Experimentation and Modeling of Jet A Thermal Stability in a Heated Tube

hammercoupleMechanics

Feb 22, 2014 (3 years and 5 months ago)

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1

Experimentation and Modeling of Jet A

Thermal Stability in a Heated Tube

Julia W. Khodabandeh
*

NASA Marshall Space Flight Center, Huntsville, AL, 35812, US

Robert A. Frederick


The University of Alabama in Huntsville, Huntsville, AL, 35899, US

High perfor
mance aircraft typically use hydrocarbon fuel to regeneratively cool the airframe and engine
components. As the temperatures increase, the fuel may react with dissolved oxygen forming deposits that
limit the regenerative cooling system performance.

This s
tudy investigates the deposition of Jet A using a
thermal stability experiment and computational fluid dynamics (CFD) modeling. The experimental portion of
this study is performed with a high Reynolds number thermal stability (HiRets) tester in which fuel
passes
th
r
ough

an electrically heated tube while

the fuel outlet temperature is held constant. If the thermal stability
temperature of the fuel is exceeded, deposits form and adhere to the inside of the tube creating an insulating
layer between the tube an
d the fuel. The HiRets tester measures the tube outer wall temperatures near the
fuel outlet to report the effect of deposition occurring inside the tube. Final de
posits are also estimated with

carbon burn

off analysis. The CFD model i
s developed and use
d to simulate the fluid dynamics, heat
transfer, chemistry, and transport of the deposit precursors. The model is calibrated to the experiment
temperature results and carbon burn
-
off deposition results. The model results show that the dominant factor
in d
eposition is the heated wall temperature and that most of the deposits are formed in t
he laminar sublayer.
The model

predicted a 7.0E
-
6 kg/m
2
-
sec deposition rate, which compared well to the carbon burn
-
off analysis
deposition rate of 1.0E
-
6 kg/m
2
-
sec.


No
menclature

a

= order of reaction with respect to the fuel

A

= speed of a reaction

b

= order of reaction with respect to the oxidizer

Dep

= deposition rate

E

= activation energy

T
I

= turbulent intensity

K

= turbulent kinetic energy

R

= universal gas constant

S

= source term

T

= tempe
rature



= turbulent kinetic energy dissipation rate




= concentration

1

= reaction step number

2

= reaction step number

b

= bulk fuel reac
tion

f

= formation

w

= wall reaction




*
Aerospace Engineer, Mechanical & Thermal Analysis Branch of the Instrumentation & Payload Systems
Department, M/S EI13, Member AIAA.


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2

I.

Introduction

n high performance aircraft, heat transfer becomes a critical design element. Ram air is used extensively for
cooling aircraft components at subsonic veloci
ties. As aircraft operate near and above the sonic velocity,
aerodynamic heating increases, and the stagnation temperature of the air precludes its use as a coolant.
1

High
performance aircraft designs typically use regenerative cooling. In regenerative
cooling, fuel is circulated around
the airframe and engine components before being injected into the combustion chamber. Since the thermal energy
absorbed by the coolant is returned to the injector, regenerative cooling does not limit aircraft performance
. As the
coolant temperature increases, however, the fuel may react with dissolved oxygen forming deposits that block
cooling lines, valves, and filters as well as degrade injector performance. The cooling line deposits form a thermally
insulating layer
between the heated components and the coolant, degrading the performance of the regenerative
cooling system. The airframe a
nd component temperatures will

rise, potentially causing failure.

Thermal stability refers to a fuel’s ability to resist degradation

and deposit formation at elevated temperatures.
When the fuel reacts with dissolved oxygen at high temperatures, bulk insoluble materials, bulk soluble gums, and
surface reaction precursors are formed. The bulk insoluble materials can be transported to
surfaces by diffusion,
turbulence, or surface forces where they may deposit onto surfaces or be repelled back into the bulk flow.

1

In
addition, the bulk soluble gums may become insoluble and form surface deposits once the thermally stressed fuel
reaches
areas of cooler temperatures.
1

Currently, the mechanisms involved in fuel degradation are not fully
understood. Further understanding of these mechanisms is needed in order to determine the maximum heat transfer
a fuel can withstand in high performance a
ircraft design.

Many investigators have conducted jet fuel thermal stability experiments and analyses over the past 30 years.
The work of those investigators who identified fundamental deposition mechanisms is summarized below.


Marteney and Spadaccini of

United Technologies Research Center conducted tests in heated tubes at typical gas
turbine engine operating conditions in order to determine the effects of temperature, pressure, flowrate, and time on
air
-
saturated JP
-
5 thermal stability.
2

The investigat
ors concluded that the local surface temperature of the heated
tubes primarily effected deposit formation. The investigators also found significantly greater deposition in the
turbulent regime than in the laminar or transitional regime. In varying test d
uration, the investigators found that fuel
deposition rates progressively increased with increasing test duration. The most significant contribution made by
Marteney and Spadaccini was plotting the JP
-
5 deposition rate versus the inverse of the initial wa
ll temperature.
This allowed the decomposition process to be fitted to an Arrhenius expression given by












RT
E
A
S
f
exp
,

(1)

where
f
S

represents the formation rate of deposit precursors,
A

is a constan
t representing the speed of the reaction,
E

is the activation energy,
R

is the universal gas constant, and
T

is the fuel temperature.

Krazinski et al. of Aero Propulsion and Power Laborato
ry at Wright Paterson Air Force Base (AFB) developed a
computational fluid dynamics and chemistry (CFDC) model for predicting the thermal decomposition rates of JP
-
5
as measured in the electrically heated
-
tube experiments of Marteney and Spadaccini.
3

The
investigators
mathematically represented the formation, transport, and deposition of precursors by solving the precursor and
dissolved oxygen transport equations simultaneously with the conservation and turbulence equations. Three global
Arrhenius express
ions were used to model the deposition chemistry. The first expression represented the
homogeneous reaction in the bulk fuel, the second expression represented the heterogeneous wall
-
catalyzed reaction,
and the third reaction represented precursor decompos
ition and removal from the deposition process. The model’s
temperature predictions were in agreement with Marteney and Spadaccini’s test data. The model was also able to
predict the deposition rates for the heterogeneous wall
-
catalyzed reaction and the hom
ogeneous bulk fuel reaction.

Ervin and Williams of the University of Dayton Research Institute conducted heated tube experiments with JP
-
8
using a three
-
part heat exchanger.
1

Three copper blocks surrounded different sections of a 180 cm long

stainless
ste
el

tube creating three distinct isothermal regions. The first two blocks were electrically heated, the third block
was water
-
cooled, and the tubing between the blocks was insulated.

The results showed that deposition has a
greater dependence on the tube
wall temperatures than on the bulk fuel temperatures. Ervin and Williams believed
that the higher temperatures near the wall, together with the catalytic effects of the stainless steel, meant the fuel
oxidation rate would be greatest near the wall. Ervin,

Williams, and Katta developed a CFD model, which predicted
deposition by solving the species conservation, Navier
-
Stokes, and turbulent energy equations.
4

The investigators
used an eleven
-
step global kinetic model to simulate deposition in the tube secti
ons where each reaction is fitted to
an Arrhenius expression. The model results show a strong dependence of deposition on wall temperature suggesting
that the deposit initiation takes place at the tube inner surface.


I


3

Moses of Southwest Research Institute
developed a deposition test experiment called the Short High
-
Heat Flux
(SHiQ) rig in order to reproduce the thermal environment of fuel injectors.
5

When compared to the deposition
results of previous researchers, a significant difference of the SHiQ test
results is that the SHiQ deposition rates
decrease with increasing Reynolds number. In order to determine why this occurred, a turbulent analytical
deposition model was developed. In the model, SHiQ velocity and temperature profiles were developed as
fun
ctions of Reynolds number. An Arrhenius expression was then applied to the temperature profiles in order to
determine where in the tube the deposit precursors formed. Moses’ analysis showed that almost all of the deposit
precursors were formed in the lam
inar sublayer. Moses then used the local streamline velocity vector and diffusion
velocity vector to determine the deposit precursor trajectories and if the precursors reached the wall before exiting
the tube. Moses found that 95% of the precursors reache
d the wall before exiting the SHiQ heated section. He
concluded that increasing the flow velocity thins the laminar sublayer, bringing the temperature gradients closer to
the wall and reducing the amount of flow at the higher temperatures. This would red
uce the number of precursors
that were formed.
5


Zhou and Krishnan of CFD Research Corporation (CFDRC) incorporated a 9
-
step deposition model for Jet A
into their general purpose CFD code called CFD
-
ACE.

6

The investigators solved the Navier
-
Stokes equat
ions along
with the conservation of species and turbulent transport equations. The 9
-
step deposition model is based on the
work of Ervin, Williams, and Katta. Zhou and Krishnan compared their CFD model to Jet A heated tube experiment
data; however, the l
ocation and magnitude of the peak deposition and temperatures in the model were slightly
different than the experiment results.

From the literature, it is clear that deposition is pr
imarily effected by temperature

and

that

deposition has a
greater depe
ndence on the tube inner wall temperature than on the bulk fuel temperature. Deposition is also found
to be greatest for turbulent flow and to increase progressively with test duration. Marteney and Spadaccini’s
contribution of fitting deposition to an A
rrhenius expression has become the basis for several global kinetic models.
Investigators have developed these models with various numbers of reaction steps in an attempt to reproduce
deposition results seen in heated tube testing.

None of the above
-
ment
ioned testing or modeling appears to evaluate the fundamental interactions of the
deposition mechanisms. Moses analytically evaluated the interactions of the flow, heat transfer, and transport
mechanisms; however, varying tube wall temperatures and chemis
try were not considered. To this end, the current
work follows similar processes employed by Moses with the addition of varying wall temperatures. Furthermore, a
CFD model was developed following the work of Krazinski et al. and Zhou and Krishnan. The C
FD model solves
all the deposition mechanisms simultaneously, including chemistry.


II.

Approach



The current modeling effort investigates the basic flow, heat transfer, chemistry, and transport mechanisms
involved in fuel deposition. The modeling is based on

an experimental study conducted in a High Reynolds Number
Thermal Stability (HiReTS) rig and subsequent carbon burn
-
off analysis. The HiReTS condition
s have been
modeled numerically

and

compared to

carbon burn
-
off
analysis
results.


The University of Alab
ama in Huntsville (UAH) is using the HiReTS rig to test the thermal stability of Jet A
fuel.

7

The HiReTS rig was originally developed by Shell Research Limited to evaluate the thermal stability of jet
fuel under realistic test conditions. Previously, the
rmal stability testing was limited to the Jet Fuel Thermal
Oxidation Tester (JFTOT) and large
-
scale test rigs. The main disadvantage of the JFTOT is that it operates in the
laminar flow regime
. Large
-
scale test rigs operate in the turbulent flow regime;
however, they require large amounts
of fuel and long test durations.
8


During a HiReTS test, fuel is pumped at pressure from a sample vessel through an electrically heated, vertical
capillary tube. As seen in Figure 1, the 316 stainless steel capillary tu
be has a length of 15.2 cm, a nominal outer
diameter of 0.16 cm, and a nominal inner diameter of 0.03 cm. The electrical heating of the tube is controlled such
that a constant fuel exit temperature is maintained for the duration of a test. If the fuel is
unstable at the HiReTS
operating conditions, it will begin to decompose producing soluble gums and insoluble solids that can deposit on the
capillary tube inner walls. These deposits produce a thermally insulating layer, which inhibits heat transfer from t
he
capillary tube to the fuel. As deposits form on the inner surface of the capillary tube, more power is required to
maintain the fuel outlet temperature causing the capillary tube temperatures to rise. A scanning pyrometer measures
the temperature rise

in the capillary tube as a function of time over a fixed length of tube. A proprietary blackened
finish coats the outside of the capillary tube in order to achieve a high emissivity for increased scanning pyrometer
accuracy. The HiReTS standard operating

conditions (SOC) include a constant fuel outlet temperature of 563 K, a

4

nominal flow rate of 0.583 cm
3
/sec, and test duration of 125 minutes. The average Reynolds number for Jet A fuel
under HiReTS SOC is 6781.

The data output from the HiReTS rig include
s capillary tube temperature as a function of time at 12 axial
locations spaced 0.025 cm apart, maximum and minimum system pressure, fuel mass flow rate, temperature of the
fuel in the sample vessel, and temperature of the fuel at the capillary tube exit.

The scanning pyrometer takes its
first temperature measurement 1mm below the top bus bar as indicted in Fig. 1. The pyrometer then moves 0.025
cm downward and takes the second temperature measurement. The pyrometer continues scanning temperatures in
thi
s manner until all twelve axial locations have been recorded, at which time the pyrometer begins again 1mm
below the top bus bar. The time lapse between temperature measurements at the same axial location is
approximately 5 minutes for 12 measurement loca
tions.








Carbon makes up 70
-
80% of the fuel decomposition deposit material, and carbon burn
-
off analysis can be used
to determine deposit mass and location.
8

Shell Research Limited has been able to correlate the HiReTS te
st
temperatures with carbon burn
-
analysis.

8

Carbon burn
-
off analysis was therefore performed on the UAH HiReTS
capillary tubes in order to calibrate the deposition models.

After a HiReTS experiment is run, the exterior emissivity coating and any interior

fuel residuals are removed
from the capillary tube. The tube is then cut into four sections of equal length. Each tube section is placed in the
high temperature furnace of a Leco Carbon Analyzer. An oxygen supply is fed to the tube such that it reacts wit
h the
fuel deposits at the high temperatures. The Leco Carbon Analyzer then measures the amount of evolved carbon
dioxide. The mass of carbon in the deposits can be calculated from these carbon dioxide measurements.

The purpose of the modeling effort is t
o understand fuel deposition; however, several unknowns exist in the
HiReTS experiments, which need to be addressed before the deposition event can be evaluated. To this end, a 2
-
D
axisymmetric heat transfer model of the HiReTS capillary tube and test con
ditions was developed to determine the
heat transfer characteristics of the system. The unknowns to be solved with this model include the electrical heating
power input to the system, the system losses, the fuel temperature at the inlet of the capillary t
ube, and the overall
deposit thermal resistance. These parameters were
used as boundary conditions in the CFD model
.

The only fuel temperature calculated in the heat transfer model was the bulk fuel temperature. In order to
understand the deposition proc
ess, additional information is needed regarding the flow and heat transfer
mechanisms. An analytical model was therefore developed for the HiReTS turbulent flow regime. The von Karman
relations for hydrodynamically developed flow were used to define the
non
-
dimensional velocity in terms of the
non
-
dimensional distance from the wall. Martinelli of Berkeley University developed expressions for the



Figure 1. HiReTS capillary tube.


5

temperature distribution as a function of tube radius for turbulent flow in cylindrical tubes.
9

These express
ions were
used to determine the temperature distribution within the fuel. Finally, the effects on fuel deposit precursor
formation and transport were also predicted using a method similar to Moses. The findings from the analytical
model were used as bound
ary conditions in

the CFD models
.

A CFD model was developed to evaluate the coupling between fluid flow, heat transfer, chemistry, and transport
processes involved in fuel deposition. The grid generator used to develop this model was CFDRC’s CDF
-
GEOM.
Si
nce deposition was assumed to only occur in the area of the scanning pyrometer, only the last 7.6 cm of the
HiReTS capillary tube were modeled. A 2
-
D axisymmetric model was developed, with the line of symmetry
positioned at the centerline of the flow. Th
e tube is modeled as a solid volume, and the fuel inside the tube is
modeled as a liquid volume. The tube inner radius is modeled as a solid/liquid volume interface in areas where no
deposits are present. The deposit geometry and location identified in th
e heat transfer model are also incorporated
into the CFD model. The deposit is modeled as a solid. The outer deposit surface is modeled as a solid/solid
interface with the tube, and the inner surfaces are modeled as solid/liquid interfaces with the fuel.

The capillary tube
model is divided into 801 axial elements and 46 radial elements, with the radial elements clustered at the solid/liquid
interfaces.

The solver used for the CFD model was CFDRC’s CFD
-
ACE+. CFD
-
ACE+ uses the pressure
-
based
formulation o
f the Navier
-
Stokes system of equations, appropriate for incompressible flows, to solve for the solution
domain primitive variables. The solution domain is divided into control volumes according to the grid defined in
CFD
-
GEOM, and the governing equations
are numerically integrated over each control volume. Finite difference
equations are formulated for each control volume cell, and an iterative solution method is used to sequentially solve
the equation sets for each primitive variable.

For the HiReTS CFD

model, the flow, turbulence, heat transfer, and chemistry modules were activated in CFD
-
ACE+. The assumptions for the flow module include incompressible, viscous, fully developed flow. The velocity
profile obtained in the analytical model was included in

the CFD model as a fixed flow inlet boundary condition. A
zero pressure gradient condition was assumed at the flow outlet. The wall interface is modeled as a no slip condition,
such that the velocity of the fluid at the wall is zero. The assumptions for t
he turbulence module include a turbulent
intensity (
T
I
) of 2%, an inlet free stream kinetic energy (
K
) calculated to be 0.1 m
2
/sec
2
, and an inlet dissipation
rate (

) calculated to be 52.2 J/
kg
-
sec. The standard
K
-


model was used to formulate the turbulent flow
transport equations. The boundary conditions for the heat transfer module include adiabatic tube ends, a constant
fuel inlet temperature,
and a uniform heat flux applied to the outer diameter of the tube. The values of the fuel inlet
temperature and the applied heat flux are those determined from the heat transfer model.

A global kinetic model based on the work of Krazinski et al. and Zhou
and Krishnan was incorporated into the
CFD
-
ACE+ gas
-
phase chemistry module. The gas
-
phase chemistry was activated rather than the liquid
-
phase
chemistry because liquid
-
phase chemistry assumes a dilute solution, which is not the case in this application.
F
urthermore, the production of deposit precursor species is not accounted for in the mass balance for liquid
-
phase
chemistry. A constant Schmidt number of 0.7 was assumed for the mass diffusion. A mixture representing air
-
saturated Jet A fuel was defined
in which a baseline oxygen concentration of 50 wppm was used for the inlet oxygen
concentration.
2

This represents an oxygen mass fraction of 5.0E
-
5. The resulting mass fraction of Jet A is then
0.99995.

The first step in Krazinski’s model is the homog
eneous bulk fuel reaction. This reaction was included in the
chemistry module as a volume reaction. The stoichiometric equation is given by




O
H
C
O
H
C
2
2
26
12
13
12
5
.
6




,

(2)

where the hydrocarbon fuel species,
26
12
H
C
, represents an n
-
dodeca
ne particle, which is similar to an aviation fuel
particle. The volume reaction source term,
1
f
S
, is given by








1
1
2
26
12
1
1
1
exp
b
b
b
a
b
b
f
O
H
C
RT
E
A
S









,

(3)

where
1
b
A

is the pre
-
exponential constant for the bulk reaction,
1
b
E

is the activation energy for the bulk reaction,
R

is the universal gas constant,
T

is the fuel temperature,


26
12
H
C

is the fuel concentration,


2
O

is the oxyge
n
concentration,
1
b
a

is the order of the reaction with respect to the fuel, and
1
b
b

is the order of the reaction with respect
to the oxidizer. The parameters
sec
10
5
.
2
3
1


m
kmol
E
A
b
,
K
R
E
b
16112
/
1

,
1
1

b
a
, and
0
1

b
b

were defined for
the Jet A bulk fuel reaction as was done by Zhou and Krishnan. Zhou and Krishnan identified a second step for the

6

formation of deposit precursors in the bulk fuel. In the CFD model, the stoic
hiometric equation used to represent
this second step is




1
C
C

,

(4)

and the corresponding volume reaction source term,
2
f
S
, is






2
2
2
2
exp
b
a
b
b
f
C
RT
E
A
S









.

(5)

sec
5
0
.
8
2
E
A
b

,
K
R
E
b
7553
/
2

, and
1
2

b
a

were used for the Jet A bulk fuel reaction.
4

The product in Eq. (4),


1
C
, represents energized deposit precursors.

The tube wall surface reaction is also represented by two global reaction steps, which are includ
ed in the model
as boundary conditions. The first reaction represents the deposition of the bulk fuel deposit precursors onto the tube
wall. This reaction is represented by the equation






B
C
C

1


(6)

and the deposition rate,
1
Dep
, is defined by






1
)
1
(
exp
1
1
1
w
a
w
w
C
RT
E
A
Dep









.

(7)

In Eq. (7),
1
w
A

is the pre
-
exponential constant for deposition,
1
w
E

is the activation energy for deposition,


)
1
(
C

is
the deposit precursor c
oncentration, and
1
w
a

is the order of the reaction with respect to the deposit precursors. The
parameters
sec
40
1
m
A
w

,
K
R
E
w
8560
/
1

, and
1

w
a

were defined for the Jet A deposition as was done b
y Zhou
and Kr
ishnan. The product in Eq.

(
6
)

represents wall deposits where


B
C

is the bulk species. The species that are
consumed in the surface reaction are converted to the bulk species, and this represents deposition. The second s
tep
in the surface reaction is the heterogeneous wall
-
catalyzed reaction. This reaction is represented by the equation


O
H
B
C
O
H
C
2
2
26
12
13
)
(
12
5
.
6





(8)

and the deposition rate,
2
Dep
, given by








2
2
2
26
12
2
2
2
exp
w
w
b
a
w
w
O
H
C
RT
E
A
Dep









.

(9)

The parameters
sec
5
0
.
2
2
m
E
A
w


,
K
R
E
w
4022
/
2

,
1
2

w
a
, and
0
2

w
b

were defined for the Jet A deposition.
4



B
C

in Eq. (8) again represents wall deposits.


In order to demonstrate the integrity of the

CFD model’s mesh, a test case was developed in which the original
mesh was increased by a factor of 1.5 in the axial and radial directions.

III.

Results and Discussion

The modeling effort is based on a test run in the UAH HiReTS rig under SOC. The temperatu
re profiles from
the scanning pyrometer are shown in Fig. 2. As seen in the figure, the tube outer wall temperatures begin relatively
cool at the initial 5 minute pass of the scanning pyrometer. The temperatures of the outer tube wall actually drop
initi
ally before beginning to increase.


The cause of this is not known; however, it is thought that this temperature
drop may be associated with the onset of fuel decomposition. At 20 minutes, the tube temperatures begin to rise
again and continue to rise as
deposits buildup on the inside of the tube forming an insulating layer between the tube
and the fuel. Peak tube temperatures are realized at the final pyrometer scan of 125 minutes. Note that at 15, 20,
and 85 minutes, the temperatures drop axially at 9.
7 and 10.0 cm. The cause of this drop is assumed instrumentation
related and not related to the deposition event. Note also that, throughout the test, the temperatures between 10.8
and 11.0 cm are cooler than the adjacent wall temperatures. This cooling
is caused by a heat leak from the capillary
tube to the top bus bar at its attachment point.

The assumption that all deposition occurred within the axial range of the scanning pyrometer can be justified by
evaluating the temperature profiles versus time in

Fig. 2. As seen in the figure, the temperatures at 9.2 cm only
diverge about 9 K while the peak temperatures at 12.4 cm diverge approximately 90 K. Since temperature increase
is associated with deposits forming at the walls, it can be postulated that mi
nimal deposits are formed upstream of
9.2 cm. As the temperatures diverge with time in the axial direction, the deposit buildup is increasing with peak
deposition corresponding to peak temperature divergence at 12.3 cm.



7






T
he capillary tube from the UAH HiReTS test was sent along with several clean tubes to the University of
Dayton Research Institute for carbon burn
-
off analysis. The capillary tube was cut into four equivalent sections.
The mass of carbon was measured in e
ach tube section. The average value of carbon was also measured for the clean
tubes. Tube Sections 1
-
3 represent the capillary tube upstream of the scanning pyrometer measurements. The carbon
mass values for Sections

1
-
3 are 12
-
15 μg. The average measurement for the clean tubes is 14 μg. Sections 1
-
3 are,
therefore, considered to represent an insignificant amount of carbon mass. Tube Section 4 includes the portion of
capillary tube traversed by the scanning pyrometer.

The carbon mass in this section is 114 μg. This is significant in
comparison with Sections 1
-
3, further justifying the assumption that all deposition occurs within the range of the
scanning pyrometer.


In order to determine the HiReTS capillary tube heat

flux, fuel inlet temperature, and top bus bar heat leak, the
clean tube model was analyzed with respect to the initial HiReTS experiment tube temperature and fuel exit
temperature.

In order to determine the HiReTS capillary tube deposit resistivity and
the corresponding increase in
tube heat flux, the deposition model was analyzed with respect to the final HiReTS experiment tube temperatures
and the carbon burn
-
off analysis results. The same fuel inlet temperature and top bus bar heat leak determined in

the
clean tube model were applied to the deposition model. The mass of the deposit determined in the carbon burn
-
off
analysis was adjusted to remove the clean tube average. The resulting mass for tube Section 4 is 100 μg. The
HiReTS experiment temperat
ure profiles provide information on the deposit geometry, which is incorporated into
the heat transfer model. As mentioned previously, the temperature increase of the tube outer wall is assumed
attributable to the deposition process. Since the temperatur
es diverge axially with time with peak divergence
occurring at 12.3 cm, it is assumed that the cross
-
sectional geometry of the deposit is triangular.
The test and model
tube temperatures along with the deposit profile are shown in Fig. 3.

In order to comp
are the CFD model to the heat transfer model and analytical model trends, the chemistry module
was initially left inactive while the flow, turbulence, and heat transfer modules were activated. The axial velocity
component for the last 7.6 cm of clean tube

is shown in Fig. 4. The thermal effects on the flow field are apparent in
Fig. 4 as the velocity increases with increasing temperature and decreasing fuel viscosity. The maximum velocity is
approximately 18 m/sec, and the greatest velocity variation occ
urs in the laminar sublayer and buffer layer.

The temperature profiles from the CFD model are shown in Fig. 5 for the last 7.6 cm of clean tube. When
compared to the HiReTS experiment tube temperatures, the CFD model produces a similar linear profile for
the
outer diameter of the tube, predicting both the top bus bar heat leak and the fuel outlet temperature. In comparison
to the analytical fuel temperatures, similar results are found in that the highest fuel temperatures and steepest
temperature gradient
s occur close to the wall. The radial temperature gradient within the turbulent core; however, is
more pronounced in the CFD model than in the analytical model. This difference is attributable to the fact that the
fuel thermophysical properties varied with

temperature in the CFD model whereas they were based on the average
bulk fuel temperature in the analytical model.



560
580
600
620
640
660
680
700
720
740
9.4
9.9
10.4
10.9
11.4
11.9
12.4
Axial Location, cm
Temperature, K
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
110
115
120
125
Elapsed Time, min
Final temperature readings
Flow Direction
Initial temperature readings

Figure 2. UAH HiReTS SOC test scanning pyrometer results.


8


























The integrity of the CFD model’s mesh was evaluated using a test case in which th
e original mesh was increased
by a factor of 1.5 in the axial and radial directions. The velocity profiles gave the same result as the original mesh
with only a slight increase in the velocity magnitud
es. A more notable difference wa
s seen in the tempera
ture
results with the increased mesh reducing the temperature gradients within the tube. The increased mesh tube
temperatures differ by approximately 3% of the original mesh values. Comparison of the total heat imbalance for
the two mesh cases showed tha
t the imbalance is slightly less for the 1.5x mesh, indicating better convergence. The
total heat imbalance for both cases is well within the acceptable convergence range, and therefore, the original mesh
is considered adequate.



*

The radial dimension is shown scaled by a factor of 70 for visual clarity.

Figure 4. Fuel’s axial velocity component for a clean t
ube.


0
0.0003
0.0006
0.0009
0.0012
0.0015
0.0018
0.0021
0.0024
0.0027
9
9.5
10
10.5
11
11.5
12
12.5
13
Axial Location, cm
Deposit Thickness, cm
300
350
400
450
500
550
600
650
700
750
Tube Outer Wall Temperature, K
Deposit Thickness
Final Tube Wall Temperatures - Test
Final Tube Wall Temperature - Model
Initial Tube Wall Temperature - Test
Initial Tube Wall Temperatures - Model


Figure 3. Predicted temperatures and deposit thickness compared to HiReTS test results.


9




The final deposition configuration determined from the heat transfer model was also added to the original CFD
model in order to evaluate the deposit’s effect on the flow field and the temperature profiles. The axial velocity
component for the last 7.
6 cm of tube wi
th deposition is shown in Fig. 6
. As seen in the figure, the deposit presence
alters the flow field such that the axial velocity increases as the flow passes through the progressively restrictive
deposit region. The maximum velocity occurs

at the point of peak deposition with a magnitude of 22.5 m/sec. Just
downstream of the deposit region, the velocity decreases as the cross
-
sectional area is increased.


The temperature profiles from the deposition CFD model are shown in F
ig. 7

for the l
ast 7.6 cm of tube. When
compared to the HiReTS experiment results, the CFD model peak temperatures are approximately 57 K higher than
the experiment temperatures. The CFD model is able to predict the experiment fuel outlet temperature. When
compared to
the heat transfer model temperatures, agreement is found in the tube wall outside of the deposition
region and in the fuel. Since the capillary tube is stainless steel, which is a relatively poor conductor, it is possible
that peak temperatures are not ca
ptured by the twelve HiReTS experiment instrumentation locations. Furthermore,
the coarser mesh used in the heat transfer model would result in averaging of the temperatures, lowering peak
values.




*

The radial dimension is sh
own scaled by a factor of 70 for visual clarity.

Figure 6. Fuel’s axial velocity component for d
eposition.




*

The radial dimension is shown scaled by a factor of 70 for visual clarity.

Figure 5.

Tube and fuel temperatures for a clean t
ube.




10




The chemistry module was activated in the original CFD model to evaluate the coupling between flow, heat
transfer, chemistry and transport processes during fuel decomposition and deposition. The reaction rate for the first
step of the bulk fuel volu
m
e reaction is shown in Fig. 8
. The reaction rate for the second step of the bulk fuel
vo
lume reaction is shown in Fig. 9
. These reaction steps are in series with the final products including

the deposit
precursors. Fig. 8 and 9

show that the volume reacti
on rate occurs for a fuel temperature of 540 K and above. This
result is in line with Marteney and Spadaccini’s findings.






*

The radial dimension is shown scaled by a factor of 70 for visual clarity.

Figure 8. Reaction rate for first step of volume r
eaction.




*

The radial dimension is shown scaled by a factor of 70 for visual clarity.

Figure 7. Tube and fuel t
empera
ture profiles for d
eposition.




11


The deposition rate for the surface reaction is shown in Fig.

10
. The s
urface reaction includes 1) deposition due
to transport of the bulk fuel deposit precursors to the wall and 2) deposition due to a wall
-
cataly
zed reaction. As
seen in Fig. 10
, deposition occurs along the entire 7.6 cm length of tube, gradually increasing
towards the tube exit.
Sin
ce the volume reaction in Fig. 8 and 9

only occurs near the tube exit, any deposition upstream of the volume
reaction is a result of the

wall
-
catalyzed reaction only.

Recall from the heat transfer model that deposition was
assume
d to only occur within the area of the scanning pyrometer temperature measurements. It was assumed that
little if any deposition occurs upstream of the scanning pyrometer measurements; however, no regard was given to
potential deposition downstream of the

top bus bar. Without additional temperature data for the end of the capillary
tube or higher fidelity carbon mass analysis, there is no indication as to whether deposition may have been present in
this area. Considering the deposition locatio
n assumed i
n Fig. 7
, a final deposit mass of 100 μg, and test duration of
125 min, the corresponding deposition rate would be approximately 1.0E
-
6 kg/m
2
-
sec. The deposition rate at the
same location in the CFD model is approximately 7.0E
-
6 kg/m
2
-
sec. The wall
-
cataly
zed reaction rate which Zhou
and Krishnan used for Jet A may be too high for this particular HiReTS experiment. It is also possible that the
difference in composition between Jet A and n
-
dodecane is a factor in the deposition rate differences.



*

The radial dimension is shown scaled by a factor of 350 for visual clarity.

Figure 10. Deposition rate from bulk fuel reaction and wall
-
catalyzed r
eaction.




*

The radial dimension is shown scaled by a factor of 70 for visual clarity.

Fig
ure 9. Reaction rate for second step

of volume r
eaction.




12

IV.

Conclusion

The rate at which fuel deposition occurs in aircraft jet engine cooling tubes is driven by many factors. An
understanding of the fundamental deposition mechanisms and their interactions is needed in order to determine the
maxi
mum heat transfer a fuel can withstand in high performance aircraft. This study investigates the flow, heat
transfer, chemistry, and transport mechanisms involved in fuel deposition through analytical and numerical
modeling. The modeling effort is based
on an experimental study conducted in UAH’s HiReTS rig in which Jet A
was tested under SOC. Carbon burn
-
off analysis performed on the resulting deposits indicated that most the
deposition occurred near the exit of the capillary tube where the temperatures

were the hottest. An insignificant
amount of deposition was found in the cooler upstream sections of the tube.

A heat transfer model was developed of the HiReTS rig in order to better understand the HiReTS boundary
conditions and to predict the deposit p
roperties and configuration. An analytical model was developed in order to
understand the effects of turbulence on the fuel flow field and temperature distribution. The effects on fuel deposit
precursor formation and transport were also investigated.
A

CF
D model was developed for the exit
-
half of the
capillary tube to evaluate the coupling between fluid flow, heat transfer, chemistry, and transport processes. The
model was anchored by recreating the conditions of the previous heat transfer and analytical
models and comparing
the results. Bulk fuel reactions and surface reactions were then included in the CFD model in order to predict
deposition. The CFD model predicted that wall
-
catalyzed deposition occurred over the entire 7.6 cm length of tube
with depos
ition due to the bulk fuel reaction occurring only near the tube exit. Comparing the CFD model
deposition rates to the carbon burn
-
off analysis deposition rate estimate, it is found that the rates differ by a factor of
seven. It is possible that the wall
-
catalyzed reaction rate is too high in the CFD model or that the difference in
composition between Jet A and n
-
dodecane is a factor.

The models can be used as a tool to evaluate future HiReTS experiment results under various operating
conditions. The pr
ocess followed in this study for identifying the HiReTS boundary conditions, flow and
temperature profiles, and deposition rate and configuration can be applied. Although the fundamental deposition
mechanisms should remain constant from experiment to expe
riment, there are several additional parameters which
may effect fuel deposition experiment results. These include tube surface roughness, fuel batch variations, and
possible contaminants. Due to the difficulty involved in identifying the contribution of
such parameters, they should
be eliminated whenever

possible.



Acknowledgments

This study is sponsored in part by Grant NCC8
-
200 through NASA Marshall Space Flight Center.

The authors would like to thank Dr. Kader Frendi and Dr. Brian Landrum of UAH for
providing guidance and
support throughout the development of this study. The authors would also like to thank Ms. Sarah Brown and Ms.
Jessica Emens of UAH for providing the experimental data used in this study and Dr. Steven Zabarnick of the
University of

Dayton Research Institute for providing the carbon burn
-
off analysis results. Thanks to Tim Edwards
for supplying the fuels used in these tests. Jordan Farina and Tony Hall of UAH are acknowledged for laboratory
setup and assistance. Thanks to Dr. Cliff

Moses of SwRI for providing guidance with the analytical effort. Lastly,
thanks to Mr. William Kuykendall of ESI for providing assistance with developing the CFD
-
ACE+ models.


References

1
Ervin, J. S., and Williams, T. F., “Dissolved Oxygen Concentrati
on and Jet Fuel Deposition,”
Industrial and
Engineering Chemistry Research
, Vol. 35, 1996, pp. 899
-
904.

2
Marteney, P. J., and Spadaccini, L. J., “Thermal Decomposition of Aircraft Fuel,”
Transactions of the ASME
,
Vol. 108, October 1986.


3
Krazinski, J. L
., Vanka, S. P., Pearce, J. A., and Roquemore, W. M., “A Computational Fluid Dynamics and
Chemistry Model for Jet Fuel Thermal Stability,”
Transactions of the ASME
, Vol. 114, January 1992.

4
Ervin, J. S., and Williams, T. F., “Global Kinetic Modeling of Av
iation Fuel Fouling in Cooled Regions in a
Flowing System,”
Industrial and Engineering Chemistry Research
, Vol. 35, 1996, pp. 4028
-
4036.


5
Moses, C. A., “A Study of Reynolds Number Effects on Deposit
-
Forming Mechanisms in Fuel Systems for
Advanced Gas Tur
bine Combustors,” Final Report SwRI Project 03
-
2978, May 2001 (unpublished).


6
Zhou, N., and Krishnan, A., “Numerical Simulation of Jet Fuel Heat Transfer and Deposition at Supercritical
Pressure,” AIAA
-
1997
-
3042, July 1997.


13


7
Emens, J.M., Brown, S.P., F
redrick, R.A., Jr., and A.J. Wood,

“High Reynolds Number Thermal Stability
Experiments, AIAA Paper 2004
-
4089, July 2004.



8
Bauldreay, J. M., Heins, R. J., Houlbrook, G., and Smith, J., “High Reynolds Number Thermal Stability
(HiReTS) Rig for Realistic,
Rapid Evaluation of Distillate Fuel Thermal Oxidative Stability,”
6
th

International
Conference on Stability and Handling of Liquid Fuels
, October 1997.


9
Martinelli, R. C., “Heat Transfer to Molten Metals,”
Transactions of the ASME
, Vol. 69, November 1947
.