), Propulsion Combustion: Fuels and Emissions, Taylor & Francis,

Washington, DC., 1998, pp. 359–407.

[3] I. Glassman, Proc. Combust. Inst. 22 (1988) 295 – 311.

[4] C. K. Law, Combustion Physcis, Cambridge University Press, New York, USA,

2006.

[5] S. J. Shanbhogue, S. Husain, T. Lieuwen, Prog. Energy Combust. Sci. 35 (1)

(2009) 98–120.

[6] V. Sankaran, S. Menon, J. Turb. 2 (2002) 011.

[7] S. Menon, in: T. Lieuwen, V. Yang (Eds.), Combustion Instabilities in Gas

Turbine Engines: Operational Experience, Fundamental Mechanisms, and

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277 – 314.

[8] S. Candel, J. Prop. Power 20 (1) (1988) 59 – 68.

[9] Pratt&Whitney, G. E. A. Engines, NASA/CR=2005-213584/VOL1.

[10] T. J. Poinsot, D. Veynante, Theoretical and Numerical Combustion, 2nd

Edition, R. T. Edwards, Inc., Philadelphia, PA USA, 2005.

[11] C. K. Law, Proc. Combust. Inst. 31 (2007) 1 – 29.

[12] P. Pepiot-Desjardins, H. Pitsch, Combust. Flame 154 (1-2) (2008) 740 – 760.

[13] N. Peters, Proc. Combust. Inst. doi:10.1016/j.proci.2008.07.044.

NASA/TM—2011-217111 41
[14] G. Boudiera, L. Y. M. Gicquela, T. J. Poinsot, Combust. Flame 155 (1-2) (2008)

196–214.

[15] M. Gorokhovski, M. Herrmann, Annu. Rev. Fluid Mech. 40 (2008) 343 – 366.

[16] O. Desjardins, H. Pitsch, J. Comput. Phys. doi:10.1016/j.jcp.2008.11.005.

[17] H. Watanabe, R. Kurose, S. Komori, H. Pitsch, Combust. Flame 152 (1-2)

(2008) 2–13.

[18] S. B. Pope, Prog. Energy Combust. Sci. 11 (2) (1985) 119–192.

[19] N. Peters, Turbulent Combustion, Cambridge University Press, Cambridge, UK,

2000.

[20] H. Pitsch, Annu. Rev. Fluid Mech. 38 (2006) 233–266.

[21] H. Pitsch, O. Desjardins, G. Balarac, M. Ihme, 46th AIAA Aerospace Sciences

Meeting and Exhibit, Reno, Nevada, Jan. 7-10, 2008 AIAA-2008-604.

[22] N. Patel, S. Menon, Combust. Flame 153 (1) (2008) 228 – 257.

[23] H. El-Asrag, S. Menon, Proc. Combust. Inst. 31 (2007) 17471754.

[24] S. Menon, in: LES of Complex Transitional and Turbulent Flows, Kluwer Press,

Dordrecht, 2000, pp. 329 – 352.

[25] J. C. Oefelein, V. Sankaran, T. G. Drozda, Proc. Combust. Inst. 31 (2) (2007)

2291 – 2299.

[26] V. Raman, H. Pitsch, Combust. Flame 142 (4) (2005) 329347.

[27] M. Boileau, G. Staffelbach, B. Cuenot, T. Poinsot, C. Brat, Combust. Flame

154 (1-2) (2008) 2–22.

[28] S. V. Apte, K. Mahesh, M. Gorokhovski, P. Moin, Proc. Combust. Inst., in

press (2008) 10.10.16/j.proc.2008.06.156.

NASA/TM—2011-217111 42
[29] L. Selle, G. Lartigue, R. Koch, K. U. Schildmacher, W. Krebs, P. Kaufmann,

D. Veynante, Combust. Flame 137 (4) (2004) 489–505.

[30] J. Galpin, A. Naudin, L. Vervisch, C. Angelberger, O. Colin, P. Domingo,

Combust. Flame 155 (1-2) (2008) 247–266.

[31] K.-S. Im, M. C. Lai, R. R. Tacina, 34th AIAA/ASME/SAE/ASEE Joint

Propulsion Conference and Exhibit, Cleveland, Ohio AIAA 1998-3269.

[32] R. R. Tacina, C. Wey, K. J. Choi, 37th AIAA/ASME/SAE/ASEE Joint

propulsion conference and Exhibit, Salt Lake City, Utah AIAA 2001-34065.

[33] S. L. Yang, Y. K. Siow, B. D. Peschke, R. R. Tacina, J. Eng. Gas Turbine Power

125 (2003) 804–811.

[34] J. Cai, S.-M. Jeng, R. R. Tacina, 43rd AIAA Aerospace Sciences Meeting and

Exhibit, Reno, Nevada AIAA 2005-1425.

[35] S. Honnet, K. Seshadri, U. Niemann, N. Peters, Proc. Combust. Inst. 32 (1)

(2008) 485–492.

[36] H. Pitsch, Flamemaster, a c++ computer program for 0d combustion and 1d

laminar flame calculations.

[37] C. D. Pierce, P. Moin, J. Fluid Mech. 504 (2004) 73 – 97.

[38] M. Ihme, C. M. Cha, H. Pitsch, Proc. Combust. Inst. 30 (1) (2008) 793 – 800.

[39] M. Ihme, H. Pitsch, Phys. Fluid 20 (2008) 0055110 – 20.

[40] G. L. Hubbard, C. L. Tien, Infrared mean absorption coefficients of luminous.

flames and smoke, Heat Transfer 100 (1978) 235–239.

[41] S. V. Apte, M. Gorokhovski, P. Moin, Int. J. Multiphase Flow 29 (2003) 1503–

1522.

NASA/TM—2011-217111 43
[42] S. V. Apte, K. Mahesh, P. Moin, Proc. Combust. Inst., in press (2008)

10.10.16/j.proc.2008.05.058.

[43] F. Ham, in: Annual Research Briefs., Stanford Calif.: Center for Turbulence

Research, 2007, pp. 41–45.

[44] D. Farhad, N.-S. Liu, P. M. Jeffrey, NASA/TM-2006-214252.

[45] A. C. Iannetti, N.-S. Liu, D. Farhad, NASA/TM-2008-215422.

[46] H. El-Asrag, F. Ham, H. Pitsch, in: Annual Research Briefs., Stanford Calif.:

Center for Turbulence Research, 2007, pp. 241–253.

[47] N. Patel, M. Kirtas, V. Sankaran, S. Menon, Proc. Combust. Inst. 31 (2) (2007)

2327 – 2334.

NASA/TM—2011-217111 44
List of Figures

1 The LDI single element geometry and unstructured hexahedral

mesh. 22

2 Iso-surface of the time-averaged axial velocity (hUi = 0 m/s). 23

3 Side view (y = 0 plane) to the CRZ for the reactive flow case. 24

4 Vector plots of the mean velocity magnitude projected in the

y = 0 plane for the reactive flow case with radiation. 25

5 Instantaneous temperature distribution for the case with

radiation. (a) for the z -x plane, (b), (c) and (d) for the z -y

plane at three consecutive time snapshots at x = 11 mm. 26

6 Distribution of the time averaged heat release hQHri. 27

7 Cross sectional view through the swirler at y = 0 plane for

distribution of the time-averaged gas-phase fuel mass fraction

h Y F i combined with the RMS temperature contours (Trms). 27

8 Instantaneous droplet distribution sized by droplet mass

combined with the instantaneous temperature distribution at

the y = 0 plane. 28

9 Radiation effect on the droplet parcel histogram. (With

radiation − · − · −, without radiation −) 29

10 Time-averaged droplet mass evaporation rate in (kg/s) at the

central y = 0 plane. 30

NASA/TM—2011-217111 45
11 Radial profiles of droplet arithmetic mean and Sauter mean

diameters (Experiment data ◦, computation −) 31

12 Radial profiles of mean droplet axial velocity (Experiment

data ◦, computation −) 32

13 Comparison of time-averaged centerline axial velocity hUi.

Non-reactive flow (Experiment ✷, computation −), reactive

flow (Experiment ◦, computation with radiation − · −,

computation with no radiation · · ·). 33

14 Mean axial velocity hUi at different axial locations (Experiment

data ◦, computation −). 34

15 RMS axial velocity Urms at different axial locations

(Experiment data ◦, computation −). 35

16 RMS axial velocity along the centerline (Experiment data ◦,

computation −). 36

17 Radial profiles of the shear stress ug′v

′

37

18 Mean velocity component in the y direction h UY i

(Experiment data ◦, computation −) 38

19 Comparison of the centerline mean temperature hTi.

(Experiment ◦, computation without radiation (−) and with

radiation (· − ·). 39

20 Mean radial temperature profiles h T i (Experiment ◦,

computation −) 40

NASA/TM—2011-217111 46
21 Time averaged centerline species mass fractions profiles in ppm

(hY COi and hY NOi) without radiation (−) and with radiation

(· − ·). 41

NASA/TM—2011-217111 47
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Radiation-Spray Coupling for Realistic Flow Configurations 

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14. ABSTRACT

Three Large Eddy Simulations (LES) for a lean-direct injection (LDI) combustor are performed and compared. In addition to the cold flow 

simulation, the effect of radiation coupling with the multi-physics reactive flow is analyzed. The flame let progress variable approach is used 

as a subgrid combustion model combined with a stochastic subgrid model for spray atomization and an optically thin radiation model. For 

accurate chemistry modeling, a detailed Jet-A surrogate mechanism is utilized. To achieve realistic inflow, a simple recycling technique is 

performed at the inflow section upstream of the swirler. Good comparison is shown with the experimental data mean and root mean square 

profiles. The effect of combustion is found to change the shape and size of the central recirculation zone. Radiation is found to change the 

spray dynamics and atomization by changing the heat release distribution and the local temperature values impacting the evaporation 

process. The simulation with radiation modeling shows wider range of droplet size distribution by altering the evaporation rate. The current 

study proves the importance of radiation modeling for accurate prediction in realistic spray combustion configurations, even for low 

pressure systems. 

15. SUBJECT TERMS

Combustion; Computational fluid dynamics; Thermal radiation; Turbulent flow; Sprays; Large eddy simulation (LES); Radiation; 

Lean-direct injection (LDI); Turbulent flames 

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