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OCR for page 171
Optimizing Turbulence Generation for Controlling
Pressure Recovery in Submarine Launchways
S. Jordan (NavalUnderseaWarfareCenter,USA)
ABSTRACT
E cess pressure recovered withm submarin hull
cavities c m lead b u favorable conditions for safe
operation A notable example would be the submarin
vehicle Izmmchway when She vehicle outlet Ed pump
inlet are m far proximity along the h 11 h~zsmuch as
th mam outlet co figuration is cylind ical, this
topology p mmits insertion of p riodic wall-mounted
devices for controlling its pa ssure recovery capability
This control is centered on m mifesting z pressure loss
though turbulence ingestion caused by the he's
presen Thus, She work herein presents z mmmerical
m- e tigation by the Izrge~ddy simulation DIES) of
periodic symmetric ribs with z nib height to nib spacing
ratio of 5 m z cylind ical duct The salient cortical
structures produced by the rib's on sts are shown as
w 11 as the turbulent statistics hat comprise the n w
kin tic en rgy nsponsible for the pnssure loss (or
red ction in pressure recovery) A comparison of She
predicted frictional coefficient with the zt-sez
measur merits shows flat the Fictional coefhcient is
independent over Rey olds mmmbers sparming It least
th ee crders-of-magnitude
INTRODUCTION
NO y design engineers require trict conhol over
the extent of pressure recoven d insid submarin
recessed hull cavities Ed vehicle kunchways to Insure
successful underset operations during reconnaissance
Ed delense missi ms in cases where She differed e
betw en the hyd odynamic performance of the
submarin vehicle shutterway n cess with respect to the
pump inlet cavity promotes z reverse flow th ough She
com cting I muchway mech mism, m adverse pressure
a. dient pa Exists across the vehicle just prior to
I much This pressure differed e must be overcome by
She pump itself dmmg tart~p Funh n ore, given
sufficient pressure differ e, m initial breachward
movement of the vehicle may occur that m result in
unacceptable hunch damage The following work
presents z flexible measure for conhollmg She level of
pressun recovered in the submarin I muchway to
avoid the adverse hunching conditions just described
Specifically, f is measure in olves plac merit of
periodic ribs in the submarin cylmd ical shutte way
end of the vehicle kunchway that m suitable
minimize She level of the pressure recovered (or
maximize pressure loss) of She Eternal flow
Roughening surfaces with small discnte ribs is
thoroughly under tood qualitatively for etch ing Ed
conholling mass Ed heat t msfer rates This
k owledge arose k gely fiom She experimental Ed
mmmerical investigations that demonstrated then
importance in designing efficient ducts for mech mical
systems such as zucraft engin s Ed mmclear reactors
The ribs Themselves are t pically mounted periodically
along She i mer walls of th duct Ed generate n w
turbulent regions withm the core sheamwise flow
This erJkmced t rbulent activity greatly improves She
mixing Ed or cooling characteristics of the ribbed
surface over the traight walled duct Gen .. fly, the
zccomp Eying pa ssure loss is viewed as z design
penalty of the nib el ment, but as m the pose t
application f is consequen e is m effective me ms for
controlling She pressun gradient within the duct
The flow characteristics of ribbed wall ducts in
the fully rough regime (independent of Rey olds
mmmt:erl fall basically under on of two categories
IPmrz, 1969) Roughen surfaces with sh > 4 are
termed 'k-type" bec mse She rib pa sen e disturbs the
con flow character (s h d notes th pit h to height
ratio of each rib element) l~rge-scale vortices shed
from the rib cre ts whose shucture remains Intact whi e
convected downsheam by the core flow By contrast, z
roughen d surface with s h < 4 signifies gen ration of
cordin d cortical struct res oscillating 1 en een th ribs
with minimal i fluen e on She core flow
characteristics Unlike the k-t pe', She mean
.- ~ zmwise outer flow of this 'd -type' roughness c m be
qmsnrhied by the logarithmic kw (using imler
variables) that extends down to the viscous subbyer
along She rib costs in She literature, on will find
OCR for page 172
m my empirical relationships for approximating the
frictional factor pressme loss) of rib~oughened walls
m the fully turbulent regime (see Fig I Ed Table I for
several of th m) U fort mutely, given ~ specific rib
height, She choice of its pitch for achieving m optimum
frictional factor is not easily obtained using these
relationships By examming the origin of each
relationship, one will see that She disparity among th m
arises principally from the various parameters chosen
for each experiment such as She te t section, h D (or
h/D ) ratio Ed r mge of s h ratios st died Thus, the
collapse of These relationships onto ~ unique expression
for the f ictional coefficient apparently reveres
red fining She s h parameter
Alternatively, the choice of s h for optimi ing the
pressme loss in th submarine shutte way must be
based on She e perimental measurements of Berger Ed
Hhu (1979) Although they did not report m empu ical
expression for She frictional coefficient, they produced
quantitative local me m mass Ed heat t msfer
dishibutions within ~ roughened circular cylinder
They tested ribs 3 < s/h < 10 which showed Chat the
highest me m mass h msfer coetllcifftrs were achieved
for h = 5 over ~ wide r we of Rey olds mmmbers
Berger Ed Hhu concluded font She ratio s h = 5
achieves favorable heat Ed mass tr msfer distributions
1 e. mse flow reattachment Ed separation occur
simult meouslybetw en subsequent ribs
Thus, the present pap r is concerned with ~ 'k-
type' roughness having sh = 5 as m effective
loss (or minimi i g the me m pressure recovery) withm
~ cylind ical duct To asce tam the domi mt turbulent
physics that me responsible for producing the static
pressure loss Ed She resulting fiictiomal loss
coefhcie t, ~ computation was conducted using the
k Shoddy simulation LE3 1 methodology Since the
energy-domim~te scales of the t rbulent field primarily
attribute to th tatic poet me loss, LES is w 11-suited
for this purpose The impet s of the LES methodology
is f 11 resolution of the energybearmg scales of the
turbulent motion while mod hng the smaller scales font
tend towards homogeneous Ed isotropic conditions
The salient turbulent featmes of She flow are presented
in this paper Including its struct He Ed statistical
quantities font on noble fiom She rib's presence
Aldhough She prese t computations depict flow
characteristics for ~ Rey olds mmmber se- eras orders of
magnitude low r f m f 11-scale, She me m pressme loss
is verified by at-sea met tuemem3 taken fiom ~ full
scale prototype test onboard ~ US Na y submarine
0.1 _
1 - (3~\ 3
~` .~N
:
_ Webb (iill1 -
_ __ WaSSel ~ MrIlS (~979)
1 10 100
p/h
Figme I Empu ical Relationships for Dere mini g the
Fricti m Factor for Rib Roughened Ducts
Table I Parameters Determined for the Relationships
mFig 1; f =2[ltu(r/h)+uy 3] 2, oh =C(r/h)t
04
04
041
04C
04 _
_ E r
11 450 _
t 375
t 375 l
tC 3 50 _
tC 1 20
Go 3
653 024
5 053
I of. O. 50
1 43 0 35
GOVERNING
METHOD
EQUATIONS AND SOLUTION
To provide sufhcie t patial resolution of She
salient turbulent activity in She cylind ical duct, grid
point clustering is necessary around the rib elements
Concunently, application of ~ LES formulation to this
grid topology reduces proper h m formation Ed
filtering of th cylmd i 91 coordinate form of She full -
resolution equation system nncomp~ , Ale Navier-
Stokes Ed contimmity equations) to ~ curvilmear
coordinate famework The procedure suggested by
Jord m (1999) is follow d herein where She fu st patial
operation is formal h m fommation of each term in the
original equations The h msfommed system appears as
Contimmity:
at/ q
(1)
OCR for page 173
Moment m [she tmwise (x), radMI (r), cl cumfet ntMI
(3)]:
a r~pV~ aT¢t iq j V~ a r\rZ: p
at ak ak
+~[J7gk aV~]
a ~ ~ J-v ~v~ = r a [k¢~ P
+ I ~ a |~gk~aVr 1| rV +2aF¢tV~ 1
ar,/ Vd ali::,qiV9+EVv~= aTk~tP
+Re[a~k(Fg a ~ | r([V~ 2 )¢k |]
whet each temm is show t m its non-dimensiorul
conservativefomm; xj=(x,r,0), qj=(rv~ ,ve) md
gt =hj~t~, where hj =(r J.4r) he coefficients
(t~ md ~/; dertote the metrics md the Jacobi m of fhe
tt msformation, respectively Filtermg fhe ~hove
cylind icM sy tem derives the LES fommuLtion hus,
the t sultmt grid-frltered equctions m curvilmear
coordit~tes for cylind icM geometries become
Contimmity:
au+av+aw=0
a; a~ a:
Momentum:
a r~ a T7}~ a R/~ p D
at a~k a k a~k
+ I a (~gk aVx |
aW au}v, ~_ _ a~-~}~ a t
Rel4(~ a ~ r(~' (k
(3)
(48)
(4b)
a r`~0 +a U~:v~ ~VIVC = aF¢9 P+a~k
(2a) +Re~(~g a¢J r(~vs 2 a k 1
where the resolvable conttavari mt velocity
compot nts (U}) m fhe convective terms are defn d;
U}=~/~}~ qj he subgrid scMe (SGS) shess tensor
t ~' is defmed in conttavari mt form es t }=U} v~ U}v~
Accord6ng to Jord m (1999), fhe metric coefficients are
considered es filtered bee mse fhey me evalllated
mmmericMly et discrete pomts Mong the curvilit ar
Imes(denotedbyatilde)
he ctove LES sy tem was time~dvanced by c
vari mt of the fractiot~l- tep method (Jordan md
Rag~h, 1996) his techmiqtt utilizes c s ml-staggered
disct ti ction molecule that is refommuLted in
boundary-frtted cylind icM coordit~tes he diff sive
derivatives w t time ~dvanced by fhe Crcr~k-Nicolson
scheme to elimit~te fhe high viscous stability
re triction t ar fhe rib rrests, while fhe non-lmear
terms w t time tdvanced by m explicit Adtms-
Bcshforfh scheme SpatMlly, the convective
derivative s w re cpproximate d by fhir d -or de t accu rcte
upwindbiased fmite differet es wifh fhe dfffusive
terms discretized using st mdard second-order-accurcte
finte volume dfffet t es he Pt ssure-Poisson
equction of fhe fractiot~l-step procedure was Mso
cenhM differet d to the second order Addbtiot~1
det tils of fhe solution medhodology, along wifh several
test cases, c m be found in Jord m md Rcgab (1996)
DYNAMIC SUBGRID SCALE MODEL
For the nbs comput ttion. Ml of fhe turbulent scMes
removed by the filter opemtion w re modeled by m
eddy viscosity rektionship modified for dyt tmic
computation of the model coeffrcient (Smcgormsky,
1963), (Germ mo et M, 1991) he dynamic
coefficient will give the conect csymptotic behavior of
the turbulent stt sses when cpproaching fhe nb wMls
md minimize SGS conhibutions in the low turbulent
regions betweert tbsequent ribs he tt msfcrmed
form of the dyt tmic model is expt ssed es
t ~'+1/~g,i'7~ =2C~ S S,}
(5)
where C is the dynamic coefficient md the frltered
mehic term 5} is defit d ~s S}=~/:S,dj~=s~.
