M.S. Raju

ASRC Aerospace Corporation, Cleveland, Ohio

Dan Bulzan

Glenn Research Center, Cleveland, Ohio

Assessment of Some Atomization Models Used in 

Spray Calculations

NASA/TM—2011-217029

March 2011
NASA STI Program . . . in Profi le

Since its founding, NASA has been dedicated to the 

advancement of aeronautics and space science. The 

NASA Scientifi c and Technical Information (STI) 

program plays a key part in helping NASA maintain 

this important role.

The NASA STI Program operates under the auspices 

of the Agency Chief Information Offi cer. It collects, 

organizes, provides for archiving, and disseminates 

NASA’s STI. The NASA STI program provides access 

to the NASA Aeronautics and Space Database and 

its public interface, the NASA Technical Reports 

Server, thus providing one of the largest collections 

of aeronautical and space science STI in the world. 

Results are published in both non-NASA channels 

and by NASA in the NASA STI Report Series, which 

includes the following report types:

• TECHNICAL PUBLICATION. Reports of 

completed research or a major signifi cant phase 

of research that present the results of NASA 

programs and include extensive data or theoretical 

analysis. Includes compilations of signifi cant 

scientifi c and technical data and information 

deemed to be of continuing reference value. 

NASA counterpart of peer-reviewed formal 

professional papers but has less stringent 

limitations on manuscript length and extent of 

graphic presentations.

• TECHNICAL MEMORANDUM. Scientifi c 

and technical fi ndings that are preliminary or 

of specialized interest, e.g., quick release 

reports, working papers, and bibliographies that 

contain minimal annotation. Does not contain 

extensive analysis.

• CONTRACTOR REPORT. Scientifi c and 

technical fi ndings by NASA-sponsored 

contractors and grantees.

• CONFERENCE PUBLICATION. Collected 

papers from scientifi c and technical 

conferences, symposia, seminars, or other 

meetings sponsored or cosponsored by NASA.

• SPECIAL PUBLICATION. Scientifi c, 

technical, or historical information from 

NASA programs, projects, and missions, often 

concerned with subjects having substantial 

public interest.

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientifi c and 

technical material pertinent to NASA’s mission.

Specialized services also include creating custom 

thesauri, building customized databases, organizing 

and publishing research results.

For more information about the NASA STI 

program, see the following:

• Access the NASA STI program home page at 

http://www.sti.nasa.gov

• E-mail your question via the Internet to help@

sti.nasa.gov

• Fax your question to the NASA STI Help Desk 

at 443–757–5803

• Telephone the NASA STI Help Desk at

 443–757–5802

• Write to:

 NASA Center for AeroSpace Information (CASI)

 7115 Standard Drive

 Hanover, MD 21076–1320
M.S. Raju

ASRC Aerospace Corporation, Cleveland, Ohio

Dan Bulzan

Glenn Research Center, Cleveland, Ohio

Assessment of Some Atomization Models Used in 

Spray Calculations

NASA/TM—2011-217029

March 2011

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

International Conference on Computational and Experimental Engineering and Sciences (ICCES 2011)

organized by the Hohai University

Nanjing, China, April 18–21, 2011
Acknowledgments

The authors would like to extend their sincere appreciation to Dr. Jeff Moder for his many valuable contributions to the

spray code, LSPRAY-III. This work was supported by the NASA’s fundamental aeronautics/supersonics and

subsonic-fi xed-wing project offi ces with Dr. N.-S. Liu acting as the technical monitor.

Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5301 Shawnee Road

Alexandria, VA 22312

Available electronically at http://www.sti.nasa.gov

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

The paper presents the results from a validation

study undertaken as a part of the NASA’s fundamental aeronautics initiative on high altitude emissions

in order to assess the accuracy of several atomization models used in both non-superheat and superheat spray calculations. As a part of this investigation we have undertaken the validation based on four

different cases to investigate the spray charactereristics of (1) a flashing jet generated by the sudden release of pressurized R134A from cylindrical nozzle,

(2) a liquid jet atomizing in a subsonic cross flow,

(3) a Parker-Hannifin pressure swirl atomizer, and

(4) a single-element LDI (Lean Direct Injector) combustor experiment. These cases were chosen because

of their importance in some aerospace applications.

The validation is based on some 3D and axisymmetric

calculations involving both reacting and non-reacting

sprays. In general, the predicted results provide reasonable agreement for both mean droplet sizes (D32)

and average droplet velocities but mostly underestimate the droplets sizes in the inner radial region of a

cylindrical jet.

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. (6))

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

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

Assessment of Some Atomization Models 

Used in Spray Calculations 

M.S. Raju 

ASRC Aerospace Corporation 

Cleveland, Ohio 44135 

Dan Bulzan 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

NASA/TM—2011-217029 1
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 investigation is two-fold:

(1) To develop a solution procedure based on

the existing CFD models for the modeling of a superheated spray. 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. The reasons for its occurrence are mainly two-fold [11-14]: it is because the

same liquid fuel is often used as a coolant and the nozzles operate at low back pressures, and rapid depressurization across a fuel injection system may lead to

flash injection because thermal inertia initially tends

to maintain its internal liquid temperature above the

saturation temperature when exit pressure falls into

the superheated regime. Although flash evaporation

is considered to be detrimental to engine performance

under normal circumstances, it can have some potential benefits as it is known to produce a fine spray

with enhanced atomization, increase effective spray

cone angle, and decrease spray penetration [11].

(2) The success of any spray calculation depends

a great deal on the specification of the appropriate

injector exit conditions. In order to reduce uncertainty associated with the specification of the initial droplet conditions, we have undertaken a validation effort to establish accuracy of various atomization models used in spray calculations. They include the following models for primary atomization:

(1) Blob-jet, (2) BLS (boundary layer stripping), and

(3) Sheet-breakup, and the following models for secondary droplet breakup: (1) TAB (Taylor analogy

breakup), and (2) ETAB (Enhanced Taylor analogy

breakup). Further details of these models and their

implementation can be found in [1].

In this paper, we first describe some details of

the modeling approach used in the calculation of a

superheated spray followed by a presentation of the

results from our validation cases.

SUPERHEAT VAPORIZATION MODEL

OF ZUO, GOMES, & RUTLAND [12], AND

SCHMEHL & STEELANT [15-16]

A liquid is said to superheated when it is heated

to a temperature above its boiling temperature. The

atomization associated with a superheated spray is

often referred to as flash atomization. The flashing phenomena refers to a process that is in thermodynamic non-equilibrium when a liquid is superheated [13-14]. We have adopted the modeling approach that was developed by Zuo, Gomes, and Rutland [12] and Schmehl and Steelant [15-16] for the

vaporization model under superheat conditions. 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 but it is controlled by the droplet

internal heat transfer. This modeling approach differs from the classical droplet vaporization models in

three important ways: (1) the droplet surface mass

fraction, Yf s, approaches unity as the temperature at

the droplet surface remains at the corresponding liquid boiling temperature under superheat conditions;

(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 which in turn may lead to a decrease in 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 [15-16]

showed that the total evaporation rate,  ̇mk, can be

calculated as

NASA/TM—2011-217029 2
m ̇ k = m ̇ k,f lash +  ̇mk,t (1)

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

given by

m ̇ k,f lash = 4πr2

kαs

(Tk − Tb)

lk

(2)

where Tk is the internal droplet temperature and the

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

is given by the Adachi correlation [17]:

= 0.76(Tk − Tb)

0.26 (0 ≤ Tks − Tb ≤ 5)

αs = 0.027(Tk − Tb)

2.33 (5 ≤ Tks − Tb ≤ 25) (3)

= 13.8(Tk − Tb)

0.39 (Tks − Tb ≥ 25)

which is valid over a wide range of superheat conditions. The vaporization rate due to external heat

transfer,  ̇mk,t, in Eq. (1) 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] (4)

where the Spalding heat transfer number, Bt, is

Bt =

Cp(Tg − Tks)

lk,ef f

(5)

and 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

(6)

which is an useful parameter as it represents the total

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

interior. Finally, the Nusselt number, Nu, and the

corresponding droplet regression rate, dsk

dt , are given

by

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

g

) (7)

dsk

dt = −

m ̇ k

2πrkρl

(8)

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).

VAPORIZATION MODEL VALID UNDER

NON-SUPERHEAT CONDITIONS

Under moderate superheat conditions, only a

fraction of the vaporization takes place under superheat conditions (Tk > Tb) and the remainder takes

place under non-superheated 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 simple

classical D2-theory:

m ̇ k = 2πrkρg Df gs Sh ln(1 + Bk) (9)

where the Spalding mass transfer number, Bk, and

the Sherwood number, Sh, are given by

Bk =

(yf s − yf )

(1 − yfs)

(10)

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

g

) (11)

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

the the droplet interface and yf is the mass fraction

of the fuel species in the surrounding gas.

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 (12)

if Tk ≤ Tb, and

dTk

dt = −

3αs

rkρlCpl

(Tk − Tb) (13)

if Tk > Tb

SOME EFFECTS OF SUPERHEAT ON

PRIMARY ATOMIZATION

NASA/TM—2011-217029 3
Flash evaporation is known to produce a fine

spray with enhanced atomization, increase effective

spray cone angle, and decrease spray penetration [18].

Here, we consider the effects of flash evaporation on

the primary atomization by following the approach

of Zuo et al [12]. Its effect on the initial droplet size,

dis, is defined as a function of both engine pressure

and a superheat parameter:

dis = din(

P

Patm

)

0.27[1−χ(

Patm

P

)

0.135] 0 ≤ χ(

Patm

P

)

0.135 ≤ 1

(14)

where din is the corresponding droplet droplet size

under normal evaporating conditions without flash

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

χ =

I(Tk) − I(Tb)

l(Tb)

(15)

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. (14), 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 [19]. 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 observations

from VanDerWege et al [20] and Reitz [21].

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

(16)

where θn is in degrees for a spray vaporizing under

normal conditions without flash evaporation. This

correlation was developed based on the experimental

data of Reitz [21]. These modifications from Zuo et al

[12] were originally reported in conjunction with the

sheet breakup primary atomization model but their

validity with other primary atomization models needs

further investigation.

RESULTS & DISCUSSION

A FLASHING JET GENERATED BY A

CYLINDRICAL NOZZLE

We have spent considerable time on the literature survey in trying to identify some relevant experimental data for validation purposes. Of the limited

data available, the recent experimental investigation

by Yildiz et al [13-14,22] seems to be more promising

as it contained data for two-phase jet flows associated

with the near-field flashing phenomena generated by

the sudden release of pressurized R134A from nozzles

of different sizes with orifice-exit diameters ranging

from 1, 2, and 4 mm. The experiments were performed mainly to simulate the effects of flashing phenomena generated by either of pressurized propane

or butane. The reported data contained the particle image velocimetry (PIV) measurements of gas

and droplet velocities, the phase Doppler anemometry (PDA) measurements of droplet sizes, the thermocouple measurements of temperatures, and the high

speed images of flow visualization. While the data

appeared to be worth pursuing, the reported experimental data contained a great deal of uncertainty

with respect to the specification of the initial conditions. It is also noteworthy that the data had not

gone through a rigorous review in terms of its applicability for validation purposes.

In the VKI experiments [13-14,22], the overall

superheat conditions ranged between 40 to 50o C and

the tank pressure ranged between 700 to 942 KPa

[23]. For the conditions considered, the onset of jet

breakup was observed to occur outside of the nozzleexit between 2-27 mm for the 1mm nozzle, and 4-20

mm for the 2mm nozzle. But for the 4mm nozzle, a

cloudy behavior was observed starting at 12mm with

no discernible point of jet disintegration [23]. Our

CFD calculations are focused primarily on predicting the flow characteristics further downstream beginning with the onset of jet breakup. At the start of

jet dispersion, the pressurized liquid would undergo

some expansion due to vaporization of the pressurized liquid depending on the degree of superheat and

the entrainment of surrounding air [23]. Because of

this expansion, the effective size of the expanded jet

would be larger than the orifice exit [23]. Therefore,

there is a need for estimating both the size and expansion angle of the jet from the observed experimental

data [23].

In our present calculations, we have focused

mainly on the case involving the 1mm nozzle for

which the most extensive data were reported. For

this case, the initial liquid temperature is 293 deg.

K which corresponds to a superheat temperature of

46 deg. C. The initial liquid stagnation velocity is

NASA/TM—2011-217029 4
estimated to be about 34 m/s based on the given upstream and back pressures. Based on the data and

the assumptions discussed in Ref. [23], the initial size

of the jet at the point of jet breakup is estimated to

be about 9mm. This is based on an initial estimated

expansion angle of 55 to 60 deg. from X=1 to 3D.

All the calculations were performed on a 2D axisymmetric grid with 79101 triangular elements. The

calculations were advanced until a steady state solution was reached by making use of the following

time steps: ∆tg (= local time step used in the flow

solver, s) was determined based on a CFL number

of 1, ∆tinjection (time-step at which a new group of

droplets is introduced) = 2.0 ms, and ∆tk (time step

used in the spray solver) = 0.0075 ms. The initial

gas conditions were prescribed based on the nondimensional velocity profile reported in Ref. [14].

The initial droplet injection velocity and the initial

liquid temperature are specified to be 34 m/s and

293 deg. K, respectively.

In this paper, we present the results obtained

from two sets of calculations. Both the calculations

are based the blob-jet model for primary atomization

and the ETAB model for secondary droplet breakup.

In Calculation 1, no effect of flash-induced atomization is taken into account. In Calculation 2, the effects of flash-induced atomization are taken into account as described earlier.

First, we would like to show the observed and

predicted spray patterns. Fig. 1 shows an experimental photograph obtained by means of a high-speed

photography for the two-phase flashing jet generated

by a 1mm nozzle (taken from Yildiz et al [22]). The

corresponding axisymmetric spray pattern as predicted by our CFD computations from Calculation 1

is shown in Fig. 2. It is also noteworthy that there is

no direct correspondence in the scales used between

the experiments and predictions. The results from

Calculation 2 are also similar to Calculation 1.

1. Gas Velocity Comparisons

Shown in Figs. 3a & 3b are the gas velocity comparisons with the experimental data. In the

radial profiles of gas velocity, the velocity is nondimensionalized by means of U/Umax and the radial

distance by r/D/(r/D)Umax/2.

The measurements were taken at three axial locations, x/D = 110, 220 , and 440, The normalized

experimental data represent the combined data reported over all three axial locations. It is noteworthy

that the reported gas velocities were actually based

on the measured velocities of droplets of sizes smaller

than ten microns. The non-dimensional velocity profiles from the experimental data were shown to exhibit a self-similar behavior as given by the following

correlation [14]:

U

Umax

= exp[−0.693( r

r ̄

)

2

] (17)

where  ̄r = r(Umax/2). This behavior was noted to be

similar to other correlations reported in the literature

[24-26] on both single and two-phase turbulent jets.

The velocity comparisons from Calculation 1

are shown in Fig. 3a, and those from Calculation

2 are shown in Fig. 3b. Also shown in Figs. 3a & 3b

are the profiles as obtained from Eq. (17). The predicted results are shown separately for each one of the

three axial locations, x/D = 110, 220 , and 440. In

both the calculations, the predicted gas velocities fall

entirely within the scatter range of the experimental

data. However, outside the experimental range, the

CFD results at the first two axial locations overpredict the gas velocity as given by Eq. (17).

2. Droplet Velocity Comparisons

Shown in Figs. 4a-c & 5a-c are the nondimensional droplet velocity profiles from Calculations 1 & 2, respectively. Once again the velocity is

non-dimensionalized by U/Umax, and the radial distance by r/D/(r/D)Umax/2. According to Yildiz et

al [14], the non-dimensional droplet velocity profiles

also followed a self-similar behavior as given by Eq.

(17). The experimental data was based on the PDA

measurements of all droplets with sizes higher than

10 μm. Again, the normalized experimental data represent the combined data taken over all three axial

locations. It is not entirely evident as to why the velocities for both gas phase and the droplets follow the

same correlation.

Some noteworthy aspects of the comparisons

from Figs. 4a-c & 5a-c are: (1) The CFD results

show a general trend similar to the experimental data

but exhibit a wider scatter than the experiments. (2)

In both the calculations at x/D = 110, most of the

predicted velocities are found to be located in the upper range of the experimental data. It is because of

the way we specified the initial conditions where the

initial velocities for all droplets were assumed to be

the same as the injection velocity of the liquid jet, 34

m/s. However, the predicted velocity range improves

considerably further downstream at the the last two

NASA/TM—2011-217029 5
axial locations. (3) The scatter in the predicted velocities seem to widen with the increased axial distance.

(4) The results from Calculation 1 are in slightly better agreement as more of its predicted velocities fall

within the experimental range.

3. Droplet Size Comparisons

Shown in Figs. 6a-c & 7a-c are the comparisons

between the average droplet sizes (local SMD, D32)

versus the non-dimensional radial distance, r/D.

Figs. 6a-c provide the comparisons from Calculation 1 at the three axial locations, x/D = 110, 220 ,

and 440. Similar comparisons from Calculation 2 are

shown in Figs. 7a-c.

As can be seen from the experimental data in

Figs. 6a-c & 7a-c, the experimental data exhibit a

general trend that is typical of a cylindrical liquid jet

where the larger droplets tend to be located near the

centerline [14]. Away from the centerline, the experimental data show that there is a slight increase in

the overall droplet size distribution with an increase

in the axial distance. This effect is more evident in

the comparisons between the last two axial locations.

The reasons for this behavior can be attributed to the

faster evaporation of smaller droplets which leaves the

remaining size distribution with relatively large-size

droplets [14].

Some highlights of the predictions from Calculation 1 (Figs. 6a-c) are as follows: (a) The experimental data show a much wider radial variation in

the droplet sizes when compared with the predictions

but the predictions manage to calculate the overall

SMD with a reasonable accuracy. (b) At the first

axial location, x/d =110, the droplet sizes are predicted with reasonable accuracy but at the last two

axial locations, x/d = 220 & 440, they fall short of

experimental data in the central region of the spray.

The reasons for this behavior could be attributed for

not taking into consideration the effect of droplet coalescence. It was reported to play a major role in the

central region of a non-superheated spray [27]. Unfortunately, we can’t verify this for a fact as we don’t

have a droplet coalescence model in our present code.

(c) Away from the central region, the predicted sizes

are in reasonable agreement with the experimental

behavior.

The results from Calculation 2 (Figs. 7a-c) are

similar to those obtained from Calculation 1. But the

results from Calculation 2 underpredict the droplet

sizes even more those from Calculation 1 in the central region of the spray at x/D = 110 & 220. This

reduction in the droplet sizes could be primarily attributed to the superheat correction as introduced

by Eq. (14). This correction leads to a reduction in

the initial blob size during the primary atomization

regime to about 500 μm from 1000 μm (=the injector

diameter of the cylindrical nozzle).

4. Temperature Comparisons

The reported temperature data of Ref. [22] is

based on the hot-wire thermocouple measurements

which can’t be used for making any direct comparisons with either predicted gas or liquid temperatures.

To understand the reasons behind it, we provide some

details on the nature of the temperature measurements obtained by Ref. [22]. The steady-state temperature measurements were obtained by means of

a thermocouple made up of Chrome/Alumel wire of

0.2mm diameter represents an aggregate (liquid-gas)

temperature. Therefore, its usefulness in making direct comparisons with either gas or liquid temperatures obtained from the CFD calculations becomes

difficult. This consideration becomes more evident

when we look at Fig. 8 which shows the single-point

thermocouple temperature signal versus time (taken

from Ref. [22]). Initially, the thermocouple registers

a temperature of 293 deg. K (= ambient gas temperature) before it reaches a steady-state temperature of

248.7 deg. K (≈ the boiling temperature of R134A).

Also, because of the intrusive nature of the technique

(taken by a thermocouple rack), the reported temperatures represent an aggregate temperature in the

neighborhood of the centerline.

Figs. 9a-b show the axial variation (centerline)

of the measured temperatures as well as the predicted

gas and liquid temperatures from Calculations 1 & 2.

The liquid temperatures represent the mass-averaged

droplet temperatures. The results are similar from

both the calculations. Initially the predicted gas

temperatures are close to an ambient temperature of

about 296o K before falling off to a level close to the

measured temperature of about 225o K near x/D =

20. Further downstream, the predicted gas temperatures raise above the measured temperatures due

to the entrainment of some surrounding gas from the

ambient. On the other hand, the average droplet temperatures overpredict the measured temperatures initially before falling below the experimental data further downstream. It is also noteworthy that the experimental data show that a considerable amount of

vaporization takes place under non-superheated conditions where the measured temperatures are lower

NASA/TM—2011-217029 6
than the boiling temperature of R134A (=247 o K).

A LIQUID JET ATOMIZED IN A SUBSONIC

CROSS-FLOW

This case was undertaken mainly to test the following models: BLS or blob-jet for primary atomization & ETAB for secondary droplet breakup. The

experimental data for this validation case was taken

from Ref. [28]. It involves the modeling of a liquid jet atomizing in a subsonic cross-flow based on

a 3D calculation (non-reacting & turbulent air-flow).

In this experiment, a liquid jet is injected vertically

upward into a subsonic wind tunnel with the nozzle

exit flush with the bottom wall [28]. The tunnel has

a width of 125 mm, a height of 75 mm, and a length

of 406 mm. The nozzle exit diameter is 0.5 mm. The

reported measurements include droplet size, axial velocity, and volume flux at three x/D (=200, 300, &

500) locations. The test conditions for the case studied are as follows: The water is used as a test liquid

with a liquid density of 998 kg/m2, viscosity 0.000956

kg/m/s, and surface tension 0.0705 N/m. The liquid

mass flow rate is about 0.0025 kg/s and a corresponding initial liquid velocity of 19.3 m/s. The cone spray

angle is specified to be 10 degrees. For the gas phase

at the inlet: the reference pressure is 140,000 Pa, the

ambient temperature is 298 K, the air density is 1.633

kg/m3, & the Mach number is 0.2 which corresponds

to an axial velocity of 103.8 m/s (v=w=0.0).

We have performed two different calculations

for this case: the first with the blob-jet primary atomization model and the second with the BLS primary

atomization model. Both the calculations make use of

the ETAB secondary droplet breakup model and the

standard k-epsilon model for gas turbulence. They

were performed on a grid with a mesh size of 34560.

The grid for this case was provided by CFDRC. Fig.

10 shows the 3D perspective view of the axial gas

velocity contours together with a spray pattern from

Calculation 1. In this figure, the inlet boundary is

located at x = 0, the exit boundary at x = 0.3, the

bottom and top walls are located at y = 0 & 0.08, respectively, & the symmetric boundary conditions are

applied at z = -0.05 and 0.05. The air flow is from

the back to the front and the inflow air velocity is

maintained at about 104 m/s. The velocity contours

indicate that there is a little change in the overall

gas velocity from 104 m/s other than a slight fall-off

downstream of the nozzle exit in the region between

the bottom wall and the spray. The spray is injected

from the middle of the bottom wall at x = 0.05. The

spray is deflected towards the gas flow soon after its

injection from the bottom wall. The outward spreading of the spray is also evident from the time of its

inception near the nozzle location before it exits out

of the computational domain.

Fig. 11 shows the droplet velocity comparisons

at x/D = 200. The comparisons include the experimental data, and the results from both BLS and blobjet primary atomization models. The results for the

axial, radial and tangential velocities are shown in

separate figures. Unfortunately, there is no reported

experimental data for the radial and tangential velocities. The experimental data for the axial velocities

are mostly in reasonable agreement with the predictions obtained from both blob-jet and BLS models.

While it is true that the results mostly underpredict

the experimental data, the comparisons show slightly

better agreement with the results obtained from the

blob-jet model. The BLS model mostly overpredicts

the radial velocities from the blob-jet model by a

small measure. The tangential velocities from both

the models fall within the scatter range of each other

but the results from the blob-jet model show a much

wider scatter range. Similar comparisons are found

in Fig. 12 at x/D = 300.

Fig. 13 shows the droplet size (D32) comparisons at x/D = 200. The comparisons include the experimental data, and the results from both the BLS

and blob-jet primary atomization models. The results from the blob-jet model are in better agreement

but mostly underpredict the experimental data. Similar comparisons are found in Fig. 14 at x/D = 300.

PARKER-HANNIFIN PRESSURE SWIRL

ATOMIZER

This case is undertaken mainly to test the following models: the sheet-breakup model for primary atomization, & the ETAB model for secondary

droplet breakup. The experimental data for this case

was reported by Ref [29]. It involves the modeling of

a liquid spray generated by a pressure swirl atomizer

based on an axisymmetric calculation (non-reacting

& turbulent air-flow). In this experiment, the injector

is located in the middle of a centerbody configuration,

it has an exit diameter of 0.0012 m, and the internal

pressure drop across the injector is 344500 Pa. The

liquid mass flow rate is 0.00125 kg/s, the liquid fuel is

C12H23, and the initial liquid temperature is 300 deg.

K. It produces a hollow cone spray with a full-cone

angle of 82 deg. & a half-cone angle of 15 deg.

NASA/TM—2011-217029 7
The calculations for this case were performed

on a 2D axisymmetric grid with 10201 triangular elements. The grid for this case was again provided by

CFDRC. The calculations are advanced until a steady

state solution was reached by making use of the following time steps: ∆tg (= local time step used in the

flow solver, s) was determined based on a CFL number of 1, ∆tinjection (time-step at which a new group

of droplets is introduced) = 1.0 ms, and ∆tk (time

step used in the spray solver) = 0.01 ms. Along the

left boundary of the 2D grid, a split boundary condition is implemented: a wall boundary condition is

applied over the centerbody region from y = 0.0 to

0.019 m, and a inflow boundary is applied over y =

0.019 to 0.3 m. At the inflow boundary, the axial gas

velocity (u) is assumed to be uniform at 1.2 m/s, the

initial gas temperature is 300 deg. K, and the initial

radial velocity profile is prescribed based on a linear

interpolation: at y = 0.019 m, v = -0.9m/s, at y =

0.1 m, v = -0.5 m/s, & at y = 0.3 m, v=0. The lower

boundary of the 2D grid is determined based on a

symmetric boundary condition, and the exit boundary conditions are implemented at both the upper

and left boundaries.

The predicted spray pattern is shown is Fig. 15.

Fig. 16 shows the droplet axial velocity comparisons

at two axial locations, x = 7.5 and 12.5 cm. The

comparisons include the experimental results [29], our

predicted results as well as those predicted results reported from the calculations of [29]. The predicted

results represent the mass-averaged droplet velocities.

At both axial locations, there is a decent comparison

between the CFDRC and our predicted results but

both mostly underestimate the experimental data in

the middle. Fig. 17 shows the comparisons for the

droplet radial velocities. Again, there is a good comparison between the CFDRC and our predicted results but mostly underpredict the experimental data

in the middle of the spray. The average drop size

(D32) comparisons are shown in Fig. 18. Our results fall short of the experimental data at both axial locations but the comparisons are in reasonable

agreement with the CFDRC results at the first axial

location but fall short at the next axial location.

SWIRL-STABILIZED REACTING SPRAY

GENERATED BY A SINGLE-ELEMENT LDI

EXPERIMENT

This case is undertaken mainly to test the following models: the sheet-breakup model for primary

atomization, & the TAB model for secondary droplet

breakup. The experimental data for this case was

provided by Cai et al [30]. It involves the modeling of a reacting spray generated by the LDI experiment. The LDI concept was developed as a part of

the next generation combustor development program

at NASA GRC [30]. Its aim was to achieve higher

efficiency and lower combustion emissions while operating at higher engine pressures and temperatures.

In the LDI approach, this was accomplished without

any premixing by means of an advanced fuel injector

and air swirler assembly design which ensures nearly

uniform fuel and air mixing before entering the combustor.

Fig. 19 shows the test section of the experiment reported in [30]. The air passes through a

six helicoidal vane swirler followed by a convergingdiverging 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 Parker-Hannifin, 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 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. Fig. 20 shows the spray

article distribution together with the the temperature contours and the spray article distribution. The

temperatures range between 400 to 2300 deg. K. The

high temperature region originates downstream of the

injector from the middle of the combustor and then

spreads radially outwards towards the wall boundaries.

Shown in Fig. 21 are the axial velocity comparisons at six different axial locations. Although there

is a qualitative comparison, the results clearly show

that the predictions underestimate both the size and

location of the central recirculation region. As can be

seen from the first axial location, the predictions considerably overestimate the magnitude of the negative

velocity at the centerline but starting from the second

axial location and onwards, the predictions reverse

direction and underestimate the centerline velocities.

It is because the experimentally-observed central recirculation is located downstream of the predicted reNASA/TM—2011-217029 8
sults. It was reported that that diverging venturi suppresses the formation of any noticeable corner vortex

as it forces the outer flow to attach itself immediately next to the side wall [30]. Its effect is seen in

the formation of a strong wall jet flow before hitting on the wall [30]. As a result of the ensuing flow

through the corner, the axial velocity falls as seen

from the location of the observed main peak and the

wall boundary. However, the calculations underestimate the axial velocities in the corner region by a

considerable measure. The comparisons could be improved by taking into account the unsteady nature of

the flow. The comparisons for the radial velocities at

different axial locations are shown in Fig. 22. Again

as in the axial velocity comparisons, the comparisons

are in qualitative agreement but mostly underestimate the experimental results in the first four axial

locations. The high radial velocities observed at the

first two axial locations near the wall could again be

attributed for reasons of a strong corner flow observed

in the experimental results [30]. The comparisons for

the tangential velocities are shown in Fig. 23. The

predictions mostly underestimate the the experimental results but provide reasonable comparison at the

first axial location.

Fig. 24 shows the comparisons for the Sauter

mean droplet sizes (d32). There is a good comparison

in general. It is interesting to note that droplets start

to disappear from the central region and the spray

develops into a doughnut-shape further downstream

as seen in the last two axial locations. It is because

most of the smaller droplets start to disappear after

vaporizing from the middle, where gas temperatures

start to rise because of combustion, while the larger

droplets move radially outwards. It is also intersting

to note that the droplet distribution becomes more

uniform at the last two axial locations. It is because

as the smaller droplets start to vaporize more quickly,

it leaves the remaining distribution with a more fairly

uniform large-size droplets.

Fig. 25 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 dropletsize group and the data for the 60-75 microns represent the velocities of the largest droplet-size group.

Our calculations are based on the mean-size droplet

representation and as such the predicted sizes are expected to fall closer to the 60-75 microns size group

and are also expected to fall between the two dropletsize groups. The comparisons are mostly in good

agreement and fall mostly closer to the large-size

droplet group. However, there is some underestimation in the middle of the first axial location and in the

outer region of the second axial location. It is noteworthy that the radial spreading rate of the spray is

well predicted.

Fig. 26 shows the droplet radial velocity comparisons. Again there is a good agreement between

the predicted and the experimental results of the

large-size droplets. However, there is some underestimation in the middle of the first axial location

and in the outer regions of the second and third axial locations. It is also interesting to note that radial

velocities for 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 closer to the gas velocity where the

radial velocities are higher as evidenced in Fig. 22.

The droplet mean tangential velocity comparisons are

shown in Fig. 27. The predicted results are closer to

the experimental data of the large-size droplets at the

first two axial locations. The calculations mostly underpredict the experimental results in the next four

locations. In determining the initial droplet tangential velocities, no swirl component was specified. Perhaps, the comparisons could be improved by providing an additional swirl component to the initial liquid

velocity.

CONCLUDING REMARKS

Here we provide a summary of our validation results involving both superheated and nonsuperheated liquid sprays.

(1) We have studied the two-phase jet characteristics of a superheated spray generated by the

sudden release of pressurized R134A from a cylindrical nozzle. The predicted profiles for both gas and

droplet velocities show a reasonable agreement with

the measured data. They exhibit a self-similar pattern as given by a correlation reported in the literature. There is a need for improvement in the atomization modeling when it comes to the droplet-size

comparisons for the following reasons: the experimental data show a much wider radial variation in

the droplet sizes when compared with the predictions

but the predictions manage to calculate the overall SMD with a reasonable accuracy, the predicted

droplet sizes mainly fall short of experimental data

NASA/TM—2011-217029 9
in the central region of the spray, and the predicted

sizes are in reasonable agreement with the experimental behavior away from the central region. Both the

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

non-superheated conditions. Since we can’t make direct comparisons with the hot-wire temperature measurements, there is a need for more data on separate

gas and liquid temperatures for a proper validation

of the vaporization models used in our present study.

(2) Our second validation involves the modeling of a liquid jet atomizing in a subsonic cross-flow

based on a 3D calculation (non-reacting & turbulent

air-flow). This investigation is undertaken mainly to

test the following models: BLS or blob-jet for primary

atomization & ETAB for secondary droplet breakup.

The results (droplet size and velocity) from the blobjet model are in reasonable agreement with the experimental data. However, the results from the BLS

model are found to be slightly less favorable.

(3) Our third validation involves the modeling

of a liquid spray generated by a pressure swirl atomizer based on an axisymmetric calculation (nonreacting & turbulent air-flow). This investigation is

undertaken mainly to test the following models: the

sheet-breakup model for primary atomization, & the

ETAB model for secondary droplet breakup. The

comparisons include mean droplet axial and radial

velocities and average droplet sizes (D32). The predicted results are in reasonable agreement with the

predicted CFDRC results but mostly underestimate

the experimental data.

(4) Our fourth validation involves the modeling of a reacting spray generated by a single element

LDI experiment based on a 3D calculation (turbulent

air-flow). This investigation is undertaken mainly to

test the following models: the sheet-breakup model

for primary atomization, & the ETAB model for secondary droplet breakup. The predicted gas-phase results underestimate both size and location of the central recirculation region but the predictions provide

better agreement for the droplet size and droplet velocities.

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.

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

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

Sciences Meeting, Orlando, Florida, January 5-

8, 2009.

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.

NASA/TM—2011-217029 10
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.

13. 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.

14. 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.

15. 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.

16. 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.

17. 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.

18. 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.

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

222, 1989.

20. 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.

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

22. Yildiz, D., Rambaud, P., Van Beeck, J., Buchlin, J.-M., “A Study on the Dynamics of a

Flashing Jet,” Von Karman Institute for Fluid

Mechanics, Final Contract Research ReportEAR0030/2002.

23. ”CFD Modeling of Flashing Jet Dispersion,”

Fluids Mechanics Research Group, University of

Hertfordshire, United Kingdom, FLIE ReportFeb. 2005.

24. Hetsroni, G., and Sokolov, M., ”Distribution of

Mass, Velocity, and Intensity of Turbulence in a

two-phase Turbulent Jet,” J. Appl. Mech., vol.

32, pp.315, 1971.

25. Pope, S.B., ”Turbulent Flows,” Cambrige University Press, 2000.

26. Bayvel, L.P., and Orzchowski, Z, ” Liquid Atomization,” Taylor & Francis, Combustion: An

International Series, !st edition, 1993.

27. Reitz, R.D., “Modeling Atomization Processes

in High-Pressure vaporizing Sprays,” Atomization and Spray Technology, Vol. 3, pp. 309-337,

1987.

28. Wu, P.-K., Kirkendall, K.A., and Fuller, R.P.,

”Spray Structures of Liquid Jets Atomized in

Subsonic Crossflows,” Journal of Propulsion and

Power, vol.14, No.2, pp. 173-182, March-April,

1998.

29. Benjamin, M.A., and 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.

30. 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 2005-1424,

January 2005.

NASA/TM—2011-217029 11
Fig. 1 R134−A Jet under 700 kPa at 23 deg. C for the 1mm nozzle 

 (taken from Yildiz et al [22])

Fig. 2 An axisymmetric view of the predicted spray pattern from

 Calculation 1.

NASA/TM—2011-217029 12
27

(r/D)/(r/D(UMAX/2))

U/UMAX

0 1 2 3

0

0.90.80.70.60.50.40.30.20.1

1

1.21.1

experimental dataexperimental correlationpredicted at x/D =110predicted at x/D = 220predicted at x/D = 440

(a) Calculation 1

(r/D)/(r/D(UMAX/2))

U/UMAX

0 1 2 3

0

0.90.80.70.60.50.40.30.20.1

1

1.21.1

experimental dataexperimental correlationpredicted at x/D =110predicted at x/D = 220predicted at x/D = 440

(b) Calculation 2

Fig. 3a-b Gas velocity comparisons from Calculations 1 & 2 of the VKI validation case.

NASA/TM—2011-217029 13
(r/D)/(r/D(UMAX/2))

U/UMAX

0 1 2 3

0

0.90.80.70.60.50.40.30.20.1

1

1.21.1 experimetal data

experimental correlationpredicted

(a) x/D = 110

(r/D)/(r/D(UMAX/2))

U/UMAX

0 1 2 3

0

0.90.80.70.60.50.40.30.20.1

1

1.21.1 experimetal data

experimental correlationpredicted

(b) x/D = 220

(r/D)/(r/D(UMAX/2))

U/UMAX

0 1 2 3

0

0.90.80.70.60.50.40.30.20.1

1

1.21.1 experimetal data experimental correlation

predicted

(c) x/D = 440

Fig. 4a-c Droplet velocity comparisons at three axial locations from Calculation 1 of

the VKI validation case.

NASA/TM—2011-217029 14
(r/D)/(r/D(UMAX/2))

U/UMAX

0 1 2 3

0

0.90.80.70.60.50.40.30.20.1

1

1.21.1 experimetal data

experimental correlationpredicted

(b) x/D = 220

(r/D)/(r/D(UMAX/2))

U/UMAX

0 1 2 3

0

0.90.80.70.60.50.40.30.20.1

1

1.21.1 experimetal data experimental correlation

predicted

(c) x/D = 440

(r/D)/(r/D(UMAX/2))

U/UMAX

0 1 2 3

0

0.90.80.70.60.50.40.30.20.1

1

1.21.1 experimetal data

experimental correlationpredicted

(a) x/D = 110

Fig. 5a-c Droplet velocity comparisons at three axial locations from Calculation 2 of

the VKI validation case.

NASA/TM—2011-217029 15
r/D

Diameter (microns)

0 5 10

0

80604020

240220200180160140120100

experimental datapredicted

(a) x/D = 110

r/D

Diameter (microns)

0 5 10

0

80604020

240220200180160140120100

experimental datapredicted

(b) x/D = 220

r/D

Diameter (microns)

0 5 10

0

50

250200150100

experimental datapredicted

(c) x/D = 440

Fig. 6a-c Mean droplet size comparisons at 3 axial locations from Calculation 1 of

the VKI validation case.

NASA/TM—2011-217029 16
r/D

Diameter (microns)

0 5 10

0

80604020

240220200180160140120100

experimental datapredicted

(a) x/D = 110

r/D

Diameter (microns)

0 5 10

0

80604020

240220200180160140120100

experimental datapredicted

(b) x/D = 220

r/D

Diameter (microns)

0 5 10

0

50

250200150100

experimental datapredicted

(c) x/D = 440

Fig. 7a-c Mean droplet size comparisons at 3 axial locations from Calculation 2 of

the VKI validation case.

NASA/TM—2011-217029 17
 Fig. 8 Temperature signal in time from the thermocouple 

 measurement (taken from Yildiz et al [22])

NASA/TM—2011-217029 18
Axial distance, m

Temperature, K

0 0.2 0.4 0.6 0.8

300280260240220200180

Gas (predicted)Experimental dataAverage drop (predicted)

(b) Calculation 2

Axial distance, m

Temperature, K

0 0.2 0.4 0.6 0.8

300280260240220200180

Gas (predicted)Experimental dataAverage drop (predicted)

(a) Calculation 1

Fig. 9a-b Axial variation of temperature near the centerline from Calculations 1 & 2 of

the VKI validation case.

NASA/TM—2011-217029 19
NASA/TM—2011-217029 20
27Radial velocity, m/s

y/D

0 1 2 3 4 5 6 7 8 9 10

0

80604020 BLS

blob-jet

Tangential velocity, m/s

y/D

0-1.5 -1 -0.5 0 0.5 1 1.5

80604020

BLSblob-jet

Axial velocity, m/s

y/D

50 100

0

80604020

BLSblob-jetexp.

Fig. 11 Droplet velocity comparisons at x/D =200 for the liquid jet in a cross flow.

NASA/TM—2011-217029 21
27Axial velocity, m/s

y/D

50 100

0

80604020

BLSblob-jetexp.

Tangential velocity, m/s

y/D

0-1.5 -1 -0.5 0 0.5 1 1.5

80604020

BLSblob-jet

Radial velocity, m/s

y/D

0 1 2 3 4 5 6 7 8 9 10

0

80604020

BLSblob-jet

Fig. 12 Droplet velocity comparisons at x/D =300 for the liquid jet in a cross flow.

NASA/TM—2011-217029 22
27

Droplet size, microns

y/D

0 50 100 150

80604020

140120100

BLSblob-jetexp.

Fig. 13 Droplet size comparisons at x/D=200 for the liquid jet

in a cross flow.

NASA/TM—2011-217029 23
27

Droplet size, microns

y/D

0 50 100 150

80604020

140120100

BLSblob-jetexp.

Fig. 14 Droplet size comparisons at x/D=300 for the liquid jet

in a cross flow.

NASA/TM—2011-217029 24
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

Fig. 15 Predicted spray pattern for the Parker-Hannifin validation case.

NASA/TM—2011-217029 25
27

Fig. 16 Axial droplet velocity comparisons for the

Parker-Hannifin validation case.

Radial distance, m

Axial velocity, m/s

0 0.05 0.1 0.15

86420

141210

0.075 m (CFDRC pre.)0.125 m (CFDRC pre.)0.075 m (our pre.)0.125 m (our pre.)0.075 m (exp.)0.125 m (exp.)

NASA/TM—2011-217029 26
27

Fig. 17 Radial droplet velocity comparisons for the

Parker-Hannifin validation case.

Radial distance, m

Radial velocity, m/s

0 0.05 0.1 0.15

86420

141210

0.075 m (CFDRC pre.)0.125 m (CFDRC pre.)0.075 m (our pre.)0.125 m (our pre.)0.075 m (exp.)0.125 m (exp.)

NASA/TM—2011-217029 27
27

Fig. 18 Droplet size comparisons for the Parker-Hannifin

validation case.

Radial distance, m

Droplet size, microns

0 0.05 0.1 0.15

50

300250200150100

0.075 m (our pre.)0.125 m (our pre.)0.075 m (CFDRC pre.)0.125 m (CFDRC pre.)0.075 m (exp.)0.125 m (exp.)

NASA/TM—2011-217029 28
 Fig. 19 Test setup of the single−element LDI experiment

 (taken from Cai et al [30]).

NASA/TM—2011-217029 29
NASA/TM—2011-217029 30
Fig. 21 Gas mean axial velocity distributions.

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

Y, m

Axial velocity, m/s

-0.02 -0.01

0 0.01 0.02

-20-40

0

20

X=0.005m

Y, m

Axial velocity, m/s

-0.02 -0.01

0 0.01 0.02

-10-20

0

2010

X=0.076m

Y, m

Axial velocity, m/s

-0.02 -0.01

0 0.01 0.02

-10-20

0

2010

exp.pre.

X=0.015m

NASA/TM—2011-217029 31
Fig. 22 Gas mean radial velocity distributions.

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

-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

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=0.076m

Y, m

Radial velocity, m/s

-0.02 -0.01 0 0.01 0.02

-10-20-30

0

2010

exp.pre.

X=0.015m

NASA/TM—2011-217029 32
Fig. 23 Gas mean tangential velocity distributions.

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=0.029m

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=0.076m

Z, m

Tangential velocity, m/s

-0.02 -0.01

0 0.01 0.02

-10-20

0

2010

exp.pre.

X=0.015m

Z, m

Tangential velocity, m/s

-0.02 -0.01

0 0.01 0.02

-10-20

0

2010

X=0.046m

NASA/TM—2011-217029 33
Fig. 24 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 exp.

pre.

X=0.005m

Y, m

Mean droplet diameter, microns

0 0.005 0.01 0.015 0.02 0.025

0

80604020

120100

X=0.020m

Y, m

Mean droplet diameter, microns

0 0.005 0.01 0.015 0.02 0.025

0

80604020

120100

X=0.038m

Y, m

Mean droplet diameter, microns

0 0.005 0.01 0.015 0.02 0.025

0

80604020

120100 X=0.009m

NASA/TM—2011-217029 34
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

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

-10-20

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=0.029m

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.)pre.

X=0.038m

Fig. 25 Spray mean axial velocity distributions.

NASA/TM—2011-217029 35
Fig. 26 Spray mean radial velocity distributions.

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

0

40302010

X=0.009m

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

-5

50

201510

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

X=0.020m

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

NASA/TM—2011-217029 36
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=0.020m

Z, m

Tangential velocity, m/s

0 0.005 0.01 0.015 0.02 0.025 -5

50

1510 X=0.029m

Fig. 27 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

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

X=0.038m

NASA/TM—2011-217029 37
REPORT DOCUMENTATION PAGE Form Approved 

OMB No. 0704-0188 

The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the 

data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this 

burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. 

Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB 

control number. 

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 

1. REPORT DATE (DD-MM-YYYY)

01-03-2011 

2. REPORT TYPE

Technical Memorandum 

3. DATES COVERED (From - To)

4. TITLE AND SUBTITLE

Assessment of Some Atomization Models Used in Spray Calculations 

5a. CONTRACT NUMBER

NNC06BA07B 

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Raju, M., S.; Bulzan, Dan 

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

WBS 984754.02.07.03.19.02 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

John H. Glenn Research Center at Lewis Field 

Cleveland, Ohio 44135-3191 

8. PERFORMING ORGANIZATION

 REPORT NUMBER

E-17694 

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

Washington, DC 20546-0001 

10. SPONSORING/MONITOR'S

 ACRONYM(S)

NASA 

11. SPONSORING/MONITORING

 REPORT NUMBER

NASA/TM-2011-217029 

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified-Unlimited 

Subject Categories: 07, 20, 61, and 64 

Available electronically at http://www.sti.nasa.gov 

This publication is available from the NASA Center for AeroSpace Information, 443-757-5802

13. SUPPLEMENTARY NOTES

14. ABSTRACT

The paper presents the results from a validation study undertaken as a part of the NASA’s fundamental aeronautics initiative on high altitude 

emissions in order to assess the accuracy of several atomization models used in both non-superheat and superheat spray calculations. As a 

part of this investigation we have undertaken the validation based on four different cases to investigate the spray characteristics of (1) a 

flashing jet generated by the sudden release of pressurized R134A from cylindrical nozzle, (2) a liquid jet atomizing in a subsonic cross 

flow, (3) a Parker-Hannifin pressure swirl atomizer, and (4) a single-element Lean Direct Injector (LDI) combustor experiment. These cases 

were chosen because of their importance in some aerospace applications. The validation is based on some 3D and axisymmetric calculations 

involving both reacting and non-reacting sprays. In general, the predicted results provide reasonable agreement for both mean droplet sizes 

(D32) and average droplet velocities but mostly underestimate the droplets sizes in the inner radial region of a cylindrical jet.

15. SUBJECT TERMS

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

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF

 ABSTRACT

UU 

18. NUMBER

 OF 

 PAGES

42 

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email:help@sti.nasa.gov) 

a. REPORT

U 

b. ABSTRACT

U 

c. THIS 

PAGE

U 

19b. TELEPHONE NUMBER (include area code)

443-757-5802 

Standard Form 298 (Rev. 8-98)

Prescribed by ANSI Std. Z39-18