477
NOMENCLATURE
RANS Reynolds‐averagedNavier‐stokesequation
FANS Favre‐averagedNavier‐stokesequation
SST Shearstresstransport
Re
nz NozzleexitReynoldsnumber
U
in Nozzleinletvelocity(m/s)
v
i Velocitycomponents(m/s)
pPressure(Pa)
τ
ijTotalstresstensor(m
2
/s
2
)
e
0Totalenergy(J/s)
Φ Cumulativemassentrainmentratio
ĸLocalmassentrainmentratio
ψNormalizedtemperaturedistribution
C
p Coefficientofstaticpressure
y
+
Non‐dimensionalwalldistance
ρDensityofair(kg/m
3
)
μDynamicviscosity(m
2
/s)
μ
tTurbulentviscosity(m
2
/s)
λThermalconductivity(W/mK)
λ
tTurbulentthermalconductivity(W/mK)
kTurbulentkineticenergy(m
2
/s
‐2
)
ωSpecificturbulentdissipationrate(s
‐1
)
TLocaltemperature(K)
T
0 Ambienttemperature(K)
T
g Gasturbineexittemperature(K)
Superscript
Study of Inline-slot Ejector Diffuser Under Varying
Ambient Conditions: A Passive Infrared Suppression
Device for Ships
L.Singh,S.N.Singh&S.S.Sinha
IndianInstituteofTechnologyDelhi,NewDelhi,India
ABSTRACT:Passiveinfrared(IR)suppressiondevice,commonlyknownasejectordiffuser,isanintegralpart
ofthedefencesystem ofa ship.The definitiverole ofpassive IRsuppressor to counter the IR tracking and
lockingoftheshiphasmadethemindispensable
foranycombatmarine.Thegasturbineexhaustgasesarethe
leading heat source on a ship. The exhaust temperature of the gases ranges between 650K‐850K. At such
temperatures,theshipcanbeeasilydetectedbytheenemythroughIRimaging.Theroleoftheejectordiffuser
isto
(i)lowerthegasturbineexhaustgasestemperaturetothelimits(<450K)suchthattheIRlockingofthe
marinecanbeavoided,and(ii)recoverstaticpressuresuchthattheengineperformanceofthegasturbineis
notaffected.Ejectordiffuserhastheabilitytoentrainambientairand
allowmixingitwiththeexhaustgases
thereby, lowering the temperature of the exhaust gases. However, the mixed exhaust gases temperature
dependsontheambientairtemperaturewhichunderextremeconditionscanfluctuatefrom273Kto323K.This
temperature range can affect the temperature characteristics of an ejector diffuser. The
present study
undertakesthe effect ofambienttemperature ontheperformance ofinline‐slotejector diffuser.Theambient
temperature(T0)hasbeenvariedintherange273K≤T0≤323Kinthestepof10K.Ithasbeenfoundthatthe
mass entrainment increases (≈ 8%) as the ambient temperature decreases. The
core temperature at the exit
decreases, from 457.58 K to 417.75K, with a decrease in the ambient temperature. However, no significant
changesinstaticpressurerecovery.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 14
Number 2
June 2020
DOI:10.12716/1001.14.02.28
478
˜Favre‐averagedquantity
̄Reynolds‐averagedquantity
1 INTRODUCTION
Theshipmovement,tracking,andmissilelockingby
the enemy is often achieved by the use of infrared
scanning.Thehotspotspresentontheshipstructure
and exhaust gases acts as the source to infrared
scanning.Thus,thesurvivability
ofshipwilldepend
uponsuccessfuldodgingtheenemysurveillance.This
is achieved through the deployment of infrared
suppression system (IRSS) which boost the stealth
capabilities of a ship. The passive IRSS helps in
reducingtheexhaustgasestemperaturesuchthatthe
IRsignaturesarecurtailed.ThepassiveIRSSdevice
is
commonlyknownasejectordiffuser,andisinstalled
atthedownstreamofthegasturbineengine[1].The
aim of ejectordiffuser is to entrain coldambient air
andmixitwiththehotexhaustgasesbeforetheyare
emitted in the environment. Figure 1 shows the
schematic of the
ejector diffuser along with its
components (i) nozzle, (ii) mixing tube, and (iii)
slotteddiffuser.ThepopularityandincreaseuseofIR
guided missiles over other (acoustics, laser, visual,
radar) missiles [2] requires deeper understanding of
passiveIRSSdeviceunderallvaryingconditions.
Ejector diffuser being used in the combat
ships
(confidential), little information is available in open
literature. Sen [3] conducted study on the conical
steppedejectordiffuserandinvestigatedtheeffectof
various geometrical parameters such as length of
overlap at step slots, diffuser wall thickness, and
inclined slot openings. While the length of overlap
does not offer any
gain in diffuser performance,
increase in wall thickness adversely affects the
performance. Singh et al. [4] studied square shaped
step ejector diffuser and reported drop in mass
entrainment by 26% for wide angle diffuser. In
another article [5], effect of number of slots on the
performance was reported wherein increase
in slot
numbersdoesnotofferanygaininmassentrainment
although results in marginal increase in static
pressure recovery. Chen et al. [6] studied oblong
shaped ejector diffuser and observed better
performance than conical ejector diffuser under
moderate swirl conditions. A concept of inline‐slot
wasintroducedbySinghet
al.[7]tounderstandthe
mass entrainment characteristics of a conical ejector
diffuserwherebettermassentrainmentandpressure
recoveryisachieved.
Figure1.Typicalejectordiffuseranditscomponents.
Inthe presentinvestigation,the effectof ambient
temperatureontheperformanceofinline‐slotejector
diffuser is studied. As the ambient temperature
fluctuates over the year and also with location, the
systematicstudy of theambient temperaturechange
on the ejector diffuser performance needs to be
investigated. Under extreme
ambient conditions, the
temperature can fluctuate upto 50K. Hence the
performance of ejector diffuser under varying
ambienttemperatureisanimportantstudy.
2 PROBLEMFORMULATION
The numerical approach has been adopted to study
theeffectofambientconditionsontheperformanceof
inline‐slot ejector diffuser. The gas turbine exhaust
gases
temperature is fixed at 700K, thus nozzle exit
massflowrateremainssameinallthecases.Further,
the ambient temperature is varied in the range of
273K≤T0≤323K in steps of 10K. The cases for the
presentinvestigationareshowninTable1.
Table1.Casesforthecurrentinvestigation
_______________________________________________
CaseAmbientTemperature
_______________________________________________
CaseA273K
CaseB283K
CaseC293K
CaseD303K
CaseE313K
CaseF323K
_______________________________________________
All other geometric details, boundary conditions,
and dynamical parameters between the cases are
same.
Atwo‐dimensionalaxisymmetricdomainhasbeen
adopted to carry out the numerical study. Figure 2
shows the computational domain, boundary
conditions, and the labels for all important
dimensions. The labels along with their values
are
explained in Table 2. The computational domain
consists of nozzle, mixing tube, inline‐slot diffuser,
tailpipe, and the plenum surrounding the ejector
diffuser.Thedimensionsoftheplenum,adoptedfrom
the literature [6], are sufficiently large so that the
imposed boundary conditions at the plenum has
minimal interference with the
flow characteristics of
ejector diffuser. In the present study, the ambient
479
temperature value is assigned at the plenum
boundaries.Theotherimportantboundarycondition
isspecifiedattheinletofthenozzle,aportionofthe
left boundary, where a fixed velocity (Re
nz=5.0× 10
4
)
and temperature (700K) are specified. Re
nz is
calculatedfortheflowconditionsat700KU
in=60m/s,
ρ
in=0.505kg/m
3
,μin=3.3889552e
‐5
kg/m‐s.Theboundary
conditions at the wall of the ejector diffuser are no‐
slipfor flow variables andthermal coupled wall for
theheattransfervariable.
Figure2.Computationaldomainandboundaryconditions.
Table2.Dimensionofejectordiffuser
_______________________________________________
Name DescriptionValue
_______________________________________________
Dnz nozzleexitdiameter50mm
L
nznozzlelength1Dnz[4]
L
sd standoffdistance2.25Dnz[8]
D
mx mixingtubediameter 2.25 Dnz[8]
L
mx mixingtubelength8Dnz[8]
L
df lengthofdiffuser11Dnz[3.4]
L
tp lengthoftailpipe4Dnz[3,4]
L
pl lengthofplenum65Dnz[6]
D
pldiameterofplenum21Dnz[6]
AR
mx arearatioofmixingtubeinlet 2.25[8]
tonozzleexit
_______________________________________________
Thecomputationaldomainisdiscretizedusingthe
structured meshing approach where quadrilateral
cells are generated to discretize the computational
domain. As the present study employs SST k‐ω
turbulence model, y
+
≤1 has been maintained to
capture the near wall gradients. The grid quality is
ensuredthroughtheaspectratio(AS)ofeachcell.The
selection of the grid is decided when the maximum
AS≤40.
3 NUMERICALDETAILS
Toconductthesimulationstudyweusedsteadystate
ReynoldsaveragedNavier‐
Stokes(RANS)andFavre
averaged Navier‐Stokes (FANS) equations. An
overheadbarrepresentsReynoldsaveragedquantity
while overhead tilde represents Favre averaged
(density weighted averaged) quantity. The set of
modelledequationsforthecurrentstudyaregivenin
Eq.(1)to(8):
0;
i
i
v
x
(1)
;
ji ij
jj
j
j
tot
i
vv p
xxx
(2)
0
;
tot
j
j
jjj
eq vp
xxx
(3)
;
tot lam turb tot lam turb
ij ij ij
j
jj
qq q
(4)
2
3
lam
j
ik
ij
ij
ji k
v
vv
xx x
(5)
22
33
turb
j
ik
ij
tijij
ji k
v
vv
k
xx x
(6)
;
lam turb
t
jj
j
j
TT
qq
x
x
(7)
;
p
v
c
R
pT
c
(8)
Furthertemperature dependent air properties are
adoptedforallthecases.The piece‐wisepolynomial
functions for the thermal conductivity (λ), specific
heatatconstantpressure(c
p),anddynamicviscosity
(μ),adoptedfrom[9],areshownbelow:
35
1.00233 10 9.04396 10 T
82 123
2.90213 10 4.63995 10TT
22 4 26 5
2.16473 10 6.96289 10 ;TT
(9)
1
9.55481 6.29068 10
p
cT
32 63
3.10144 10 6.92621 10TT
94 125
6.37568 10 2.10762 10 ;TT
(10)
78
2.57183 10 8.54743 10 T
10 2 13 3
1.0303 10 1.09789 10TT
17 4 20 5
6.76718 10 1.75005 10TT
(11)
Inthepresentstudy,SSTk‐ωturbulencemodelis
selected to conduct the numerical study [8]. The
completesetofclosureequationsforSSTk‐ωcanbe
found in [10].The validation study is performed by
comparing the predicted axial velocity profile with
theinhouseexperimentalmeasurementsonan
ejector
diffuser at multiple axial locations (see Figure 3).
Figure 4 shows the comparison of axial velocity
profile at Location AA. Similar axial velocity
comparisonplotsareobtainedforotherlocations.The
480
numerical axial velocity profile shows reasonable
matching with the experimental data points. A
maximumof18%localdeviationintheaxialvelocity
isobservedattheaxisoftheejectordiffuserwhereas
<4%deviationinthemass‐weightedaveragevalueof
theaxialvelocityisobserved.
Figure3.Radiallinesectionswhereresultsareextracted.
Figure4. Comparisonof experimental and numerical axial
velocityprofileupstreamoffirstslot.
The mesh independence study and the order of
convergence analysis has been conducted for three
grids, coarse = 0.5 × 10
5
, medium =1.0 × 10
5
, fine =
1.8×10
5
,withthegridrefinementfactorof2.Figure5
shows the plot of coefficient of static pressure C
p
versesthegridindex(GI)factor,whereGI=1/N
{2/2}
and
Nisthetotalnumberofcellsinagrid[11].Itcanbe
seenthattheerrorbetweenthemediumandfinegrid
is relatively small. Further, the selected order of
accuracy (p) for the simulation study is a second‐
orderaccurate (p=2) scheme.Figure5 showsthat
Cp
for the three grids falls on the straight line, thus
depictingtheorderofconvergenceasasecondorder
accuratesolution.Forthecurrentstudy,mediumgrid
isselectedforallthesimulation.
Figure5. Grid independence and order of convergence
analysisassecondorderscheme.
Governing equations are integrated over the
discretized computational domain by finite volume
technique (FVM). For better accuracy, a 2
nd
order
upwind scheme is employed to discretize the
equationsformomentum,k,ωandenergy.However,
inordertoachieveconvergence(convergencecriteria
of10
‐6
),a1
st
orderupwindschemewasinitiallyused
toobtainthesolution.Thenthisconvergedsolutionis
used as initialguess to obtain solution for 2
nd
order
upwind scheme. SIMPLE algorithm is used for
pressure velocity coupling to solve the pressure
correction equation in an iterative method until
convergenceisachieved.
4 RESULTSANDDISCUSSION
The results are presented in three parts (i) mass
entrainmentratio,(ii)thermalcharacteristics,and(iii)
staticpressurerecovery.
4.1 Effect
ofambientconditionsonthelocaland
cumulativemassentrainmentratios
The amount of mass entrained (ambient air) by an
ejector diffuser is an important performance
parameter.Astherearemultipleslotspresentonthe
surface of ejector diffuser, mass entrainment is
estimated by local mass entrainment ratio (ĸ) and
cumulative mass entrainment ratio (φ). They are
definedbyEquations12and13:
,
j
e
in
m
m
(12)
,
j
e
in
m
m
(13)
where
j
e
m represent entrained mass flow rate
through an individual slot opening and
in
m is
nozzleexitmassflowrate.
Figure6showsthemassentrainmentthroughthe
individuals’ slots. At z/L=0.11 which corresponds to
the mass entrainment through the standoff distance
(SD), Case A shows the highest entrainment while
CaseFhastheleastvalue.Thevariationbetweenthe
maximumtominimumĸat
SDis~8%.Thishighlights
that the ambient temperature affects the mass
entrainment through standoff distance. With the
increase in ambient temperature the mass
entrainmentthroughSDdecreases.
481
Figure6.Comparisonofĸforallthecases.
Figure7.Comparisonofφforallthecases.
For 0.6≤ z/L≤ 1, represent five diffuser slot
openings,thevaluesofĸatthefirstandsecondslots
forallthecasesshowsnosignificantvariation.Only
at the third slot, and onwards the variation inĸ
betweenthecasesisvisible.Thedifferenceinĸatthe
lastslotissignificantwith
thevariationbetween the
maximumandminimumvaluebeing~8%.Thus,the
change in ambienttemperature also affects the local
mass entrainment downstream of the diffuser. The
mechanism of mass entrainment takes place due to
the pressure differential across an opening, and by
momentumexchangebetweentwostreamsmoving
at
different speeds at the shear layer. However, in the
present study the changes in the flow field is
primarilygovernedbythechangeintheairproperties
as a function of temperature. Figure 8 shows the
comparisonofdensityfieldforCaseAandCaseF.It
canbeseen
thatentrainedairinCaseFislessdense
which in turn affects the density field inside the
diffuser. This will lead to variation in the mass
entrainment characteristics. The analysis of
cumulative mass entrainment ratio (φ) reveals that
maximumφ=4.36isachievedforCaseAandittends
toreducewithincreaseinambienttemperature.
Figure8.ComparisonofdensityfieldinCaseAandCaseF.
4.2 Effectofambientconditionsontemperature
distribution
To understand the distribution of infrared energy
from the exhaust gases, we plot normalized
temperature variation (
) parameter which will
revealextentofcoolingatagivenlocationofinterest.
Itisdefinedas(Equation14):
0
0
,
g
TT
TT
(14)
whereT isthe localtemperature,
0
T is theambient
temperature and
g
T is the temperature of exhaust
gas at the nozzle exit. The most important locations
are ejector diffuser exit and its walls. Further local
thermalmixingprofilesareuseful tounderstandthe
localmixingcapabilitiesofanejectordiffuserexitfor
all the cases. It can be seen that the shape
of the
thermal profiles is very similar for all the cases. All
profilestendtomergeforthelargepartoftheradial
distance.Onlyatthecore,significantvariationstend
to exits. Case A has a minimum temperature with
0.339
(T=417.75K),whicharewithinthelimits,
atthecorewhileCaseFhashighervalue
0.357
(T=457.58K). The difference can be attributed to
higher mass entrainment in Case A. Further,
is
plotted at the wall of the ejector diffuser with no
significantchangesareobservedbetweenthecases.It
showsthattheeffectofambienttemperatureismore
dominant at the core of the ejector diffuser while at
otherlocationstheeffectisminimal.
Figure9. Normalized temperature variation at ejector
diffuserexit.
482
4.3 Effectofambientconditionsonstaticpressure
recovery
Static pressure recovery is defined in terms of
coefficient of pressure recovery (
p
C ). In the case of
mass entraining ejector diffusers,
p
C is defined as
[12]:
2
,
1
2
ex in in je
p
in in in
ppm m
C
Um
(15)
where
,
ex in
p
p arethemass‐weightedstaticpressure
atthediffuserexitandreferencelocation(mixingtube
location),
,
in in
U
are density and axial velocity at
mixing tube inlet. Figure 10 shows the plot of
p
C
verses non‐dimensional length (z/L). It can be seen
that the static pressure recovery profiles for all the
cases overlaps which indicates no effect of ambient
temperatureonthepressurerecovery.
Figure10.Comparisonofstaticpressurerecoveryforallthe
cases.
5 CONCLUSIONS
A numerical study has been performed on a inline‐
slot ejector diffuser wherein the effect of ambient
temperatureisinvestigatedusingSSTk‐ωturbulence
model.Ambienttemperatureissystematicallyvaried
intherange273K≤T
0≤323Kinthestepof10Kwhile
keepingothergeometricalparameterssameforallthe
cases. Boundary conditions and dynamical
parametersremainconsistent forall thesimulations.
Performance for all the cases has been compared in
terms of mass entrainment, thermal profiles, and
staticpressurerecovery. Ithas been found
thatwith
the increase in ambient temperature, the mass
entrainmentdecreases. The variationupto 8%in the
local as well as cumulative mass entrainment ratios
are observed for the ambient temperature range
investigated. The core temperature at the ejector
diffuserexitdecreases,from457.58Kto417.75K,with
decrease in the ambient
temperature while no other
significant changes in the thermal characteristics are
observed. The static pressure recovery does not
depend on the ambient conditions at all since the
profiles for all the cases matches with each other.
Thus, the current study reveals that the change in
ambient temperature up to 50K
will affect mass
entrainmentandcoretemperaturewhiletherewillbe
noeffectonstaticpressurerecovery.
REFERENCES
[1]AM Birk and D VanDam. Marine gas turbine infrared
signature suppression: Aerothermal design
considerations. International Gas Turbine and
Aeroengine Congress and Exposition, pages
V002T03A009–V002T03A009–10,1989.
[2]Arvind Gangoli Rao. Infrared Signature Modeling and
Analysis of Aircraft Plume. International Journal of
TurboandJetEngines,28:187,2011.
[3]SaibalSen.Studies
onFlowCharacteristicsofaStepped
Conical Diffuser with Passive Suction. PhD thesis,
Department of Applied Mechanics, Indian Institute of
TechnologyDelhi,2008.
[4]Parminder Singh, S N Singh, and V Seshadri.
ExperimentalInvestigationsonNon‐CircularEjectorAir
Diffusers.39thAIAAFluidDynamicsConference,page
4213,2009.
[5]Parminder
Singh, Sidh Nath Singh, and V Seshadri.
Effect of number of slots and overlap on the
performanceofnon‐circularejectorairdiffuser.In43rd
AIAAFluidDynamicsConference,page2729,2013.
[6]QiChen.Performanceofair‐airejectorswithmulti‐ring
entraining diffusers. PhD thesis, Department of
Mechanical and
Materials Engineering, Queen’s
University,2008.
[7]LSingh,SNSingh,andSSSinha.Effectofslot‐guidance
and slot‐area on air entrainment in a conical ejector
diffuser for infrared suppression. Journal of Applied
FluidMechanics,12(4):1303–1318,2019.
[8]L Singh, SN Singh, and SS Sinha. Effect of standoff
distance
and area ratio on the performance of circular
exhaust ejector using computational fluid dynamics.
Proc.IMechE,PartG:JournalofAerospaceEngineering,
232(15):2821–2832,2018.
[9]A Maqsood. A study of subsonic air‐air ejector with
short bent mixing tube. PhD thesis, Department of
Mechanical and Materials Engineering, Queen’s
UniversityatKingston,
Canada,2008.
[10]Florian R Menter. Two‐equation eddy‐ viscosity
turbulencemodelsforengineeringapplications.Journal
ofAIAA,32(8):1598‐1605,1994.
[11]Simone Crippa. Improvement of unstructured
computational fluid dynamics simulations through
novel mesh generation methodologies. Journal of
Aircraft,48(3):1036–1044,2011.
[12]W. B. Nicoll and B. R. Ramaprian. Performance
of
conicaldiffuserswithannularinjectionatinlet.Journal
ofFluidsEngineering,92(4):827–835,1970.
