M.S. Raju

ASRC Aerospace Corporation, Cleveland, Ohio

Dan L. Bulzan

Glenn Research Center, Cleveland, Ohio

Current Status of Superheat Spray Modeling

With NCC

NASA/TM—2012-217295

March 2012
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M.S. Raju

ASRC Aerospace Corporation, Cleveland, Ohio

Dan L. Bulzan

Glenn Research Center, Cleveland, Ohio

Current Status of Superheat Spray Modeling

With NCC

NASA/TM—2012-217295

March 2012

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

48th Joint Propulsion Conference and Exhibit

cosponsored by AIAA, ASME, SAE, and ASEE

Atlanta, Georgia, July 30–August 1, 2012
Acknowledgments

This work was supported by the supersonics (SUP) project offi ce of the NASA Fundamental Aeronautics Program with

Dr. N.-S. Liu acting as the technical monitor. The authors would like to extend their sincere appreciation to

Dr. Jeff Moder for his many valuable contributions to the spray code.

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This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.

Level of Review: This material has been technically reviewed by technical management. 
ABSTRACT

An understanding of fuel atomization and vaporization behavior at superheat conditions is identified to be a topic of importance in the design of

modern supersonic engines. As a part of the NASA’s

fundamental aeronautics program (the supersonics

(SUP) project office initiative on high altitude emissions), we have undertaken an effort to assess the

accuracy of various existing CFD models used in the

modeling of superheated sprays. As a part of this investigation, we have completed the implementation of

a solution procedure for the modeling of superheated

sprays into the national combustion code (NCC),

and then applied it to investigate the following three

cases: (1) the validation of a flashing jet generated

by the sudden release of pressurized R134A from a

cylindrical nozzle, (2) the differences between two superheat vaporization models were studied based on

the predicted results of both hot and cold flow calculations involving a Parker-Hannifin pressure swirl

atomizer, (3) the spray characteristics generated by

a single-element LDI (Lean Direct Injector) combustion experiment were studied to investigate the differences between superheat and non-superheat conditions. For the validation case, the predicted results provided reasonable agreement for both gas and

droplet velocities but underpredicted the droplet sizes

by a considerable measure in the central region. For

the second case, the superheat vaporization models

of both [12-14] and [15] produced similar results for a

hot flow. For the third case, both the superheat and

non-superheat calculations produced mostly similar

results for gas temperature and velocities but the superheat calculation produced substantially faster vaporization as expected.

NOMENCLATURE

Bk Spalding mass transfer number

Bt Spalding heat transfer number

Cp specific heat, J/(kg K)

d droplet diameter, m

dt time increment, s

h specific enthalpy, J/kg

k thermal conductivity, J/(ms K)

lk mixture latent heat of evaporation, J/kg

lk,ef f effective latent heat of evaporation,

J/kg (defined in Eq. (14))

m ̇ liquid mass flow rate, kg/s

m ̇ k,f lash droplet vaporization rate under

flash evaporating conditions, kg/s

m ̇ k,t droplet vaporization rate due

to heat transfer, kg/s

nk number of droplets in kth group

Nu Nusselt number

P pressure, N/m2

P r Prandtl number

Psat saturation pressure, N/m2

rk droplet radius, m

Ru gas constant, J/(kg K)

Re Reynolds number

Sh Sherwood number

sk droplet radius-squared ( = r2

k

), m2

Sc Schmidt number

SMD Sauter mean diameter, m

t time, s

T temperature, K

Current Status of Superheat Spray Modeling With NCC 

M.S. Raju 

ASRC Aerospace Corporation 

Cleveland, Ohio 44135 

Dan L. Bulzan 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

NASA/TM—2012-217295 1
Tb boiling temperature, K

Tk kth droplet temperature, K

U gas or liquid velocity, m/s

x axial distance, m

y radial distance, m

∆p pressure drop in the injector, N/m2

μ dynamic viscosity, kg/ms

ν kinematic viscosity, m2/s

ρ density, kg/m3

θ spray cone angle, deg.

Subscripts

f fuel

g gas

inj injector

l liquid

r radial coordinate

s droplet surface

t time

x axial or x-coordinate

y y-coordinate

z z-coordinate

Superscripts

 ̄ mean, or average

 ̇ flow rate

INTRODUCTION

Our previous work on spray modeling can be

found in Refs. [1-10]. The spray solution procedure

facilitates multi-dimensional spray/gaseous combustion calculations on massively parallel computers and

unstructured grids. It also allows calculations to be

performed in conjunction with the scalar Monte Carlo

PDF (Probability Density Function) method [2]. The

objective of our present study is to extend our solution procedure to the modeling of superheated sprays

because of its importance in the design of modern supersonic engines, scramjet, and ramjet afterburners

[11-15]. It is because higher heat-load requirements

may lead to the use of the the same fuel as a coolant

and also sometimes the nozzles are required to operate at low back pressures. Also, under normal gasturbine operating conditions, it is estimated that a

small fraction of the liquid fuel may be flash boiled

[12]. There are also some reported cases of flash related engine performance problems in gasoline directinjection internal combustion engines [12]. Although

flash evaporation is considered to be detrimental to

engine performance under normal circumstances, it

can have some potential benefits: it is known to

produce a fine spray with enhanced atomization, increase effective spray cone angle, and decrease spray

penetration [11]. Because of its importance in some

NASA-related applications, we have undertaken an

assessment study to establish baseline accuracy of

various existing CFD models used in the modeling of

a superheated spray. As a part of this effort, we have

implemented a solution procedure into NCC based on

the modeling approach developed by [12-15]. More

specifically, we have implemented a superheat vaporization model and other modifications pertinent to

the atomization modeling developed by [12-14]. Also,

we have completed the integration of a computer

module that was developed by UTRC (United Technologies Research Center) and UMASS (University of

Massachusetts) [15]. The UTRC/UMASS computer

module contained a separate superheat vaporization

model, a flash-induced atomization breakup-model,

and a calculation approach that was developed to determine the JP8 two-phase properties [15]. In order to establish a baseline accuracy of the solution

procedure, we have undertaken a validation involving

a flashing jet generated by a cylindrical nozzle [16].

Also, we have performed some calculations involving

a Parker-Hannifin pressure swirl atomizer in order

to evaluate the differences between the superheat vaporization models of [12-14] and [15], and a single

element LDI reacting case in order to evaluate the

differences between the superheat and non-superheat

conditions [16].

In this paper, we first describe complete details

of the solution procedure implemented into NCC followed by a presentation of the results.

ATOMIZATION MODELING

The atomization refers to a process of the liquid jet breakup into droplets. There are many processes associated with the liquid jet breakup. They

can broadly be classified into two regimes: (1) the inner nozzle flow, and (2) the external nozzle flow. In

the inner nozzle flow, several factors (such as injector

type, geometry, and size) influence the conditions at

the injector exit (such as the velocity, the initial sheet

or jet thickness, and the angle of droplet dispersion).

Right now, we rely on widely-used correlations in determining the initial spray conditions at the injector

exit. For a better description, a more accurate analysis is needed which takes into account the physics

NASA/TM—2012-217295 2
associated with inside bubble growth, cavity formation, and internal turbulence. In the external nozzle

flow, the liquid becomes unstable under the influence

of aerodynamic instabilities and finally breakup into

droplets. When the maximum amplitude of the most

unstable wave reaches a critical value, some liquid is

stripped of the main liquid core in the form of primary droplets. These droplets may further breakup

into smaller droplets due to a process known as the

secondary droplet breakup mechanism.

Among the primary atomization models, the

following are widely used: (1) the sheet breakup primary atomization model which was developed by [17-

18] has application in the modeling of sprays generated by pressure swirl atomizers, (2) the blob jet

primary atomization model which was developed by

Ritz et al [19-21] has application with plane orifice

nozzles, and (3) the BLS (Boundary-Layer Stripping)

primary atomization model which was developed by

Khosla et al [22] has application for a liquid jet in

a cross flow. Among the secondary droplet breakup

models, the following are widely used: (1) the TAB

(Taylor Analogy Breakup) secondary droplet breakup

model which was developed by O’Rouke et al [23]

has application for lenticular-shaped droplet deformations, and (2) the ETAB (Enhanced TAB) secondary droplet breakup model which was developed by Tanner [24] has application for high-pressure

diesel-engine flows.

Most of the coding required for both the primary atomization and secondary droplet breakup

models was provided by CFDRC. These models are

applicable under both non-superheat and superheat

conditions. In the superheated regime, the thermophysical liquid properties are replaced by the twophase properties of a superheated fluid [15].

Flash Atomization Modeling

There are three components to the atomization

modeling of a superheat spray: (1) primary atomization, (2) secondary droplet breakup, and (3) flash

induced atomization. Further details on the primary

atomization and secondary droplet breakup models

can be found in [1]. For the superheated sprays, we

have to deal with a third component known as flash

induced atomization. We have followed the modeling

approach of Lee et al [15] for the flash induced atomization. In what follows we describe some details of

their modeling approach.

Flash atomization is a result of rapid evaporation associated with strong nucleation and bubble

growth occurring inside of a non-equilibrium twophase fluid [15]. When the void fraction within the

rapidly evaporating fluid reaches a certain critical

void fraction, the inner liquid core would shatter into

pieces. It seemed to have a value of 0.61 based on

the research identified in [15]. Incidentally, this condition for criticality also coincides with the packing

limit of spheres beyond which it can not accommodate any more bubbles and results in shattering [27].

In order to calculate this state of critical limit, they

employed the homogeneous relaxation model (HRM)

for calculating the mass fraction of gas, x, also known

as quality.

dx

dt =

xeq − x

θ

; θ = θo

αφβ

; (1)

where the values for α (= −0.54), β (= −1.76), and

θo (= 6.51.1004s) are taken from [28], and the void

fraction, , and the degree of superheat, φ, are defined

as follows:

 =

ρl − ρ

ρl − ρv

; φ =

Pb(h) − P

Pc − Pb(h)

(2)

Once the critical limit for the void fraction is

reached, the resulting droplets produced as a result

of flash atomization are obtained by a droplet number

density correlation developed by Kawano et al [29].

n = Ae

−E

(Tl−Tbub) e

at+b

(3)

From Eq. (3), the mean droplet size, R ̄, is calculated by equating total liquid mass before and after

the droplets are formed.

R ̄3 =

1 − c

(4/3)πn

(4)

The solution for Eqs. (1) to (4) as well as the

JP8 fluid properties needed in this calculation were

obtained by the computer coding provided by UTRC.

Also, it is noteworthy that the properties for JP8 were

predicted by means of a surrogate model of Violi.

Further details can be found in [15].

The flash induced atomization is combined with

the primary and secondary droplet breakup models

following the approach of Lee et al [15]. The aerodynamic instability mode will atomize the liquid core

when the surface disturbance reaches a certain critical

value and the flash induced atomization is responsible for shattering the liquid core when the void fraction reaches the critical value. Therefore, the control

mechanism depends on whichever mechanism is first

responsible for reaching the critical condition.

NASA/TM—2012-217295 3
Some Additional Aspects of Superheat on Primary

Atomization

Flash evaporation is known to produce a fine

spray with enhanced atomization, increase effective

spray cone angle, and decrease spray penetration [11].

Here, we consider the effects of flash evaporation on

the sheet breakup primary atomization model by following the approach of Zuo et al [12]. Its effect on

the initial droplet size generated immediately after

the first ligament breakup, dis, is given as a function

of both engine pressure and a superheat parameter

as follows:

dis = din(

P

Patm

)

0.27[1−χ(

Patm

P

)

0.135] 0 ≤ χ(

Patm

P

)

0.135 ≤ 1

(5)

where din is the corresponding droplet droplet size

under normal evaporating conditions without flash

evaporation, and χ is defined as a superheat parameter as follows:

χ =

I(Tk) − I(Tb)

l(Tb)

(6)

where I is the internal energy of the liquid. Its value

varies between 0 < χ < 1 with χ = 0 referring to zero

flash evaporation and χ = 1 to full flash evaporation.

In Eq. (5), the increase in dis due to an increase

in engine pressure by a factor of ( P

Patm

)

0.27 is based

on an experimental correlation obtained from Lefebvre [30]. It reflects the influence of chamber pressure

on wave propagation as it damps wave growth. But

the decrease by a factor of (1 − χ(

Patm

P

)

0.135) is due

to a significant reduction in droplet size caused by

both cavitation and bubble growth under flash evaporation conditions. It was introduced based on the

experimental data obtained from VanDerWege et al

[31] and Reitz [32].

As the liquid approaches boiling, it also causes a

substantial decrease in both intact liquid core length

and core droplet size leading to a modification of the

nominal cone angle, θ, as given by

θ = θn + (144 − θn)χ

2

(7)

where θn is in degrees for a spray vaporizing under

normal conditions without flash evaporation. This

correlation was developed by based on the experimental data of Reitz [32]. Both these correlations were

developed in conjunction with the sheet breakup primary atomization model but their validity with other

primary atomization models needs further investigation.

VAPORIZATION MODELING OF A

SUPERHEATED DROPLET

In what follows we first provide some details

of the two superheat vaporization models that were

implemented into NCC.

Superheat Vaporization Model of Zuo, Gomes,

& Rutland [12], and Schmehl & Steelant [13-14]

It is based on an extension of the classical D2-

theory. In the classical evaporation model, the thermal energy needed for evaporation is mostly furnished

by the external heat transfer from the surrounding

gas. Under superheat conditions, the characteristic

vaporization time resulting from the external heat

transfer from the surrounding gas is of the same order

of magnitude as that resulting from the flash evaporation. The energy needed for vaporization at the

droplet surface is partly provided by the superheat

energy stored within the droplet and it is controlled

by the droplet internal heat transfer. The modeling

approach differs from the classical droplet vaporization models in three important ways: (1) under superheat conditions, the droplet surface mass fraction,

Yf s, approaches unity as the droplet surface temperature is maintained at the corresponding liquid boiling temperature; (2) under superheat conditions, all

the external heat transfer from the surrounding gas

is made available to the vaporization process with no

apparent increase in the droplet surface temperature;

and (3) the flow of fuel vapor imparted by flash vaporization partly counterbalances the flow generated

by external heat transfer and may significantly reduce

the energy transferred from the surrounding gas.

Based on the governing equations of conservation for an isolated spherically symmetric droplet,

Zuo et al [12] and Schmehl and Steelant [13-14]

showed that the total evaporation rate,  ̇mk, can be

calculated as

m ̇ k =  ̇mk,f lash +  ̇mk,t (8)

where the flash boiled vaporization rate,  ̇mk,f lash, is

given by

m ̇ k,f lash = 4πr2

kαs

(Tk − Tb)

lk

(9)

NASA/TM—2012-217295 4
where Tk is the internal droplet temperature and the

overall heat transfer coefficient, αs (= kJ/s m2 oK)

is given by the Adachi correlation [26]:

= 0.76(Tk − Tb)

0.26 (0 ≤ Tks − Tb ≤ 5)

αs = 0.027(Tk − Tb)

2.33 (5 ≤ Tks − Tb ≤ 25) (10)

= 13.8(Tk − Tb)

0.39 (Tks − Tb ≥ 25)

The Adachi correlation is valid over a wide range of

superheat conditions.

The vaporization rate due to external heat

transfer,  ̇mk,t, in Eq. (8) is given by

m ̇ k,t = 2πrk

k

Cp

Nu

1 +

m ̇ k,flash

m ̇ k,t

ln[1 + (1 + m ̇ k,flash

m ̇ k,t

)Bt] (11)

where the Spalding heat transfer number, Bt, and the

Nusselt number, Nu, are given by

Bt =

Cp(Tg − Tks)

lk,ef f

(12)

Nu = 2(1 + 0.3Re1/2P r1/3

g

) (13)

where the effective latent heat of vaporization, lk,ef f ,

is given by

lk,ef f = lk + 4π

λlr

2

k

m ̇ k



∂Tk

∂r 

s

(14)

which is an useful parameter as it represents the total

energy loss associated with the latent heat of vaporization in addition to the the heat loss to the droplet

interior. Finally, the corresponding droplet regression

rate, dsk

dt , is given by

dsk

dt = −

m ̇ k

2πrkρl

(15)

This model is valid over an entire range of superheat conditions as long as there is some amount of

superheat energy available within the droplet (Tk >

Tb).

Superheat Vaporization model of Lee et al [15]

This modeling approach is also based on an extension of the classical D2

-theory but it differs from

the previous model of [12-14] in several important

ways: (1) neglects the effects of internal nucleation

and convection, (2) instead of invoking the Adachi

correlation for the flash induced vaporization rate,

the heat loss from the droplet interior is modeled by

qˆl =

Tinterior−Ts(P∞)

rk,t=0

, (3) the formulation is valid

only when T∞ ≥ Tbub(P∞), which means for positive Spalding heat transfer numbers.

With the assumptions employed, Lee et al [15]

arrive at the following equation for the evaporation

rate, ˆmv.

mˆ v

Tˆ∞ − Tˆ

s

emˆ v − 1

= ˆmvLˆ − qˆl (16)

where

Tˆ = CpgT /Lr, ˆmv = (4πr2

k

ρgu)/(4πλgrk,t=0/Cpg),

Lˆ = Lk/Lr. The solution for the above equation is

obtained by employing the standard Newton’s iteration.

It is noteworthy that because of the assumptions invoked in this model, the applicability of this

model may be limited in several important ways:

(1) our experience shows that the assumption of

T∞ ≥ Tbub(P∞) becomes too restrictive in most

non-reactive calculations and also in some regions of

most reactive spray calculations, and (2) the ˆql term

is modeled based on the assumption that the overall

droplet life is very short (sub millisecond range) but

in most moderate superheat conditions the droplet

lifetimes are on par with those vaporizing under nonsuperheat conditions. So its use is likely to be restricted for the modeling of smaller droplets produced

after flash induced atomization.

The solution for Eq. (16) and all the JP8 fluid

properties needed in this calculation were also obtained by the computer coding provided by UTRC.

Vaporization Model Valid Under Non-Superheat

Conditions

Under moderate initial superheat conditions,

only a fraction of the vaporization takes place under

superheat conditions (Tk > Tb) and the remainder

takes place under non-superheat evaporating conditions (Tk ≤ Tb). So there is a need to revert back to

a vaporization model valid under stable evaporating

conditions when the internal droplet temperature approaches the boiling temperature. In the present calculations, the vaporization rate under normal evaporating conditions is evaluated by means of a simplified

classical D2-theory:

m ̇ k = 2πrkρg Df gs Sh ln(1 + Bk) (17)

where the Spalding mass transfer number, Bk, is

given by

NASA/TM—2012-217295 5
Bk =

(yf s − yf )

(1 − yf s)

(18)

where yf s is the mass fraction of the fuel species at

the the droplet interface, yf is the mass fraction of the

fuel species in the surrounding gas, and the Sherwood

number, Sh, is given by

Sh = 2(1 + 0.3Re1/2Sc1/3

g

) (19)

Internal Droplet Temperature Calculation

Our experience with the validation studies

showed us that there is a definite need to include

a calculation involving the internal droplet temperature valid under both superheat and normal evaporating conditions. In our present calculations, it was

evaluated by means of a simple infinite conductivity

model.

dTk

dt =

3[lk,ef f − lk]

2Cplr

2

k

dsk

dt (20)

if Tk < Tb, and

dTk

dt = −

3αs

rkρlCpl

(Tk − Tb)

(for the superheat model of [12 − 14])

or

dTk

dt = −

3λl

rkρlCpl

∂T

∂r |ls (21)

(for the superheat model of [15])

if Tk ≥ Tb

RESULTS & DISCUSSION

A Flashing Jet Generated by a Cylindrical Nozzle

This investigation is under taken mainly to test

the following models: (1) the superheat vaporization

model of [12-14], (2) the blob-jet primary atomization

model [19-21], & (3) the ETAB secondary droplet

breakup model [24-25]. The experimental data for

this validation was provided by Yildiz et al [33-34].

It contained data for two-phase jet flows generated by

the sudden release of pressurized R134A from cylindrical nozzles of different sizes. In our present calculations, we have focused mainly on a case involving

the 1mm nozzle for which the most extensive data

were reported.

It is based on a 2d-axisymmetric geometry: 2daxisymmetric. All the calculations were performed on

a grid with 79101 triangular elements (non-reacting,

turbulent air flow).

At the start of jet dispersion, the pressurized

liquid would undergo some expansion due to the entrainment of surrounding air and vaporization of the

pressurized liquid depending on the degree of superheat. Because of this expansion, the effective size

of the expanded jet would be larger than the orifice

exit. Based on the experimental observation, the initial size of the jet at the point of jet breakup was

estimated to be about 9 mm. The initial gas velocity

was prescribed based on the experimental correlation

reported by Yildiz et al [34]. The initial gas temperature 298 K, turbulence kinetic energy, k = 1 & =

10 m2/s2. The liquid is R134A, a refrigerant. The

injector has a diameter of 0.001 m and is located in

the middle of a center-body configuration. The initial

droplet velocity was estimated to be 34 m/s based on

the pressure drop across the injector. The initial liquid temperature is 293 deg. K which corresponds to

a superheat temperature of 46 deg. C.

The results for this case were reported in our

earlier paper [16]. The predicted profiles for both gas

and droplet velocities show a reasonable agreement

with the measured data, and exhibit a self-similar

behavior as reported in the literature. The predicted

droplet sizes mainly fall short of experimental data

in the central region of the spray. Away from the

central region, the predicted sizes are in reasonable

agreement with the experimental behavior. Both the

predictions and experimental data showed that a considerable amount of vaporization takes place under

non-superheat conditions.

Parker-Hannifin Pressure Swirl Atomization

This investigation is undertaken mainly to test

the following models: (1) Sheet-breakup primary

atomization model [17-18], & (2) ETAB secondary

droplet breakup model [24-25]. The experimental

data for this validation was provided by Ref. [35].

It is based on a 2d-axisymmetric geometry. For this

case both the grid and the initial conditions were provided by CFDRC (non-reacting, turbulent air flow).

The experimental conditions for the gas phase are

NASA/TM—2012-217295 6
specified as follows: (1) the axial velocity is assumed

to be uniform at 1.2 m/s, (2) the radial velocity profile is prescribed by means of an interpolation from

the following three points: y = 0.019 m, v = -0.9m/s,

y = 0.1 m, v = -0.5 m/s, & y = 0.3 m, v=0, (3) the

gas temperature = 300 K, & (4) the turbulence kinetic energy, k = 1 & = 10 (m2/s2

). The liquid phase

conditions are specified as follows: (1) the liquid fuel

is C12H23, (2) the injector has a diameter of 0.0012 m

and is located in the middle of a center-body configuration, (3) the liquid mass flow rate is 0.00125 kg/s,

(4) the internal pressure drop across the atomizer is

344500 Pa, & (5) the initial liquid temperature is 300

K.

The experimental conditions were based on the

non-superheat evaporating conditions. The reported

experimental results involved droplet axial velocities,

droplet radial velocities, and droplet sizes. The comparisons for this case were also reported in our earlier

paper [16]. The predicted results were in reasonable

agreement but mostly underestimate the the experimental data.

We have also completed two more calculations

for the same case of Parker Hannifin but performed

under non-reacting superheat conditions. In one, the

SVM (Superheat Vaporization Model) of [12-14] was

employed and in the second the SVM of [15] was

employed. In both calculations, the properties of

C12H23 were replaced by the JP8 properties of a superheated fluid. They were calculated based on the

coding provided by UTRC [15]. The specified initial

liquid temperature was raised to 520 deg. K. For the

JP8, the boiling temperature at the normal pressure

is about 468 deg. K.

The global structure of the non-reacting spray

obtained from both the two calculations are shown in

Fig. 1. The differences between the two calculations

are considerable: (1) The results from the SVM of

[12-14] showed a temperature variation ranging from

270 to about 430 deg. K. Initially there is an increase

in the gas temperature near the spray region from

the superheated droplet. While some of the smaller

droplets vaporize completely under superheat conditions, some of the larger droplets cool off below the

boiling temperature after depleting all of the superheat energy from the droplet interior. Further vaporization from those larger droplets tend to lower

the temperatures in the surrounding gas below the

corresponding droplet surface temperature. This effect can be seen downstream in a small central region

where temperatures fall below the initial specified gas

temperature of 300 deg. K. This behavior of evaporative cooling is similar to what we have seen in the

validation case of Yildiz et al [16]. (2) The results

from the SVM of [15] show the gas temperatures to

range between 300 to 355 deg. K. This calculation

also shows a slight increase in the gas temperature

in the central region near nozzle exit. In this calculation the gas temperatures mostly stay above the

initial specified gas temperature of 300 deg. K. It is

because this superheat model is only valid for positive Spalding numbers; therefore, makes its applicability more difficult for the modeling of a non-reacting

spray.

We have also completed two more calculations

for the same case but performed under reacting superheat conditions. Again in one calculation the SVM

of [12-14] was employed and in the second the SVM

of [15] was employed. All other conditions are maintained the same as in the non-reacting superheat calculations.

The global features of the reacting spray obtained from the reacting calculations are shown in

Fig. 2. The spray particle distribution appears to

be similar in both calculations. The gas temperature

ranges between 300 to 2100 deg. K. In both calculations most of the combustion takes place downstream

of the spray in a predominantly diffusion-controlled

flame. However, in the calculation involving Lee et

al [15], the high temperature region extends further

upstream into the inner central region of the hollowcone spray.

Swirl Stabilized Reacting Spray Generated

by a Single Element LDI Experiment

This investigation is undertaken to test the following models: (1) the Sheet breakup primary atomization model [17-18], & (2) the TAB secondary

droplet breakup model [23]. The experimental data

for this validation was provided by Ref. [36]. Fig.

3 shows the test section of the experiment reported

in [36]. The air passes through a six helicoidal vane

swirler followed by a converging-diverging venturi before entering the combustor. The air mass flow rate

is 0.49 kg/min., and at the inlet, air speed=20.4m/s,

T=294.3K, P=101325Pa. The fuel nozzle is located

at the middle of the centerbody and it is a ParkerHannifin, 90-deg. hollow cone, pressure swirler. The

liquid fuel is Jet-A, the liquid mass flow rate 0.025

kg/min, and the initial liquid temperature 475 K. The

internal pressure drop across the atomizer is 350000

NASA/TM—2012-217295 7
Pa which leads to an initial liquid velocity of about

22 m/s.

The results are based a 3D calculation with a

grid size of 833024 elements. It makes use of the

following models for the gas-phase: the standard

k-epsilon turbulence model, a a single-step reduced

chemical kinetic mechanism, and the eddy-breakup

turbulence/chemistry model. The experimental conditions were based on the non-superheat evaporating conditions. The reported experimental results involved gas and droplet velocities (axial, radial, and

tangential), & droplet sizes. The comparisons for this

case were also reported in our earlier paper [16]. For

this case, the predicted gas-phase results underestimate both size and location of the central recirculation region but the predictions provide better agreement for both droplet size and velocities.

We have also completed two more calculations

for this case involving superheat conditions. In one,

the SVM of [12-14] was employed, and in the second,

the SVM of [15] was employed. In both calculations,

the liquid properties of the jet-a fuel were replaced by

the two-phase properties of JP8. Also, the specified

initial liquid temperature was raised to 520 deg. K.

Figs. 4 to 10 show the results for both gas

and droplet velocities, and droplet sizes. Shown here

are the comparisons between the experimental data,

the predicted obtained from the corresponding nonsuperheat experimental conditions, as well as the predicted results obtained from the two different superheat calculations. The comparisons for gas axial velocities at different axial locations are shown in Fig.

4, and the comparisons for the radial and tangential

velocities are shown in Figs. 5 and 6, respectively.

The gas velocities obtained from the superheat conditions are similar to those obtained from the nonsuperheat conditions and they all underestimate both

size and location of the central recirculation. The

predictions could be improved by taking into account

of the unsteady nature of fluid flow and also by incorporating a better chemical kinetic mechanism and

chemistry/turbulence model.

The comparisons for the droplet sizes are shown

in Fig. 7 at four different axial locations. The comparisons between the experimental data and the predictions from the non-superheat calculation are in

good agreement. It is also noteworthy that the radial spreading rate of the spray is well predicted.

As you move progressively further downstream, more

droplets start disappearing from the the central region. It is because of the rise in the gas temperature to near flame temperature which leads to faster

evaporation. But the comparisons differ significantly

with the results obtained from the superheat calculations. The results from both the superheat vaporization models are mostly similar. At the first axial

location, the predicted droplet sizes from the superheat conditions are higher than the experimental data

in the the central region. The reason for this increase

could partly be attributed to a decrease in the liquid density caused by a rapid bubble growth in the

superheated fluid. This would lead to a decrease in

the liquid breakup length/time because of its q ρl

ρg

dependence which in turn leads to an increase in the

initial product droplet size because of its inverse relationship to the liquid breakup time. But at the next

(second) axial location, the drop sizes mostly fall below the experimental results. Further downstream,

the effect of superheat conditions is more evident as

the predicted droplet sizes fall significantly below the

experimental data.

Fig. 8 shows the droplet mean axial velocity

comparisons at six different axial locations. Shown

are the predicted results as well as the experimental

data for two different droplet-size groups: 0-15 microns and 60-75 microns. The data for the 0-15 microns represent the velocities of the smallest droplet

sizes and the data for the 60-75 microns represent the

velocities of the largest droplet sizs. Our predicted results are expected to fall somewhere in between the

two droplet-size groups but they are expected to fall

closer to the 60-75 microns as the predicted results

are based on the mean-size (SMD) droplet representation. The comparisons with the non-superheat calculation are mostly in good agreement and fall mostly

closer to the large-size droplet group but for some underestimation observed in the middle of the first axial

location, and the outer region of the second axial location. The results from the superheat calculations

are also mostly in similar agreement in the first three

axial locations but the differences grow in the last axial locations where fewer droplets are present due to

faster vaporization under superheat condtiions. Also,

the axial velocities are underpredicted in the last two

axial locations. Fig. 9 shows the droplet radial velocity comparisons. There seems to be a reasonable

agreement between the predicted and experimental

results but for some underestimation observed in the

middle of the first axial location, and the outer regions of the second and third axial locations. Also,

it is interesting to note that the radial velocities for

NASA/TM—2012-217295 8
the small-size droplets are much higher than the corresponding larger-size droplets in the first two axial

locations. It is because the smaller droplets tend to

follow the gas velocity where the radial gas velocities are much higher because of swirl-induced recirculation. The mean droplet tangential velocity comparisons are shown in Fig. 10. The predicted results fall mostly closer to the experimental data of

the large-size droplets at the first three axial locations. They mostly underpredict the experimental

data in the next three locations but the superheat

results show a slightly better improvement. It is because smaller droplets resulting from increased vaporiztion due to superheat tend to follow the gas velocity.

The comparisons could perhaps be improved by providing an additional swirl component to the initial

liquid velocity as no swirl component was specified in

the present calculations.

CONCLUDING REMARKS

The paper describes complete details of a solution procedure that was implemented into NCC for

the modeling of a superheated spray. The modeling approach was used in the validation of a flashing

cylindrical jet, and in the model-accuracy assessment

studies based on a pressure swirl atomizer to examine

the differences between the two superheat vaporization models, and a single-element LDI reacting case

to evaluate the differences between the non-superheat

and superheat conditions.

REFERENCES

1. M.S. Raju, LSPRAY-III: A Lagrangian Spray

Module, NASA/CR–2008-215290, NASA Glenn

Research Center, Cleveland, Ohio, July 2008.

2. M.S. Raju, EUPDF-II: An Eulerian Joint Monte

Carlo PDF Module, NASA/CR–2004-213073,

NASA Glenn Research Center, Cleveland, Ohio,

April, 2004.

4. Raju M.S., and Sirignano, W.A., “MultiComponent Spray Computations in a Modified

Centerbody Combustor,” Journal of Propulsion

and Power, Vol. 6, No. 2, March-April 1990.

5. Raju, M.S., “AGNI-3D: A Computer Code for

the Three-Dimensional Modeling of a Wankel

Engine,” Computers in Engine Technology, Proceedings IMechE, London, United Kingdom, pp.

27-37, 1991.

6. Raju, M.S., “Heat Transfer and Performance

Characteristics of a Dual-Ignition Wankel Engine,” Journal of Engines, the 1992 SAE Transactions, Section 3, pp. 466-509.

7. M.S. Raju, Application of Scalar Monte Carlo

Probability Density Function Method For Turbulent Spray Flames, Numerical Heat Transfer,

Part A, vol. 30, pp. 753-777, 1996.

8. M.S. Raju, Current Status of the Use of Parallel Computing in Turbulent Reacting Flows:

Computations Involving Sprays, Scalar Monte

Carlo Probability Density Function & Unstructured Grids, Advances in Numerical Heat Transfer, vol. 2, ch. 8, pp.259-287, 2000.

9. M.S. Raju, Scalar Monte Carlo PDF Computations of Spray Flames on Unstructured

Grids With Parallel Computing, Numerical Heat

Transfer, Part B, No. 2, Vol. 35, pp. 185-209,

March 1999.

10. M.S. Raju, On the Importance of Chemistry/Turbulence Interactions in Spray Computations, Numerical Heat Transfer, Part B: Fundamentals, No. 5, Vol. 41, pp. 409-432, 2002.

11. Lucas, K.D., Tseng, C.C., Pourpoint, T.L.,

Lucht, R.P., and Anderson, W.E., “Imaging

Flashing Injection of Acetone at Jet Engine Augmentor Conditions,” AIAA Paper 2007-1182,

45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, Jan. 8-11, 2007.

12. Zuo, B., Gomes, A.M., and Rutland, C.J.,

“Modeling Superheated Fuel Sprays and Vaporization,” Int. J. Engine Research, vol. 1, no. 4,

pp. 321-336.

NASA/TM—2012-217295 9

3. Raju, M.S., “CFD Modeling of Superheated

Sprays,” AIAA-2009-1187, the 47th Aerospace

Sciences Meeting, Orlando, Florida, January 5-

8, 2009.
13. Schmehl, R, and Steelant, J.,

“Flash-Evaporation of Oxidizer During Start-Up

of an Upper-Stage Rocket Engine,” AIAA Paper

2003-5075, 39th AIAA/ASME SAE/ASEE Joint

Propulsion Conference and Exhibit, Huntsville,

Alabama, July 20-23 2003.

14. Schmehl, R, and Steelant, J., “Evaluation of Oxidizer Temperature Drop in a Combustion Chamber,” 4th International Conference on Launcher

Technology ”Space Launcher Liquid Propulsion,

Liege, Belgium, December 3-6 2002.

15. Lee J., Fotache C., Gopalakrishnan, S., &

Schmidt, D., ”Validated tools for Low Emissions

Injector Design Using Superheated/Supercritical

Fuels,” NASA/CR–Year-2010/NNC07CB05C,

Glenn Research Center, Cleveland, Ohio.

16. Raju, M.S., & Bulzan, D., ”Assessment of

Some Atomization Models used in Spray Calculations,” ICCES1120110131487, Nanjing, China,

18-21 April, 2011, also as NASA/TM-2011-

217029, Glenn Research Center, Cleveland,

Ohio, March 2011.

17. Schmidt, D.P., Nouar, I., Senecal, P.K., Hoffman, J., Rutland, C.J., Martin. J., & Reitz,

R.D., “Pressure-Swirl Atomization in the Near

Field,” 1999 SAE Congress, SAE 1999-01-0496.

18. Senecal, P.K., Schmidt, D.P., Nouar, I., Rutland,

C.J., & Reitz, R.D., “Modeling High Speed Viscous Liquid Sheet Approximation,” 1998.

19. Reitz, R.D., & Bracco, F.V., “Mechanism of Atomization of a Liquid Jet,” Phy. Fluids, Vol. 25,

ch. 10, Oct., 1982.

20. Reitz, R.D., and Diwakar, R. “Structure of HighPressure Fuel Sprays,” SAE paper 870598, 1987.

21. Reitz, R.D., “Computer Modeling of Sprays,”

Spray Technology Short Course, Pittsburg, PA

May 7, 1997.

22. Khosla, S., and Crocker, D.S., “CFD Modeling of the Atomization of Plain Jets in Cross

Flow for Gas Turbine Applications”’ IGTI Turbo

Expo: Combustion & Fuels, GT2004-54269, Vienna, Austria, June 2004.

23. O’Rourke, P.J., and Amsden, A.A., “The TAB

Method for Numerical Calculation of Spray

Droplet Breakup,” SAE Technical Paper 872089,

1987.

24. Tanner, F.X., “Liquid Jet Atomization and

Droplet Breakup Modeling of Non-evaporating

Diesel Fuel sprays,” SAE Technical Paper

970050, 1998. Also SAE 1997 Transactions:

Journal of Engines, Vol. 106, Sec. 3, pp. 127-

140, 1998.

25. Tanner, F.X., “A Cascade Atomization and

Drop Breakup Model for the Simulation of HighPressure Liquid Jets,” SAE Paper 2003-01-1044,

2003.

26. Adachi, M., McDonnel, V.G., Tanaka, D.,

Senda, J, and Fujimoto, H., “Characteristics of

Fuel Vapor Concentration Inside a Flash Boiling

Spray,” SAE Paper 970871, 1997.

27. Sher, E., & Elata, C., “Spray Formation from

Pressure Cans by Flashing,” Ind. Eng. Chem.

Process Des. Dev., Vo. 16, number 2, pp. 237-

242, 1977.

28. Downar-Zapolski, P., Bilicki, Z., Bolle, L., &

Franco, J., ”The Non-Equilibrum Model OneDimensional Flashing Liquid Flow,” Int. J. of

Multiphase Flow, Vol. 22, No. 3, pp. 473-483,

1996.

29. Kawano, D., Ishii, H., Suzuki, H., Gotto, Y.,

Odaka, M., & Senda, J., ”Numerical Study on

Flash-Boiling Spray of Multicomponent Fuel,”

Heat-Transfer-Asian Research (Wiley Periodicals, Inc.), Vol. 35, No. 5, pp. 369-385, 2006.

30. Lefebvre, A., “Atomization and Sprays,” Hemisphere Publishing Company, New York, pp. 165-

222, 1989.

31. VanDerWege, B.A., Lounberry, T.H., and

Hochgreb, S., “Numerical Modeling of Fuel

Sprays in DISI engines Under Early-Injection

Operating Conditions,” SAE Paper 2000-01-

0273, 2000.

32. Reitz, R.D., “A Photographic Study of FlashBoiling Atomization,” Aerosol Science Technology, Vol, 12, pp. 561-569, 1990.

33. Yildiz, D., Rambaud, P., Van Beeck, J., Buchlin, J.-M., “Characterization of Superheated Liquid Jet Atomization Phase Doppler Anemometer (PDA) and High-Speed Imaging,” Proceedings of FEDSM2006: 2006 ASME Joint U.S.-

European Fluids Engineering Summer Meeting,

July 17-20, 2006, Miami, Florida.

NASA/TM—2012-217295 10
34. Yildiz, D., Rambaud, P., Van Beeck, J., Buchlin,

J.-M., “Evolution of the Spray Characteristics in

Superheated Liquid Jet Atomization in Function

of Initial Flow Conditions,” ICLASS-2006, Paper

ID ICLASS06-122, Aug. 27-Sept 1, 2006, Kyoto,

Japan.

35. Benjamin, M.A., Crocker, D.S., ”Spray Characterization of a Relatively High Flow Simplex

Atomizer Using Experiment and CFD,” 32th

Joint Propulsion Conference, AIAA paper 96-

3165, July 1996.

36. Cai, J., Jeng, S.M., Tacina, R., ”The Structure of

a Swirl Stabilized Reacting Spray Issued From an

Axial Swirler,” 43rd AIAA Aerospace Sciences

Meeting & exhibit, AIAA 20424, January 2005.

NASA/TM—2012-217295 11
Radial distance, m

Axial distance, m

0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32 0.36 0.4 0

0.1

0.2

0.3

Radial distance, m

Axial distance, m

0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32 0.36 0.4 0

0.1

0.2

0.3

T: 270 296 321 347 373 399 424 450

(b) SVM of Lee et al [15].

Fig. 1 Global structure of a non-reacting spray generated by a Parker-Hannifin

pressure-swirl atomizer under superheat conditions.

(a) SVM of Zuo et al [12-14].

NASA/TM—2012-217295 12
Radial distance, m

Axial distance, m

0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32 0.36 0.4 0

0.1

0.2

0.3

Radial distance, m

Axial distance, m

0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32 0.36 0.4 0

0.1

0.2

0.3

T: 400 600 800 1000 1200 1400 1600 1800 2000

(a) SVM of Zuo et al [12-14].

(b) SVM of Lee et al [15].

Fig. 2 Global structure of a spray flame generated by a Parker-Hannifin

pressure-swirl atomizer under superheat conditions.

NASA/TM—2012-217295 13
 Fig. 3 Test setup of the single−element LDI experiment

 (taken from Cai et al [36]).

NASA/TM—2012-217295 14
Y, m

Axial velocity, m/s

-0.02 -0.01

0 0.01 0.02

-10-20-30-40

0

2010

X=0.005m

Y, m

Axial velocity, m/s

-0.02 -0.01

0 0.01 0.02

-10-20

0

2010

X=0.015m

Y, m

Axial velocity, m/s

-0.02 -0.01

0 0.01 0.02

-10-20

0

2010

X=0.029m

Y, m

Axial velocity, m/s

-0.02 -0.01

0 0.01 0.02

-10-20

0

2010

X=0.046m

Y, m

Axial velocity, m/s

-0.02 -0.01

0 0.01 0.02

-10-20

0

2010

X=0.092m

Fig. 4 Gas mean axial velocity distributions.

Y, m

Axial velocity, m/s

-0.02 -0.01

0 0.01 0.02

-10-20

0

2010

experimental datanon-superheat vaporizationSVM of Zuo et alSVM of Lee et al

X=0.076m

NASA/TM—2012-217295 15
Y, m

Radial velodity, m/s

-0.02 -0.01 0 0.01 0.02

-20-40

0

4020

X=0.005m

Y, m

Radial velocity, m/s

-0.02 -0.01 0 0.01 0.02

-10-20-30

0

2010 X=0.015m

Y, m

Radial velocity, m/s

-0.02 -0.01 0 0.01 0.02

-10-20

0

2010

X=0.029m

Y, m

Radial velocity, m/s

-0.02 -0.01 0 0.01 0.02 -10

-5

50

201510

X=0.046m

Y, m

Radial velocity, m/s

-0.02 -0.01

0 0.01 0.02 -10

-5

50

201510

X=0.092m

Fig. 5 Gas mean radial velocity distributions.

Y, m

Radial velocity, m/s

-0.02 -0.01 0 0.01 0.02 -10

-5

50

201510

experimental datanon-superheat vaporizationSVM of Zuo et alSVM of Lee et al

X=0.076m

NASA/TM—2012-217295 16
Z, m

Tangential velocity, m/s

-0.02 -0.01

0 0.01 0.02

-10-20

0

2010

X=0.005m

Z, m

Tangential velocity, m/s

-0.02 -0.01

0 0.01 0.02

-10-20

0

2010

X=0.092m

Z, m

Tangential velocity, m/s

-0.02 -0.01

0 0.01 0.02

-10-20

0

2010

X=0.015m

Z, m

Tangential velocity, m/s

-0.02 -0.01

0 0.01 0.02

-10-20

0

2010

X=0.029m

Z, m

Tangential velocity, m/s

-0.02 -0.01

0 0.01 0.02

-10-20

0

2010

X=0.076m

Fig. 6 Gas mean tangential velocity distributions.

Z, m

Tangential velocity, m/s

-0.02 -0.01

0 0.01 0.02

-10-20

0

2010

experimental datanon-superheat vaporizationSVM of Zuo et alSVM of Lee et al

X=0.046m

NASA/TM—2012-217295 17
Y, m

Mean droplet diameter, microns

0 0.005 0.01 0.015 0.02 0.025

0

80604020

120100

X=0.020m

Y, m

Mean droplet diameter, microns

0 0.005 0.01 0.015 0.02 0.025

0

50

150100

X=0.005m

Y, m

Mean droplet diameter, microns

0 0.005 0.01 0.015 0.02 0.025

0

80604020

120100 X=0.009m

Fig. 7 Mean droplet diameter (D32) distributions.

Y, m

Mean droplet diameter, microns

0 0.005 0.01 0.015 0.02 0.025

0

80604020

120100

X=0.038m

experimental datanon-superheat vaporizationSVM of Zuo et alSVM of Lee et al

NASA/TM—2012-217295 18
Y, m

Axial velocity, m/s

0 0.005 0.01 0.015 0.02 0.025

50

25201510

X=0.005m

Y, m

Axial velocity, m/s

0 0.005 0.01 0.015 0.02 0.025

-10-20

0

2010

X=0.020m

Y, m

Axial velocity, m/s

0 0.005 0.01 0.015 0.02 0.025

-10

0

2010

X=0.009m

Y, m

Axial velocity, m/s

0 0.005 0.01 0.015 0.02 0.025

-10-20

0

2010

X=0.015m

Y, m

Axial velocity, m/s

0 0.005 0.01 0.015 0.02 0.025

-10

0

2010

X=0.029m

Y, m

Axial velocity, m/s

0 0.005 0.01 0.015 0.02 0.025

-10

0

2010

0-15 microns (exp.)60-75 microns (exp.)non-superheat vaporizationSVM of Zuo et alSVM of Lee et al

X=0.038m

Fig. 8 Spray mean axial velocity distributions.

NASA/TM—2012-217295 19
Y, m

Radial velocity, m/s

0 0.005 0.01 0.015 0.02 0.025

0

5040302010

X=0.005m

Y, m

Radial velocity, m/s

0 0.005 0.01 0.015 0.02 0.025 -10

-5

50

201510

X=0.015m

Y, m

Radial velocity, m/s

0 0.005 0.01 0.015 0.02 0.025 -10

0

40302010

X=0.009m

Y, m

Radial velocity, m/s

0 0.005 0.01 0.015 0.02 0.025

-10-15

-5

50

10

X=0.029m

Y, m

Radial velocity, m/s

0 0.005 0.01 0.015 0.02 0.025

-10-15

-5

50

10

X=0.038m

Fig. 9 Spray mean radial velocity distributions.

Y, m

Radial velocity, m/s

0 0.005 0.01 0.015 0.02 0.025 -10

-5

50

201510

0-15 microns (exp.)60-75 microns (exp.)non-superheat vaporizationSVM of Zuo et alSVM of Lee et al

X=0.020m

NASA/TM—2012-217295 20
Z, m

Tangential velocity, m/s

0 0.005 0.01 0.015 0.02 0.025 -5

50

1510

X=0.005m

Z, m

Tangential velocity, m/s

0 0.005 0.01 0.015 0.02 0.025 -5

50

10

X=0.009m

Z, m

Tangential velocity, m/s

0 0.005 0.01 0.015 0.02 0.025 -5

50

10

X=0.015m

Z, m

Tangential velocity, m/s

0 0.005 0.01 0.015 0.02 0.025 -5

50

1510

X=0.029m

Fig. 10 Spray mean tangential velocity distributions.

Z, m

Tangential velocity, m/s

0 0.005 0.01 0.015 0.02 0.025 -5

50

1510

X=0.020m

Z, m

Tangential velocity, m/s

0 0.005 0.01 0.015 0.02 0.025 -5

50

1510 0-15 microns (exp.) 60-75 microns (exp.)

non-superheat vaporizationSVM of Zuo et alSVM of Lee et al

X=0.038m

NASA/TM—2012-217295 21
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Current Status of Superheat Spray Modeling With NCC 

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Raju, M., S.; Bulzan, Dan, L. 

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

An understanding of liquid fuel behavior at superheat conditions is identified to be a topic of importance in the design of modern supersonic 

engines. As a part of the NASA's supersonics project office initiative on high altitude emissions, we have undertaken an effort to assess the 

accuracy of various existing CFD models used in the modeling of superheated sprays. As a part of this investigation, we have completed the 

implementation of a modeling approach into the national combustion code (NCC), and then applied it to investigate the following three 

cases: (1) the validation of a flashing jet generated by the sudden release of pressurized R134A from a cylindrical nozzle, (2) the differences 

between two superheat vaporization models were studied based on both hot and cold flow calculations of a Parker-Hannifin pressure swirl 

atomizer, (3) the spray characteristics generated by a single-element LDI (Lean Direct Injector) experiment were studied to investigate the 

differences between superheat and non-superheat conditions. Further details can be found in the paper. 

15. SUBJECT TERMS

Spray combustion; Atomization; Turbulent combustion; Superheat spray; CFD modeling 

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