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OCR for page 474
Validation of Tab Assisted Control Surface Computation
C.-H. Sung, B. Rhee, I.-Y. Koh (Naval S reface Warfare Center, Carderock Division, USA)
A m mericcl procedure for She prediction of She forces Ed moments of c tan assisted co trol surfae (TAC)
hr. bean developed The conh ol surfae consists of c stern stabilizer, c flap, ad c tab The m meri cl procedure is
based on solvmg the mcomp~ Ale Rey olds~e~aad Na vier-Stokes equations coupled with several two~quation
turbulence models Some fectmes of the m mericcl medhod used have been highlighted in particular, She
preconditioning method, multig id method, Ed nom effecting far field bo mdary condition have been discussed The
wall bo mdary condition for She specific dissipation rate which is impo t mt in obtammg good convergence for She At
equation turbulence model have also been briefly discussed Computed results of the lif Ed d cg coefhcients of the
conh ol surfae, flap torque coefficients Ed tab torque coefhcients et various Ogles of cttak of the stabilizer Ed of
flap Ogles Ed tab angles hove been predicted within I O percent fi om the mecsmed values even et high Ogles of
attack et I 5 deg es The discrepa ies of She torque coefhcients of flap Ed tab are somewhat higher particohr fly et
high flax a d torque deflections Th re are two reasons for These higher discrepancies The fi st reason is that the
turbulence models are i h re tly w ok m the flow regime where separation is severe, Ed the second is Nat the g id
solution m both She flap Ed tab gap is not s fficient Th se will be She topics for future ir~stigatiom
INTRODUCTION
A contro I surfae h re will be defmed es
consistmg of c tern stabilizer, c flap Ed c tab Th
stabili:D:r may be fixed or movable but She flap Ed tab
are always movable Conh ol smfa s have et least
th ee major f motions applicable to both circmft Ed
mane ~ehcles (1) The tabilizer,flcp, mdtab m
be clig ed to form c high cambered control surfae to
increase the Ifft sig Tic mtly in the arospa
indu try, this is She so celled high-lfft multi~lement
pi foil (or vimg) (2) Co trol Onto es me normally
desig ed to provide adequate Ifft et lower speed
operation, but Ed ii Cole excessive conh ol may occur
et high speed A smoother control et high speed may
be achieved by keeping the stabili:D:r fixed Ed using
the flap Ed or tab for co trol (3) At high speed, m
excessively large torque c m arise m the stabilizer
This let ge torque c m be reduced by deflecting the flap
Ed or tab m th direction opposite to th direction of
the Ogle of cttak of She incoming flow
Th purpose of this paper is to report the
prog ess made in the development of c predictive
capability of the t:3rces md moments of She tab cssi ted
conh ol surfa (TAC) The desigm of efficient md
desi able control surfa s by cpplymg the predictive
capability developed here is led for future work
Th re is m extensive experimental md
computational literature on She high-lfft multi~lement
pi foil (wing) Many references c m be fo Ed in [1]
Th re is mextensive set of data of aNACA0015
pi foil with c Flip md c tab me tared by Sears et cl
[2] For marine application, work on restively low
aspect ran 3 conh ol surfaces ( templates or rudders) is
mo tly experimental Very little computational work
has a peared in the literature Forces md m oments on
conh ol surfa s (no nap nor tab) have been measured
by Whicker et cl [3] md those on c Flipped control
surfae (no tab) have been measured by Bow rs[4]
Water tunnel experiments one series of 12 rudders
with systematic variations of nap area md nap bahmce
have t en performed by Kerwin et cl [5] Th ee
variations of skeg-rudders (i e, fi ed m tin conh ol
surfaces with mova le taps) have been mvestigated m
c wind turmel[6] Th effect of gaps betw en She
rudder md th skeg hits also been mvestigated it hits
been obt rved tint fihe effect of the gap is insigmiflc mt
Unlike the cat in serospae mdushy, there are not
m my compohtional papers on conh ol turfa s
Recent ly, S o ding [7] di t us se d fihe spp l icst ion of
pote tisl theory in rudder flow predictions The effects
of naps md tabs w re not die nosed Comp rations for
OCR for page 475
rudders (no flap nor tab) based on sol ing She
R y c I ds ~~ era g dNavier-Stokes tANS) equations
with c k-c turbulence model have been repo ted by
Chum [8] The 3D computations to be reported will be
compared with the data to be reps ted m [9] mplicit
in all the Investigations discussed so far was th
css mption that the co trol surface was opercti g in c
mfform flow without the i fluence of She hull
bo mdary Icyer, the horse-shoe vortex shed by
appendages or th propeller
In She next section, the gowxning equations of
the incompressible RANS equations Ed the turbulence
models will be described The m mericcl method used
will be discussed next Only some special fectmes of
th m mericcl schemes will be highlighted omitting
mo t of the details Th experiment performed on She
TAC cone ol surface with c flap Ed c tab will be
described Ed She comparison betw en computations
Ed mecsmements will then be discussed Finally,
some conclusions will be mentioned
GOVERNING EQUATIONS
Th incompressible R y olds~erag d
Navier-Stokes tANS) equations Ed c nonlinear At
turbulence model must be solved The nonlinear At
model used h re is c st mdard At turbulence model
developed by Wilcox [ 10] coupled with c nonlinear
R y olds Hess model
ad, = A
au, + au,uj = apr + aa (Vaaa' I) (2)
at + a j (USA) ad [(V + a~v~) arm ] =
T~; ad Pit
at + ads (U,t ) ad [(v + a~Vt)aOt ] =
at :,; ad, p 2
(1)
(3)
(4)
where Uj is She Cartesi m velocity component, pt is the
pressure p divided by c const mt density p, r is the
turbulent kinetic energy, t is the specific dissipation
rate, v is th kinematic viscosity, v, is the eddy
viscosity fib en es r/t Ed -a is She R y olds shess
Senior A quad Tic R y olds stress model developed
by Speziale [l l] will be used h re, Ed m explicit
expression c m be fo Ed Here St mdard modeling
coefficients are used: p = 0 09, p = 3/40, a= 5/9 Ed
a = A = 1/2
NUMERICAL \IEIHOII
Th incompressible tANS equation are
solved by the artfficicl compressibility approach fi st
proposed by Chorin [12] Ed subsequently genercli:D:d
Ed improved by Turkel [1 3] A finite vol me method
is used Th mecnflow u e, Eqm (1) Ed (2)) is
spatially discreti:D:dbyc second-order accurate central
differ ence me Ho d with fourth- or der a ccumte
dissipation terms The logic for using the fourfh-order
accurate dissipation terms is twofold During She early
stage of time stepping, th fourfh-order accurate
dissipation terms act to suppress spurious oscillations
thus erLth mg converg rice to be re tched But once She
convergence is achieved; how ver, their co tobution
the solution is negligible bec Use they me fourth order
accurate compared to the second-order accurate spatial
discretization scheme Several upwind schemes hive
beenmggstedbyYee[14] Therecsonforusing m
upwind sch me, not c central difference sch me, to
solve the turbulent flow equation is font the flux
man i is already diagonal; th refore Here is no
cdditiorurl cost in doing c characteristic formoktion
Th time teppmg is based on m explicit one- tep
multi-stage R mge-K tta method to reach c stecdy-
state solution This approach is not only applicable to
th steady tate sol tions but c m also be extended in c
very simple maimer to solve She time dependent
equations Some discussion of this extension c mbe
fo Ed m the pcpersby Jcmeson[15] mdLinet cl
[16] Several c onvergence a cce lercti on tech i que s
including multig id, local time pep, implicit residual
smcothmg,pre33nditiomog mdbuk Viscosity
dimpinghavebeenimpleme ted l o handle c omp sex
geometry, She muhut lock g id structure is adopted
Th se m merbal tech iqws have been
implemented in a code tmed IFLOW, which is m
abbreviation for incompressible FLOW IFLOW is
i tended to be a production code for sol ring 2D, 3D,
steady Ed msteady problems The code is highly
mod par m structure se that different turbulence
model s Ed higher order sch me. c m be easily
implemented Some special features of She m merbal
schemes us d will be highlighted Hew ver, deviled
derivations will be mostly emitted
Precorld dotted Method
Th preconditioned method is developed
based en a ystem of hyperbolic equaticus, but the idea
goes back to th effc t to red t e She condition n mber
OCR for page 476
of c mchix m Ime r clgebrc For hyperbolic equations,
the objective is to make the various peeds of differe t
wave modes more or less th same so that convergence
c mbe sig if ca tly ccelemted 7his is particul rly
import mt ff fhe rtificicl compress~bility cpprocch is
cdopted to solve incompressible flows 7he recson is
th~t the so md speed, which is one of the wave modes
in fhe incompress~ble flow, propagates much fastff
th m the fluid peed 7be result is c very slow
convergence es of en enco mtered m the cttempts to
compute low Mcch n mber flows usmg c compress~ble
flow code
7be preconditioned me m flow (i e, Eqns (1) md (2))
c m be w itten in fhe conservative form es
Po~q, +F~ +Gy +Hr =0
(5)
where fhe preconditioned mchi PO md th th ee
components of flux s F. G. mdH re defnedas
(1fy)3 y ~u y ~v y ~w
P~ (Ifaty)37u Ify ~u~ y ~u Y ~uw
(Ifaty)37v y ~vu Ify ~v~ y ~vw
(Ifaty)37w y ~w y ~w Ify ~w~
P~ u v
q= u F= u2+p~ r~ , G= uv r .
v . uv r., v~ + p ~ r
w uw r~ vw r
(7)
where n, d ~ md Y are preconditioning parameters, r
Ij = x, y, ~ are Rey olds shesses For mathematical
crudysis, it is ecsier to w ite Eqn (S) in c non-
conrffvative form Neglecting fhe vicous terms, it
c m be derived es:
p Iq, + Aq~ + Bqy + Cq, = 0 (8)
7be explicit forms of mch ices A, B. md C cre omitted
here 7he preconditionmg mchi P ~ is dffferent f om
th previous one PO ~ md is given by
(i + r) q ~ y/'q ~u y/'q ~v ypq ~w
P ' tl~q ~U
t~q ~v
t~q ~w
1 0 0
0 1 0
O 0 1
(9)
7be condition a=y ensures fhe system of p rticl
differenticl eq mionr is w 11 posed How ver, the
implication of w 11 posed ess in th case of m mericcl
sohtion is not cle r h this pcper, it is a=y O md
~ 2=max( u 2,~), c=07 (10)
7hough mther tedious clg brcic m mipulations, fhe
eig r~lues md lef md right eige functiom c m be
fo md 7he maxim m of eiger~lues is used to define
c local time step 7he eige f mctions re of no use to
cenbal dffference chemes ex ept for e tablishmg c
nomeflecting bo mdary condition et f r field 7he f nal
system of equations to be solved m the conservative
form is
Since the fommulation is based on hyperbolic eq mion
only, viscous terms should be cdded to fhe flw~es F. G
mdHcsshow inEqn(7) 7heright-hmdsideofEqn
(I 1) is th fomth-order matrix dissipation terms 7be
Po ~q~+F~+Gy+H7=(po~ PA q,,~)~+
(6) (Po PB qw)Y+(Po PC q~)7 (11)
n ctri dissipation gives the most ccurcte sohtion but
h less stable bec mse c smcllff cmo mt of dissipation is
cdded As c compromise betw en ccur cy md
robu tness, vector dissipation is cdopted m this pcper
For vector dissipation, mch ices PA, PB md PC are
replacedbyfheircorre pondingradius pectra Inth
curvilme r coordim~tes, (,1=1,2,3, fhe maxim m
eiger~lue m the i-di ection is given by
Xm~=~(Ui +Jui +4~2 ai ~ ;
U'=uea',a'=V:'
MrdtigridMahod
(12)
Multigrid is one of the mo t effective methods to
ccelercte the mte of Convergff e md should be used
routinely in e ffy production code 7he cpprocch in
IFLOW subst mti~lly follows the idecs of Br mdt [ 17]
md hmeson [18] Severcl ri~tions mcludi g V-, W-
md F-cycles have ben implemented h genercl, W-
md Fcycles re more efhcient, but not sig if c mtly
so More levels of multig id cost c little more but are
more efhcient For simplicity, most computations
performed with FLOW use f ee levels of multig id m
th V-cycle 7he multig id medhod is used routmely m
IFLOW For I rge sccle computstions on complex
geometries, computatiomd st rtup is often j mpy For c
rmoothff start, c multig id startmg procedure is used
Consider c 3-level multig id comp tation: A 2-level
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Representative terms from entire chapter:
control surface
multig id com isting of the medium md coarse g ids is
rum for ctout 50 cycles Th solution is then
i terpokted to the flne g id to st ut 6he 3 -lev I
multig id compubtion ~ general, c solution cdequ~te
for engineffing cpplications c m be cchieved in 100-
500 multig id cycles This efficiency is et lecst es
good es 6he best Computatiomd Fluid Dynamics (CFD)
codes cvaibble but is far f om 6he Te tbook Multig id
Efhciff y (TME, less th m 10 cy les) cdvocated by
Achie Br mdt [19] AchievingTME isanoble gocl,
md will hav c sig iflcant impact on e gmeering
cpplications of CFD
Boundary Condfltions
Only th solid wall md 6he f ufield boumdary
conditions need to be discussed At 6he wall, the 6 ee
components of v locity md 6he tu bulent kinetic
energy rare set equ~l to :osro, 6he pressnu p is deriv d
from cssumption th~t th pressu e g cdient normcl to
th wall is :osro Finally, the wall boumdary condition
of p ff iflc dis s ip at io n rcte m or igimdly giv n b y
Wilcox p 148 m [10]) is modifled as
t0W = ~ Qw · ~= 40
(1 3)
where Q. is the vo ticityat6he wall mduO isc
const mt varying f om c valu of 6 giv n by Wilcox to
20 Th choice of ao may vary 6he convergence rcte
slightly but once Convergff e is ahiev d, 6he solu ion
is ctout 6he same The motivation in deriving the
modified wall boumdary condition (13) is to get rid of
th requi ement th~t the fi st g id normcl disbnce must
be giv n The nomdimensional normcl dist mce y+
requi ement crectes c difficu ty for coarser g ids
bec mse the flr t g id normcl di tances tend to be too
large inthe coarse g ids Wi6hEqn (13), 6he normcl
di tarme does not cppe md 6he y+ of the fi st g id
normcl dist mce of th fine t mesh should be of 6he
order I or 2
At th far fleld, the g cdients of 6he th ee compone ts
of v locity md the g cdients of the two tmbulence
qumtities rcod t are set to ffO The pressure is
obtamed by c non~eflecting condition discussed by
Hedstrom [20], Rudy md Str kv rdc [21] md Sumg
[22] This is one of the mo t importmt boumduy
conditions for e ternal flows md will be ou Imed The
idec is based on the characteristic formulation of
hyperbolic equstions, such 6~t th outgomg solution
modes will notbe refl - tedback mto 6he
computatiorud domcin to cor upt 6he solu ion To do
this, th time derivativ s of the charactffi tic vari~bles
~ correspondi g to 6he positiv eiger~lu ~ et 6he
left boumdary ~a= 0 md 6he negativ eig r~lu ~ct
th right boumdary ~a = I cre set equ~l to :osro, i e,
fori+>Oat~i=0
˘, = t,,p, + t,~u, + t,3v, + t,~w, = 0
fori
[ij =UiUJ = 2K6ij—cuff PK~(2Sij) (18)
where Sij = 2(~;+~)
By Schwartz inequality, it can be shown that
u~uj < 4K2 (19)
Taking square of the both sides of Eqn (18) gives
ru = 43 K + 2(c~fy p~m i Po' Po —2SijSij (20i
A lower bound for ~ is then obtained by combining
Eqns (19) and (20) as
o) > MU ~
(21)
The proportionality factor in Eqn (21) can be taken as
a value in the neighborhood of 2. Different values for
this factor can affect the convergence rate. But once
the convergence is achieved, they all give about the
same solution. The value used in this paper is 2.1.
DESCRIPTION OF EXPERIMENT
As mentioned earlier, the control surface
model consists of a stabilizer, a plain flap and a plain
tab as show in Figure 1. The control surface has
NACA 0018 airfoil sections. Specifically, the tip
chordlength is 8.40 in., root chordlenght is 10.66 in.,
span is 8.44 in.. Both flap and tab gaps are 1/16 in.
with the flap gap widened at both ends. At the root
section, the flap hinge axis is located at 7.63 in. and the
tab hinge axis is at 9.70 in.. The entire control surface
model is mounted on a pedestal to place the model
outside of any test section boundary layer.
The control surface model was tested in the
semi-closed jet test section of the 24 in. water tunnel at
David Taylor Model Basin. The test section is 21 in.
high by 27 in. wide with an area contraction ratio of
8.1. The control surface model was hung vertically
from the top. The strain-gaged stabilizer and flap
dynamometers measured lift, drag, and torque about
their respective hinge axes. The tab dynamometer
measured only torque about its hinge. But since the
tab dynamometer was fastened to the flap, the flap
dynamometer measured the combined loads of the flap
and the tab. The nominal test speed was 10.9 to 12.0
ft/s.
Fig 1. Grid used in the computation of flow over an
NACA 0018 airfoil with flap and tab
l
Based on a mean chordlength of 9.53 in., the Reynolds
number is 9.7 x 105. Forces and moments of the TAC
model under various combinations of the angles of
attack of the stabilizer and the deflections of the flap
and the tab were measured. The angle of attack of the
stabilizer varied from-15 to +15 degrees, flap
deflection from-27 to +27, and the tab deflection from
-60 to +60. The values of lift, drag, and torque
coefficients are based on the mean chordlength.
Corrrections due to blockage, wall, and pedestal were
made. The net blockage effects of the model on
velocity were about 1.2% for the whole range of angles
of attack. The true angle of attack of the model was
3.5% higher than the measured value. The corrected
values will be used for comparison with the computed
results.
DISCUSSION OF RESULTS
Convergence and Grid-Independent Solution
As Computational Fluid Dynamics (CFD)
plays an increasingly important role in practical
engineering applications, it is important to have some
idea about how accurate and reliable the computed
solutions are. It is possible to perform meaningful
error analysis on a simple problem in a Cartesian
computational domain with a uniform grid for inviscid
or laminar flows. However, it is not possible to
analyze the order of accuracy of a spatial discretization
scheme in a highly stretched computational domain in
a curvilinear coordinate system. The situation
becomes much worse with She cdditiorul complication
from turbulence models fffo ts to q mtffy She errors
in tANS computations for practical problemshave
produced dubious re mlts Nes erdreless, attempts mu t
be mad to e tablish co tidence m the RANS
solutions The most import mt thing to do is to assure
that the solution is monotonically convergent But 6 is
is not s fficient it is w ll k ow that c nonphysical
converged sol non canbe obtained For example, one
c m con truct c coarse g id for c turbulent flow Croat c
body with the nondimensional fir t g id normal
di twice to th wall y on the order of several h mdked
md obtain c very nicely converged solution But th
solution will not be close to th reel physics bec mse c
turbulent bo mdary dyer m not be developed for mch
c large y for c cons emmr~l two Equation turbulence
model To resolve this difficulty, c sequence of fi ff
g ids mu t be used ~ til the ch mge in She solution due
to She g id refinement is smell enough to be acceptable
to e gineering req irement Thus c cared I check of
convergence hi tory md mesh refinement to obtain c
g id-mdependent solution are the most effective
approach to establish co fidence in th results ther
researchers es m e g, [23] have adopted c similar
view
A C-g id with four blocks was used in th
computation Th fi st block w ups aro md the enti e
conhol surface, the second block is on top of the
conhol surface, the third covers She gap betw en She
stabili:D:r md the flap md She final block covers the
gap her. en the flap md th tab The water turmel is
not modeled m the computation A total of th ee
meshes w re considered The coarse mesh consists of
112 28x20,44x8x8,8x8x12, md 8x8x12 g id cells for
th first, second, thi d, md fourth block, rerpff tively
This mesh consists of c total of Croat 65K g id cells
Th medi m mesh doubles th member of g id cells in
each curvilinear coordi me direction of each block md
hr. c total m mber of g id cells of Croat half c million
Th fme mesh will have the n mber of g id cells
increased by 50 percent in each direction of ecchblock
of She medi m mesh, gi ing c total m mber of g id
cells of clout 1 6 millions it will be en that the
solution obtained by the tine md She medi m mesh
are almost identical, indicating that c g id mdependent
solution hr3 been achieved
Th bo mdary conditions imposed are the
following The farfleld bo mdary conditions et both
th upper md bWff wakes are zero g cdient for the
thee components of the Cartesi m velocity, She
turbulence q entities r md to md She nonretl - ting
bo mdary condition for the pressure The nom flectmg
bo mdary condition is import mt for go od convergence
md accuracy es mentioned eafliff On She outflow
bo mdary et She top of the computational domain are
imposed fixed values for the 6 ee components of th
Cartesi m velocity, th two turbulence q mtities r md
en md ffO g cdient of the pressure Because of She
presence of She pede till, the symmetric bo mdary
condition is applied et the bottom of the computational
domain Non-slip bo mdary condition for the velocity
md zero g cdient for the pres mre are applied et the
wall bo mdary The turbulent kinetic energy Wishes
et She wall md the dissipation rare et She wall hr. been
described earthy For ocher bo mdaries mch es
betw en g id blocks md She interface betw en She
upper Ed the Has ff wake, exact bo mdary conditions
are applied
Some t pical converg rice histories of the
root-me m-square of pressure for the case without flap
Ed tab deflections Ed She case vifh 20 deg e.
deflections for both flap Ed tab are show m Figure 2,
where residue is defined es She root-me m-square value
of She dime once betw en She cu ant c Scouted
peer de mdthekstcdculatedo o Itcmbesenthat
flap Ed two deflections do not tern to affect
co orgence rate Th residues for both cases dkop
more th m 6 ee orders of magnitude m 200 multig id
cycles The forces Ed moments become tteadv at
about 200 multig id cycles it should be noted Shut She
Fig 2. Root-mean square residue of pressure vs.
muddg id eydes
>:
limp t' tab I'
iii ' ~ 0
mugged Ados
'mS'
200
dkop m the osiduo duo to She multig id sto ting
procedu e has not been mcluded m Figure 2 This
explains why log vend b ) outs at somewhere
h no en I Ed 2, mstead of 0
Forces and Moments
In the following discussion, the medium grid
with a total of about half a million grid cells was used
for the computed results. The grid consists of four
blocks with grid size of 224x56x40, 88x16x16,
1 6x 1 6x24, and 1 6x 1 6x24. The Reynolds number
based on the mean chordlength is 9.7x105. The
coefficients of the forces and moments are also defined
using the mean chordlength as the characteristic
length. The lift and drag coefficients will be defined as
the total forces applied to the entire control surface.
The flap torque coefficient will include both the torque
applied to the flap and the tab while the tab torque
coefficient will include the torque applied to the tab
alone.
Figure 3 shows the comparison between
measurement and computation of the lift coefficient as
the angle of attack of the stabilizer varies from -6 to
+15 degrees with no deflections for both flap and tab.
The error bars on the data show 10% discrepancy in
measurements. The lift coefficient is almost linear
indicating insignificant viscous effect in this range of
angles of attack. Both the predictions by the fine and
the medium grids agree well with the measurement.
However, the coarse grid prediction starts to deviate
form the measurement by more than 10% after an
angle of attack of 9 degrees, indicating insufficient grid
Figure 3. Comparison of calculated and measured
lift coefficients with flap and tab at zero deflection
n
no
0.4
'0.2
-n ~
the drag coefficient is overpredicted by more than 20%
in the neighborhood of the zero angle of attack and
within 10% for greater than 10 degrees. The coarse
grid prediction is even worse, again due to insufficient
grid resolution. The effect on lift coefficient of
varying the flap deflection from-15 degrees to +15
degrees is shown in Figure 5, where angle of attack for
the stern stabilizer remains zero.
Figure 4. Comparison of calculated and measured drag
coefficients with flap and tab at zero deflection
n no
n no
n n4
nn2
v-6
~ Meas. ~
//
,/ ~
~ /~
. ~
0 3 6 9 12 15
stern stabilizer angle (oc)
Fig 5. Comparison of calculated and measured lift
coefficients with stern stabilizer and tab at zero
deflection
-6 -3 0 3 6 9
stern stabilizer angle (oc)
resolution.
12 15
Figure 4 shows the comparison of the drag
coefficient under the conditions as similar to those in
Figure 3. Although a grid independent solution has
been achieved between the fine and the medium grids,
0.6 it ~
0.4:
n
-no
.
-0.4 _
o ,~
1 1 1 1 1
-15 -10 -5 0 5 10 15
flap deflection (a)
A grid independent solution has been
achieved between the fine and the medium grid up to
10 degrees of flap deflection. At 15 degrees of flap
deflection, the fine grid prediction is still within 10%
of the measured values but the medium grid prediction
C' ~ 1
degenerates rapidly. The coarse grid prediction is
inadequate beyond 5 degrees of flap deflection. One
physical feature is worthy of mentioning. Consider a
lift coefficient of 0.2 trig 31. This lift can be achieved
by an angle of attack of slightly less than 6 degrees of
the entire control surface. It can also be achieved by a
flap deflection of about 10 degrees but at a much
smaller torque requirement. This is the essence of
using a flap and also a tab which would be discussed
later.
Finally, the effect on lift, flap torque, and tab
torque coefficients of varying the tab deflection from -
60 degrees to +60 degrees are presented in Figures 6
through 8, respectively. Here, the stabilizer is at zero
angle of attack and the flap has no deflection.
Figure 6. Comparison of calculated and measured
lift coefficients with stern stabilizer and flap at
zero deflection
0.4
0.2
i\
Car O
-0.2
. _
—Leas. //
·~
-0.4
-60 -40
-20 0 20
tab deflection (6t)
40 60
Figure 7. Comparison of calculated and measured
flap torque coefficients with stern stabilizer and
flap at zero deflection
0.03
~
0.02
0.01
O
-0.01
-0.02
A grid independent solution has not been
obtained in the calculation of the lift coefficient as
shown in Figure 6. However, the prediction of the lift
from the fine grid is within 10% of measurement even
at high tab deflection of 60 degrees. There is one
discrepancy when tab deflection is less than 10
degrees. The slope of the measured lift is linear near
zero tab deflection but is not zero. The predicted
slope is almost zero when tab deflection is less than 10
degrees. If the measurement were correct, the
discrepancy could be explained as insufficient grid
resolution around the tab. The small increase in the lift
due to a small tab deflection has not been picked up
even by a grid as large as 1.6 million grid cells. It was
mentioned earlier than a lift coefficient of 0.2 can be
achieved by either an angle of attack of about 6
degrees of the entire control surface or by a flap
deflection of about 10 degrees. This lift can also be
obtained by a tab deflection of 40 degrees with even
smaller tab torque requirement. The comparison of the
flap torque coefficient is shown in Figure 7. It has a
similar characteristic as the lift coefficient shown in
Figure 6. A grid independent solution has not been
achieved at high tab deflection, and the slope near zero
tab deflection is much flatter than the measurement.
The predicted slope of the tab torque coefficient near
zero tab deflection seems to agree better with the
measurement but the predicted torque coefficient at
high tab deflection deviates from the measurement by
more than 10%. It should be noted that the tab torque
coefficient is smaller than the flap torque coefficient
by approximately one order of magnitude. This is the
main reason that the tab assisted control surface is of
great practical interest.
Figure 8. Comparison of calculated and measured
tab torque coefficients with stern stabilizer and
flap at zero deflection
~~"~
Lit
-0.03 0 -4 .o -20 ( ) 20 4 0 0
tab deflection (6t)
0.004
n non
0.002
0.001
~~ O
-0.00 1
-0.002
-0.003 _
-0.004 0 -40
l
\~-t-
:~ ~
_~e _
— — — COE i
——- Me. i
Fin. ~
_:
; IS.
rse
ilum
. ~
Hi\
.
,. ~
I I ~
40 60
-20 0 20
Tab deflection (6t)
CONCLUSIONS
A m mericcl procedure for 6he prediction of
the forces md moments of c tab cssi ted conhol
suricce hcs ben developed The procedure is based
on solving th incompressible Rey olds-avffcged
Navier-Stokes equations coupled with c ~ q
turbulence model Computed results of lif, flcp, md
tab torque coeffcie ts w re compared wi6h the
mecsured data et c R y olds n mbff of 9 7xl05based
on th me m chordieng h Th ee meshes wi6h g id si:D:
of 65K, one hak million, md 1 6 millions w re used to
investigate 6he g id independent sol tion A g id
independent solution was cchieved in mo t of the cases
except for some cases with high flcp md tab
deflections The trend of 6he chmges in th forces md
moments due to 6he varictions in 6he mgle of cttack of
th stabilizer md 6he deflection of 6he flcp md tab hcs
been completely captured ~ mo t cases investigated,
th predictions are wi6hin 10% of the mecsurements
Some exceptiom are 6he tab torque coefhcients et high
t~o deflectiom md the slopes of the lif md flcp torque
coefficients near ffO tab deflection it is suggested
th~t both the turbulence m odel md the g id resolution
need to be improved The fcct 6~t even wi6h c g id es
large es 1 6 million cells, c g id indepff de t sol tion
c m only be cchieved in most, b t not cll cases,
indicates thm more efhcient m mericcl schemes md
turbulence models cre urgently needed D spite cll
th se limitations,6he predictive procedure presented
here is ckecdy c useful tool for 6he desigm of efhcient
conhol surfaces
ACKNOWLEDGMENTS
T is work is f mded by the Of hce of Naval R search,
Code 333, mder 6he Mech~mcs md E ergy
Conversion Science md Techmology Division
PE0602121) D PchickPmtell is the techmiccl
momtor of this prog cm Dr Ngmyen Thmg is the
momtor et David Tcylor Model Bcsin Helpf I
discussions of e periment md mecsured date wi6h Mk
David Bochinski et David Tcylor Model Bcsm are
g ctefully cckmowledged Computff resources
provided by th Department of D fense High
Performarme Computing Modemization Office DOD-
HPCMC) ctNAVO mddhe A ctic R gion
Supercomptmg C nter in Fci b mk, AK are clso
g ctefully cckmowledged
REFERENCES
I AGARD Co ferff e Proceedi gs 515 on "High-
Lif System Aerodynamics", September, 1993
2 Richard I Sears md Robe t B. Liddel, "Wmd-
Tunnel mvestigation of Comol-Suricce Characteristics,
V - A 3 Percent-Chord Plam Flap O 6he NACA 0015
Airfoil" NACA Wartime R port 454, June 1942
3 Whicker, L Foigff md L o F. Fehlner, " Fre-
Stream Characteristics of c Fcmily of Low-Aspect
Rctio, All-Movable Conhol Suricces For Application
to Ship Desigm", David Tcylor Model Bcsm R port
933, December 1958
4 Bow rs, Allen, " Wind Tunnel ~vestigation of th
Characteristics of c Fkpped Control Suricce Mo mted
on c Simulated Submarine Hull", University of
Maryl md Wmd Tunne I R p ort N o 259, June, 1959
5 Ke win, Ju tine E, Philip Mmdel md S. D m
L wis, " A E pffimentcl Study of c Series of Fkpped
Rndders", Journcl of Ship R search, December, 1972
6 Goodkich, G J. mdA F. Molkmd,"WindTurmel
Ir~ tigation of Semi-Bclar~ced Ship Skeg-Rndders",
Th Roycl Imtitute of Na~l A chitects, pp 285-307,
1979
7 Soding, H. "Limits of Potenticl Theo y in Rndder
Flow Predictiom ", Tw nty-Second Symposi m on
Naval Hydkodynamics, Wcshington, D C, pp 264-
276, A mst 9-14, 1998
8 Ch~u, ShieWn, "Computation of Rndder Force md
Moments in Umform Flow", Ship Techmology
R searchVol 45, pp 3-13, 1998
9 Gowmg,Scott,T mgNgmyenmdDavid
Bochinski, "T. A C Test Static R mlts in 6he 24"
Wctff Turmel", NSWC, CD, not yet published, 1999
10 Wilcox, D C, Turbulence Modeli g for CFD,
DCW ~dustries, loc CA, 1993
11 Spezicle, Charles G. "Comparison of E plicit md
Traditiorul Algebraic Shess Models of Turbulence",
A AA Journcl vol. 35, No 9, Septffmber 1997
12 Chorin,A J,"AN mericclMethodforSolving
Incompressible Viscous Flow Problem", Journcl of
Computatiom~l Physics, vol. 2, 275, 1967
1 3 Turkel, E, "Prff onditioned Medhods for Solvmg
th Incompress~ble md Low Speed Compress~ble
Equations", Jourm~l of Computatiom~l Physics, vol. 72,
277, 1987
14 Yee, H. C, "A Ckss of High-Resolution E plicit
md implicit Shock-Ccpturing Methods", NASA
T - hmiccl Memor md m 101088, February, 1989
15 Jcmeson, A, "Time Dependent Calcoktions Using
Multig id wifh App lications to Unstecdy Flows Pc t
Airfoils md Wi gs", A AA 91 -1596, June 1991
16 Liu,C,X 2hengandC H. Sung "Preconditioned
Multig id Methods for Um tecdy Incompress~ble
Flows", Jourm~l of Computatiorurl Phy ics, vol. 139,
35-57, 1998
17 Br mdt, A, "Multig id Techmiques: 1984 G ide,
with Applications to Fluid Dynamics", 1984, 191
pages, ISBN-3-88457-081-1; GMD-St dienNr 85;
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pp 166-201, October 1-4, 1985
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1998
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Conditions for Nonlinear Hyperbolic System", Jourm~l
of Comp tatiorurl Physics, vol 30, pp Z2-237, 1979
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1981
22 S mg, C H ,"A E plicit R mge-Kutta Medhod for
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DISCUSSION
Y Taharc
Oskskc Prefectme University
Jcp m
Inyourcomputation,kmmar-to-t rbulentflow
tr me m on was not considered, Although your
exp rimentcl condition (i e, Red I O ) apparently
implies that theIe exists Icminar-flow region on the
wing (stabilizer m your definition) surface
Inclusion of the effects is generally essential for
accurate prediction of hyd odynamic fmces
especially for d cg component [I thorn et cl,
1993,2000] In addition, the con- emigre two
equation m odel used in your work may not be
suitable for the purpose
REFERENCES:
Taharc, Y. et cl, "An Application of RcNS
Equation Medhod to StruVBulb Co figuration of
Americc's Cup Sailing Yacht Ed Comparison
with E periments," J. Ksmsci Society of Naval
Achitects,No 'Al', f 993, pp 163-171
Taharc, Y. et cl, "Development of Ballast Bulb
for ACC Scilmg Yacht E peciclly for
Ire anti - trion on Basic Low Drag Form," J.
Ksmsci Society of Naval A chitects, No 234,
2000,pp 51-59
AUTHOR'S REPLY
Due to c relatively high turbulence level in c
water tum 1, early experimental tests indicated
that the flow was t rbulent et c Rey olds mmmber
of cutout one million based on c me m
chordlengfh of 9 53 inches For this reason,
computations were made cssummg the fl w was
completely t rbulent Tr msition from Icminar to
turbulence was not considered Admittedly,
turbulence models are not perfect for c complex
flow ouches She one m. e tigatedhere
However, the t - at t rbulence model usedhere
worked quite sati factorily m our opmion it is
believed chat fu ther improvement of accuracy
c mbe made by increasing the grid size,
particularly m the leeward side of the flow
region This will be investigated m the f ture
