471
NOMENCLATURE
SAS ScaleAdaptiveSimulation
SFS SimplifiedFrigateShip
SHOL ShipHelicopterOperatingLimit
TTCP TheTechnicalCo‐operationProgram
CFL Courant‐Friedrichs‐Lewynumber
PSD PowerSpectralDensity(m
2
s
‐2
/Hz)
U
Free‐streamcrossflowvelocity(m/s)
u,v,w Velocitycomponentsinx,y,zdirection
V
Resultantvelocity(
22 2
uvw
)
ψWindOverDeckangle(degree)
ρDensityofair
L
HDK Lengthofhelodeck(m)
h
HGR Heightofhelohangar(m)
l
reFlowrecirculationlength(m)
y
+
Non‐dimensionalwalldistance
kTurbulentkineticenergy(m
2
/s
‐2
)
ωSpecificturbulentdissipationrate(s
‐1
)
t*Non‐dimensionaltime,inCTSunits
tPhysicaltime(sec)
ΔtTime‐step(
0
U
)(sec)
CTS ConvectiveTimeScale(
LU
)
Δ
0 GridSpacing
Δt* Non‐dimensionaltimestep(
tCTS)
V
s Shipvelocity(m/s)
V
wind Atmosphericwindvelocity(m/s)
LReferencelengthoftheship(m)
V
rRelativewindvelocity,(
s
wind
VV )
L
,B,H Shiplength,width,andheight
L
d,Wd,HdDomainlength,width,andheight
ʋ
tEddyviscosity
μ
tDynamiceddy‐viscosity
ITurbulenceintensity
An Investigation of Ship Airwakes by Scale Adaptive
Simulation
S.Shukla,S.N.Singh&S.S.Sinha
IndianInstituteofTechnology,Delhi,NewDelhi,India
R.Vijayakumar
IndianInstituteofTechnology,Madras,Chennai,India
ABSTRACT:Anearlyassessmentoftheshipairwakesflowcharacteristicisoneofthemostchallengingtasks
associatedwiththedesigningofvessels.Thepresenceofshipairwakecreatesverycomplexflowphenomena
due to the presence of strong velocity gradients in space and
time and widely varying high levels of
recirculationandturbulence.Undersuchcondition,thelandingandtake‐offoperationofahelicopteroverthe
shiphelodeckisverycomplexandaccuratepredictionrepresentsacomputationalchallenge.Wepresenttime‐
accuratescale‐adaptivesimulation(SAS)ofturbulentflowaroundasimple
frigateshiptogaininsightintothe
flow phenomena over the helodeck. Numerical analysis is carried out after several grids and time‐steps
refinementtoensurethespatialandtemporalaccuracyofthenumericaldata.Theinstantaneousiso‐surfaceof
eddyflowstructuresandvorticityhavebeenanalysedacrossthevertical
andlongitudinalplane.Resultsshow
good agreement with experimental data. Comparisons of mean quantities and velocity spectra show good
agreement, indicating that SAS can resolve the large‐scale turbulent structures which can adversely impact
ship‐helocombinedoperations.Overall,theSASapproachisshowntocapturetheunsteadyflowfeatures
of
massivelyseparatedshipairwakecharacteristicswithreasonableaccuracy.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 14
Number 2
June 2020
DOI:10.12716/1001.14.02.27
472
StStrouhalnumber
f
Naturalsheddingfrequency(Hz)
C
d,CL,Cm Coefficientofdrag,liftandmoment
X,Y,Z Longitudinal,transverseandvertical
co‐ordinatedirection
1 INTRODUCTION
Theshipbornehelicopteroperationsareubiquitousin
every naval organisation. These operations are
integral to the primary and secondary roles of the
naval fleet. In this context, the shipborne helicopter
operations from
a small vessel is a critical part of
present‐day naval operations. Safe shipborne
helicopter operations require a clear understanding
of the ship environment‐viz. ship airwake, helo
downwash, vessel hydrodynamics for quiescent
landing periods, sea state and other ambient
atmospheric conditions. Foremost, the ship airwake
flow characteristics play a
significant role in
combinedship‐helicopteroperations[1].
Flow over the ship helodeck even at stable sea
conditionsisturbulentandquitecomplexinnature.
For small naval ships, the challenges associated
with the shipborne helicopter operations is further
aggravated due to the bluff ship superstructures
andconfinedhelodeckarea.Presence
ofsuchlarge
bluff superstructures create complex airwake
environment over helodeck. The resultant airwake
flow contains (i) widely time‐varying turbulence
structures, (ii) steep velocity gradients, (iii) highly
separatedflow,and(iv)the interactionofunstable
separatingshearlayersandvorticeswhichcanhave
a significant impact on the shipborne
helicopter
operations [2]. An accurate assessment of the
resultant ship airwake flow phenomena is an
outstandingchallengefornavalarchitectsaswellas
researchers.
A significant number of papers dealing with
computational studies on different physical and
numerical aspects of ship‐helo dynamic interface
are gathered during our literature survey [3].
Investigations covering the unsteady ship airwake
characterisesstartedintheearly2000’s[4‐7].These
reported studies have highlighted that the RANS
basedturbulencemodelsarethemostpreferreddue
toitssuitabilityandwiderangeofapplicationsata
relatively less computational cost. Hence makes it
more robust for
parametric computation of such
complexshipairwaketurbulentflowsamongother
computational methods. However, this approach
cannot resolve the flow scales, due to the
involvementofseveralmodelledtermandarbitrary
coefficients.Thus,theaccuracy/predictionofRANS
based models varies considerably.On the other
side,thedirectnumericalsimulation
(DNS)resolves
theentirerangeandofferscomprehensivedetailsof
the temporal and spatial scales of flow. However,
this method is so computationally demanding that
thisapproachcannotbepracticalforhighReynolds
numberproblemslikeaship.
To overcome the drawback of both methods,
several time‐dependent simulation techniques,
namely,
lattices boltzmann method (LBM) and
Largeeddysimulations(LES)havebeenutilizedin
predicting the ship airwake flow characteristics [5,
8]. The LES approach can resolve the large eddies
whereas, the smaller eddies are modelled using
differentsub‐gridscale(SGS)models.However,the
usage of LBM and LES is
practical but not an
affordable tool at the early design stage wherein
numerous parametric simulations are required for
engineeringapplications.Thus,thereisaneedofa
numerical technique which achieve the solution
close/equivalent to experiments at relatively less
computational cost. As an alternative, several
numerical methods have been developed to
bridge
the gap between the LES and RANS approach
namely;hybridLES‐RANSbasedmodels;Detached
Eddy Simulation (DES) [9], and Scale‐Adaptive
Simulation (SAS) [10], hybrid URANS/Vorticity
Transport method [11], Partially‐Averaged‐Navier‐
Stokes(PANS)[12].Morerecently,LES,PANS,and
DESapproachhasbeenusedtoinvestigatethe
ship
airwakeflowphenomena[6,8].
The SAS method is a hybrid LES‐RANS based
model originally proposed by Menter and Egorov
[10]. This method represents an alternative time‐
dependent simulation technique which is does not
necessarly require a very fine grid resolution and
allowstodynamicallyadjusttheresolvedstructures
inaURANS simulation. Therefore, the SAS model
shows a behavior similar to the LES in unsteady
regions of the flow field. This allows an efficient
passage from RANS to scale resolve simulation,
especially for the complex geometries. The SAS
approach has previously been used for several
massivelyseparatedbluff
bodyflows,suchasflows
aroundairfoil[13],cylindersandsimplifiedvehicles
[14‐15]. All these investigationsshow thatthe flow
predictions of SAS are in reasonably good
agreement with the experimental data, and can
resolve the spatial and temporal turbulence scales,
atrelativelylesscomputationalcost.
In
this paper, SAS simulations of flow past a
generic simplified frigate ship (SFS2) at Reynolds
number (Re) 2×10
5
have been performed. The
specific objectives of the current study are; (i)
assessment of the capability of SAS approach in
predicting unsteady turbulent ship airwake flows,
and (ii) understand
the unsteady airwake flow
physics around a simplified frigate ship.
Availability of such scale resolved approach at
relatively less computational cost would lower the
burdenofexpensiveandriskyseatrialprocess.
Thispaperisorganisedintofoursections.Section
2 presents computational approach including
backgroundoftheSASmodel,
descriptionoftheship
geometry, computational domain, grid, solver
settings,andphysicalconditions.Section3highlights
the results and discussions. Finally, Section 4
concludesthepaperwithasummary.
2 COMPUTATIONALAPPROACH
Thissection describes the adopted methodology in
terms of (i) numerical method, (ii) computational
domain, grid and boundary conditions,
and (iii)
solversettings.Inthepresentstudy,wefocusonthe
top‐sideshipairwakeimpactonhelodeckonly.
473
2.1 NumericalMethod
The ship airwake flow phenomena has been solved
numericallywiththeSASapproach.TheSASmethod
is based on the introduction of the von Karman
length scale (
, into the transport equations of
SSTmodel[10].ThevonKarmanlengthscaledefined
as;
vK
U
Lk
U
; 2.
ij ij
US SS
; (1)
22
22
ii
kj
UU
U
x
x
;
1
2
j
i
ij
ji
U
U
S
xx
(2)
where,
is the first derivative of the velocity
vector,
is the second derivative of the velocity
vector,and
isvonKarmanconstant.
Inclusion of the von Karman length scale term
allowsthemodeltoadjustitslengthscaletoalready
resolvedscalesintheflowandtherebyprovidealow
eddyviscosityvaluetoallowthemodeltooperatein
‘LES’ mode. For more details on SAS method
formulationsee[10].
2.2 Geometry,ComputationalDomainandGrid
Wehaveconsideredthe SFS2 ship geometry forthe
present study. The SFS2 is a baseline frigate ship
geometry,anddevelopedasapartofaninternational
collaboration under the auspices of The Technical
Cooperation Program (TTCP) [16]. The TTCP
proposedtwo
modelsnamelytheSFS1andSFS2,as
shown in Fig. 1 (dimensions are in feet). Literature
reveals that both the SFS geometry have been used
frequentlyforstudiesofbareshipairwakesinorder
to validate the various CFD codes, and to generate
validationdatathroughmodeltesting[1‐7].
Figure1. Schematic of simplified frigate ship (SFS)
geometry;SFS2
The selection of computational domain is based
on low blockage ratio and suggestive information
from earlier reported literature [3]. The rectangular
domain incorporating SFS2 (1:100 scale) geometry
considered for the study is shown in Fig. 2.
Structured hexahedral grids with boundary layer
elements(nearbodies)areusedforthepresentstudy.
Afinalgridsizeofnearly6.1millioncellsisadopted
post validation and grid independence studies. The
overall grids across the computational domain and
refinement near fuselage are shown in Fig. 3. Grid
refinement region across the helodeck region is
providedforbetterflowfieldaccuracy.Foraccurate
near
wall treatment and resolving the viscous
boundary layer, variation of boundary layer grids
acrosstheshipsurfaceismeshedwithkeepinganon‐
dimensionalwalldistance(
lessthan4,asshown
inFig.4.BasedonstandardCFDpractices,asuitable
sizefunctionisappliedwiththeexponentialgrowth
ratioof1.2withgridspacing(
=2×10
‐3
m)toensure
thesmoothcellgrowthfromtheship.
Figure2Schematicofcomputationaldomain
Figure3. Schematic of structured grids across the
computational domain at X‐Y and X‐Z section highlights
gridrefinementregion
Figure4.Variationofnon‐dimensionalwalldistancealong
theshipsurface
2.3 SolverSettingandBoundaryConditions
All numerical simulations are performed using a
finite‐volume based CFD code Ansys Fluent. SAS‐
SSTclosureequationsetofturbulentkineticenergy
(k ) and specific dissipation rate (ω) are integrated
overthediscretizedcomputationaldomainbyfinite
volume method (FVM). For better
accuracy, the
spatial discretization of momentum, k andωhas
been done by second order upwind scheme.
Pressure implicit with splitting of operator (PISO)
algorithmis used forpressure velocitycoupling to
solvethepressurecorrectionequationinaniterative
methoduntilthedesiredconvergenceisachieved.
474
The time‐step for this current study has been
selected based on the literature survey [3] provided
the CFL number≤1 across the computational
domain.Thisledtoalowerlimitoftime‐stepvalue,
Δt = 1×10
‐4
s. The upper limit of time‐step has been
decided based on the convective time scale, CTS =
6.5×10
‐3
s. Later, we also performed time‐step
independence to test the spatial and temporal
sensitivity of numerical data between these limits.
Finally, the time‐step value,Δt = 1×10
‐3
s has been
foundappropriate,thoughthesmallertime‐stepcan
also be selected which will resolve more turbulent
energyathigherfrequency.
The following boundary conditions are
prescribed;
Inlet is provided at upstream of the ship. A
uniform flow velocity (U∞ = 21.33 m/s) is given
with the
turbulence intensity of 1% of the
freestream kinetic energy at a length scale of 0.3
cmatstandardatmosphereconditions.
The wall boundary condition with no‐slip is
appliedatboundaryofthecomputationaldomain.
This implemented the bottom, top and side
surfaceofthecomputationaldomainasstationary
wall
boundary.
Similarly, the ship geometry is assigned as wall
withno‐slipcondition.
Outlet is assigned as a fixed static pressure
conditionwiththefluxconstrainedtobeparallel
tothefree‐streamflowatatmosphereconditions.
3 RESULTSANDDISCUSSIONS
This section includes a comparison of numerical
results with experimental data to validate the
numericalmethodology. The coordinate axis system
isdefinedsuchthat‘X’ispositivetowardsthestern,
‘Y’ is positive towards starboard and ‘Z’ is positive
upwards.Allthedistancesarenormalisedrelativeto
the helodeck geometric parameters, i.e. the
longitudinal,lateralandverticallocations
havebeen
normalised by helodeck length, beam and height
respectively.
3.1 Validation
Numericalvalidationexerciseisundertakenagainst
theexperimentaldataofNationalResearchCouncil
of Canada (NRC) reported by Forrest et al. [6] for
headwind condition (ψ = 0
0
). Comparison of the
experimental and numerical data for all three
components of mean velocity is plotted at location
of deck
/ across the ship beam at
non‐dimensional height of
/ = 1 in Fig. 5.
Overall, the comparison of predicted and
experimental results is found to be reasonably
matching with minor variations in the axial
component(u)ofthevelocity.
Figure5. Comparison of mean velocities at 50% deck
length,plottedathangarheight(Z/h
dHGR=1),atψ=0
0
3.2 Shipairwakeflowcharacteristics
This section brings out the headwind airwake flow
characteristics to assess the capability of SAS
approach in predicting unsteady turbulent ship
airwake flows. The unsteady ship airwake flow
characteristics investigation involves analysis of the
(i)timehistorydata,(ii)powerspectraldensityplot
of velocity
spectra,and (iii) profile of instantaneous
flowstructures.
Our analysis of the time history of longitudinal
and lateral velocity at centre point of helodeck
(X/L
HDK = Z/hHGR = 0.5) and their power spectral
densityplot is shownin Fig. 6 and Fig. 7. It canbe
seen that both the velocity component sustains
unsteadinessthroughoutthephysicaltimeof11.5sec.
Italsoshowsthatthelongitudinalandlateralvelocity
variedintherangeof18m/sto
3/sand3m/sto‐10
m/s,respectively.
Figure6.Timehistoryoflongitudinalandlateralvelocityat
centrepointofhelodeck(X/L
HDK=Z/hHGR=0.5),ψ=0
0
Figure7. PSD plot of longitudinal and lateral velocity at
centrepointofhelodeckvelocity(X/L
HDK=Z/hHGR=0.5),ψ=
0
0
Further, the PSD plot of both the velocity
component highlights the ability of SAS to capture
reasonable turbulent structure at all the frequency
rangefrom1to1000.Theresultsofspectralanalysis
475
also indicate that the lateral velocity contains
relativelymore energy atfrequenciesabove100 Hz.
We also observed that the peak of spectral analysis
liesnearlyat1.25Hzwhichmatchesreasonablywell
withthereporteddata[2,6].
Finally, the instantaneous flow structures have
been analysed through instantaneous contour
of
vorticityandiso‐surfacesofλ
2criterioninFig.8and
Fig. 9.λ
2 is defined as the 2
nd
Eigen value of the
S
2
+Ω
2
,whereSandΩarethestrainrateandrotation
tensorsrespectively.Asmallnegativevalueofλ
2can
showcoherentstructuresofaflow.
Fig.8showsthevariationoflongitudinalvorticity
acrossthesymmetryplane.Aqualitativeanalysisof
vorticity variation on this plane (area considered to
be covered by contours colored red the magnitude
ranges 6.4‐30 s
‐1
) shows presence of high vorticity
region in the vicinity of the helo‐hangar
superstructure. Further, Fig. 9, highlights the iso‐
surface of negative values ofλ
2 around the ship. A
significantnumberofcoherent,structurescanbeseen
overthehelodeck.Whenanimationsoftheflow‐field
are viewed, these structures are convected
downstream from the hangar edge and also shed
from the ship ‘funnel’. These large‐scale eddies are
mainly responsible for the velocity fluctuations
observed
in Fig. 6. Moreover, we found that these
eddystructuresarehighlyassociatedwiththeWOD
conditions and change dramatically with respect to
thewinddirections.
Figure8.Contourofvorticityatsymmetryplane(Y/B=0)
acrossship,ψ=0
0
Figure9. Iso‐surface contour ofλ2 value (indicating eddy
vortex structures colored by turbulence intensity) across
ship,ψ=0
0
;TopView
4 CONCLUSIONS
Provisionofsafemarineaviationfacilitiesfromship’s
helodeck entails study of ship airwake. The current
study investigates the generic flow features of the
unsteadyshipairwakes.Theresultsshowthateddy
flowstructuresvastlydominatetheflowphysicsover
the helodeck region. The SAS model predicts the
unsteady
airwakeflowphysicswithgoodagreement
in the mean values and spectral quantities as
comparedtoexperimentaldata.Overall,thepresent
study demonstrates that the SAS model has the
abilitytoreasonablycaptureandsustainanunsteady
solutionforgenerationoftime‐accurateairwakedata.
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