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OCR for page 569
The Experimental and Numerical Study of Flow Structure
and Water Noise Caused by Roughness of the Body
Lijin Gao and Lian-cli Zhou
(China Ship Scientific Research Center, P. O. ll6, Wuxi, liangsu 214082, China)
ABSTRACT
It is well known that eddies shed from rough
surface is a main source of water noise. In this paper,
the water noise caused by the roughness of the surface
of the foil (NACA0020) is numerically and
experimentally studied. In the numerical simulation, a
mathematical roughness, which comes from the no-slip
condition of vortex method, is introduced. The
numerical results indicate that the vortex 's shedding
could be avoided under some mathematical roughness.
It corresponds to forward multi-layer in dynamic
phenomena. The experiment tried to find how to realize
the mathematical roughness in physics. The experiment
results showed that certain riblets or slots on the
surface could be related to different kinds of
mathematical roughness.
KEY WORDS: mathematical roughness, FMM,
forward multi-layer, drop off, breakdown
INTRODUCTION
The quieter submarine is very important nowadays.
So how to decrease the noise of the submarine becomes
more and more important. As engine and other noises
have been reduced in these days, the internal noise
levels of many speeding submarines are significantly
affected by the water noise. The main sources of water
noise are as follows: Pressure fluctuations in the
turbulent boundary layer; 2)turbulence-excited wall
vibrations; Teddies generated by surface roughness;
Teddies shed at tail fins.
Drag and water noise all consume energy, so how
to reduce drag and lower water noise are the same thing
in the essence of consuming energy. Surface roughness
has been used to reduce the drag for many years. But
few people make relation of surface roughness with
water noise. Now there exists a new way to reduce drag
and lower water noise, which arranges slots and riblets
on the surface of the body.
Study of viscous drag reduction using riblets has
been a field of significant research during the last
decade. Drag reduction of as much as 4-8% has been
measured in a variety of simple two-dimensional flows
at low speed, see e.g. Coustols & Savill (1992), Choi
(1989), or Sundaram (19924. Riblets with symmetric V
grooves (height equal to spacing) with adhesive-backed
film manufactured by the 3M Company have been
widely used in most early work that has revealed
enormous consistency in the degree of drag reduction
observed as well as many aspects of flow structure.
Coustols (1989 & 1991) reported his results of drag
reduction of 2.7% on LC1OOD airfoil and 6% on an
ONERA D swept airfoil model at or = 0deg
respectively. Caram & Ahmed (1992) studied the near
and intermediate wake region of a NACA0012 airfoil
covered with 3M riblets at or = 0deg . Total drag
reduction determined from the wake survey indicated a
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Vi waah & M kmd (1995) m a supffcritical anfoil
co ffed with 3M riblets have showed skin f iction dLag
reducti m of 6-12% (m 6he t rage of 0 5-ldeg) at
h a sonic Mah m mber
But all 6he aove studies ae focused on te tmg ad
dLag reducti m, 6hffe is little effcrts m 6heory ad
I wffmg watff noise in 6his paff, how to low r the
watff noise level by surfae r mg~mess is mve tigated
he concept of madhematical roug mess is inhoduced,
which deduced fr m 6he no-slip condition of vertex
method he results sh w that mahematical roug~mess
cmld kep in 6he vertex's sheddmg, ad it ca be
c msidered as forward multi-lay r in dy amic
phff omff a (Ga Lijm & 2h m Lia di 2000) But how
to reah:D: 6he mahematical roug~mess m phy ics is a
challenge he expffiment remlts show that certam
r~blet or slot on 6he surfae has some relati m wi6h the
mathematical roug mess
~ 6his papff, 6he i fluence of the roug mess is
mvestigated An adative n mffical scheme, based on
vort:x medhod, is used to solve a time-depff dff t f 11
Na ier-Stokes equati m he aaly es of flow fleld data
ad s md field data mdicate 6hat 6hffe are s me shong
relatims ammg 6he vertical motions ad tructures
associated with the surfae roug~mess he chage of
surfae roug~mess might be a new way to lOWff watff
noise
NUMERICAL METEIOD
he flow was governed by m teady two-
dimffsimal mcompressible Na ier-Stokes equations,
which ca be expressed m 6he vorticity trasfcrmation
as:
~+u Va'=v a'
. `(':,t)=U:(t)
u(~) tU
D
~D
t~
(1)
where u(x,t) was 6he velocity, 0 was 6he vorticity,
V denoted 6he kmffmaticr viscosity, U: was the
velocity of the body, U was 6he i flnite velocity D
was the domam of 6he flow ad gD denoted 6he
bo mday of the d mam Usmg 6he defmiti m of 6he
vorticity ad 6he contmnity (V u = 0 ), it could be
show 6hat u is related to Q) by the following
Poisson equati m:
V ~u = V X a' (2)
he velocity-vorticity formulati m helped m
elimmatmg 6he pressure f om 6he mk ow s of the
equati ms H we ff, fcr b mded d mam it mtrodued
additional c mshams in 6he kmffmaticr of 6he flow fleld
ad req ired the hasformatim of 6he velocity
bo mday c mditi ms to vorticity forms ~ 6his paer,
equati m (1) was d6screted m a Lagragia fi me usmg
particle (vertex) medhods he following formulatim
was used:
d = u(~, t)
ta' = vV ~ a'
dt
whffe, x~ was vorticity-carrying fluid elffments ~
vort :x medhod, 6he vcrticity field was conridffed as a
discrete s m of the md6vidual vorticity flelds of the
particles, having ccre radiuse, shength Eft) ad
a mdi idual dishibuti m of VfftiCity t7(x,t). so:
a'(x,t)=~F,(tf7(x,t)
.=l
Hffe t7(x,t) was deflned as a Dinac Delt f mction m
a board Sff se m 6he n m tadad aalytical spa, the
mteg al of this f mcti m over 6he f 11 spa must be I ~
vort :x medhod, at last 6he following equation w mld be
solved:
(3)
d
dt
I N:~)
2 ~E,KlfX, X;)+uo(~'t)
N:V
(4)
v~lrl r,JGI6/, ,D (s)
dt +v~Hfx'~xm) 3 f~m)
r,fo)=c,fx' ,O)h: i=1,2, ~Nft)
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Representative terms from entire chapter:
boundary condition
Here, UO was the solution of the homogeneous equation
with the no-through boundary condition; K(Z)=ZI~Z~2;
Gf x,t ~ was the Green's function kernel in an
unbounded domain; H(xa,t) was the influence function
of the body surface; Kl~x,t) and Gl~x,t) were the
convolutions of K and G with 77. In vortex
method, the no-slip boundary condition accounted for
the generation of vorticity on the surface of the body.
The surface of the body acted as a source of vorticity
and the task was to relate this vorticity flux on the
surface of the body to the no-slip condition. In the
present formulation, equation (5) were not integrated
simultaneously but instead of a fractional step algorithm
was employed. We solved successively for the
convective and the viscous part of the equations. At
each sub-step the relevant kinematic (no-through) and
dynamic (no-slip) boundary conditions were enforced.
The more information about vortex method could be
seen in Chorin's (1989) and Koumoutsakos's (1994,
1995, 1996~.
The straight forward method of computing the right-
hand side of (5) required o(N29 operations for N vortex
elements. If N was very large, it must be a time-
consuming procedure. This was the N-body problem,
which was how to calculate the interactions among the
N discrete points in a system. It was very important in
the fields of molectroics, celestial mechanics and so on.
Traditionally, it required o(N29 calculation operations,
Barnts-Hut introduced the concept of tree and reduced
the computation to the order of O(NlogN). Now the
FMM (fast multi-pole method) method was introduced
in this paper, and it reduced the work to O(N).
The vortex method based on the FMM was the
main frame of our scheme, called fast vortex method.
Note that the number of particles N was a function of
time. As the particles adapt to resolve the vorticity field
that was guaranteed around the surface of the body was
subsequently convected and diffused. New EXPERI~NT
computation elements were added as needed.
Mathematical roughness
The charge of the roughness was enforced in the
second sub-step of the fractional step. In this paper, the
effect of the flow structure, vortex structure near the
surface of the body and the water noise are observed
when the roughness on the surface of the body was
changed.
After the enforcement of the no-through boundary
condition, a tangential vortex sheet on the surface of
the body could be observed, and the strength was yes) .
The mathematical roughness was introduced by the
following formula:
v—~ s ~ = Loci s ~ 9'(( ~ (6)
an at
here, am / an was the normal vorticity flux on the
surface the body; Xt was the time step of the
fractional method; ok s J was the function which
embodied the influence of the roughness. The function
of s J could be continuous function, constant, discrete
points and so on. In general, different values of orbs)
expressed different roughness of the surface of the
body. It was briefly described below:
o Slip boundary condition;
0~1: Partial-slip boundary condition;
1: Standard no-slip boundary condition;
>1: Backward multi-layer slip boundary condition;
the velocity, BK8103 and BK8105 were used to
measure the pressure fluctuation to get the water noise.
Fig. 1: Equipment of the Experiment
In order to investigate the influence of the
roughness of the surface and how to realize the
mathematical roughness in physics, two models were
considered. One model had normal surface, the other
had rough surface on which some little cylinders of 2-
3mm diameter and 1-2mm height were distributed
orderly. The rough surface model could be shown in
the Fig. 2:
RESULTS
Fig. 2: Model of Roughness Surface
To investigate the influence of roughness, four
cases were calculated under the same Reynolds number
about 105. In the experiment, horizontal velocities were
measured by LDV at several velocity sections. The
horizontal velocities were given in this paper at these
same sections. The numerical and experimental
horizontal velocities were compared in Fig. 3-Fig. 6. In
these figures, (a) described the numerical velocity field,
(b) described the experimental velocity field.
0.06
0.05
0.04
0.03
0.02
0.01 _
o
0.05 0 0.05 0.1
(a) Numerical velocity field with oc( s ~ = 1.0
(b) Experiment velocity field with normal roughness
Fig. 3: Velocity field compared at 0° attack angle
~ full wing with normal roughness)
0.06
0.04
0.02
~ l
- o . s
, s , ~
~0.05
s
(a) Numerical velocity field with oc( s ) = 1.5
0.06
0.04~
= ,,,,
..
. .
. o Js
me, s
,~ . ~
a. .
I I I I I I
0 -0.05 0
.. ~ ~
. . a , .
0. . .
`~ ~` ;
I Or
0.05
. ..
. ~
, , , I
0.1
(b) Experiment velocity field with relative roughness
Fig. 4: Velocity field compared at 0° attack angle
~ full wing with relative roughness)
0.1
0.08
0.06
0.04
0.02
o
-0.02
. ~ ,.
-0.04
, . . . , . . . . , . . . . , . . . . , . . . . ,
-0.05 0 0.05 0.1 0.15
(a) Numerical velocity field with oc( s ) = 1.0
0.1 r
0.05 ~
O
= =
_ ~9 ~ Her
Ox' l l l l l l l l l l l l l l l l l l l l l l l l
- `7~ -0.05 0 0.05 0.1 0.15
x
(b) Experiment velocity field with normal roughness
Fig. 5: Velocity field compared at 15° attack angle
(full wing with normal roughness)
0.1~
0.05 t
of
---9 ~ ~ ~ ~ 'a
W. - ~ = _=
~ ~9 ~ ~._`g~ .. ----2
-0.05 0 0.05 0.1 0.15
(a) Numerical velocity field with oc( s ) = 1.5
O.lr
0.05
O
-----9 -----9
~ 9
I. —9
.___9 _-- -
.____9
l l l l l l l l l l l l l l l l l l l l l
-0.05 0 0.05 0.1 0.15
(b) Experiment velocity field with relative roughness
Fig. 6: Velocity field compared at 15° attack angle
~ full wing with relative roughness)
In Fig. 3, a 0° attack angle foil with normal
roughness (no-slip boundary condition) was
investigated. The results show that the computed
velocity field agrees with the experimental ones. In Fig.
4, a 0° attack angle foil with relative roughness, which
was used in experiment, was investigated. The
mathematical roughness of or(s)=l.S corresponded
to the relative roughness in the experiment. The
boundary layer thickened because of the relative
roughness under 0° attack angle. In Fig. 5, a 15° attack
angle foil with normal roughness (no-slip boundary
condition) was investigated. The results show that the
computed velocity field agrees with the experimental
results. In Fig. 6, a 15° attack angle foil with relative
roughness, which was used in the experiment, was
investigated. The mathematics roughness of
oc( s ) = 1.5 corresponds to the relative roughness in the
experiment. The results indicated that the separation of
the flow was strengthened and the seperated position
moved ahead. It means that the positive mathematical
roughness (backward multi-layer slip boundary
condition) made the breakdown of vortex appear early.
But the numerical flow field did not agree with the
experiment well. There were some problems in the
experiment.
Fig. 7-Fig. 10 describe the vortex structure in four
different cases. In these figures, (a) and (b) describe the
unsteady vortex structure of same case.
w~/is
.~ ~
~~ Ace Ace Use ~~ ~ ~ ~ ~~ ~~ ~
As
~ ~.~
~~.~
~4 . ~ ~ ~ . W.= ~ . ~ ~ . ~ ~ ~ W.~ ~ A ~ ~ ~ . ~ ~ ~ . ~ ~ . ~~
(a) t=1.65s
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ Lit
=
Age . , 95
~ .~?
WOOD
~~ tW~ ~0 ~
X X
(b) t=2.25s
Fig. 7: Vorticity contours at 0° attack angle with
~( s ) = 1.0
Its Retie? air ~~ ~~ Oxi ~ exit O. - O.
Jew ~ ~ o.
~.~1 ~ worm ~ ~
me. - woo -
~ . ~ ~ ~ . W.= ~ . ~ ~ . ~ ~ ~ We ~ A ~ ~ ~ A ~ ~ ~ . ~ ~ . ~~ ,
~ R ~
Warm
(a) t=l.65s
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 2 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ X ~ ~ X ~~
n~uw ~ WWW~ ~~ ~ ~ ~] ~
~~/~ do/ ~
~ . ~ ~ ~ . We ~ . ~ ~ ~ ~ ~ ~ ~ We ~ . ~ ~ ~ A ~ ~ . ~ ~ . ~
(b) t=2.25s
Fig. 8: Vorticity contours at 0° attack angle with
orLs)=l.S
wax ~ ~ ~~ ~~ ~ ~'~ ~4 ~ it. ~ ~ is. ~ ~ ~~= ~~
e ~ ....................................................................................................................................................................................
~ ~ i~ ~~ W~,~ ~.m ~.~ ~ i~ ~ i? ~~=
(a) t=1.95s
~ ~ ~ ~ ~ ~ ~ ~ X ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ X ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
r-
, ~W
WW
~WW
,
.
Wit,= ~
A
.... ...
.A at, ~ ~ W at, ~ W ~ ~ ~ ~ at, ~ at, ~ ~ ~ . ~ ~ ~ . ~ ~ ~ . ~ ~ A
(b) t=2.55s
Fig. 9: Vorticity contours at 15° attack angle
withoc( s ) = 1.0
S?3R ~ ~ ~X~ it/ >= ~, ~ ~, ~ it. ~ ~ it. ~ ~ ~~= ~~
as, i
.
~.m ~.~ 3~ i
(a) t=1.95s
~9..~<
~~ warm me ~~ ~~
~~ -
(b) t=2.55s
Fig. 10: Vorticity contours at 15° attack angle with
orLs)=l.S
In Fig. 7 and Fig. 9, a Karman vortex structure
was observed under normal roughness under 0° and 15°
attack angle repectively. In Fig. 8, it shows that the
vortex structure was decreased under mathematical
roughness of or(s)=l.S at 0° attack angle.In FiglO,
the mathematical roughness of oc( s ~ = 1.5 made the
vortex strengthen and the breakdown of vortex appear
early.
Fig. 11 describes the numerical water noise under
15° attack angle in different mathematical roughness.
The positive mathematical roughness increases the
water noise.
55:
50:
45
m
40
35
30
i' J: V:
. , · . · .
0 5 10
X-Hz
(a) a( s ~ = 1.0
~ - in-\,,\
j . j
15 20
Intffnational Co fffff e m D ag R ducti m, A M
Savil cd, Applied Scientiflc R search, Vol. 46, No 3,
Kluwer Acadffmic, Norw 11, MA, 1989
E. Comtols, 'Pfffermance of Intemal Mmipulators m
Subsonic Th ee Dimensi mal Fl ws', R cent
Developments m Turbulff cc M magements, K S. Choi
cd, Vol. 6, Kluwer Academic, Nerw 11, MA, pp 43-64,
1991
J.M. Caram & A. Ahmed, 'D velopment of W kc of
m Al foil with Riblets', A AA Journal, Vol 30, No 1 4
pp 2817-2818, 1992
E. Coustols & V Sehmdit, 'Sy 6hesis of Expffimenta
Riblet St dies m Trmsmic Cmditims', Turbulffce
C mhol by Passive M ms, edited by E C mstols,
Kluwer Acadffmic, Dordkecht, The Nethfflmds, pp
123-140, 1990
PR. Vrswanath & R Mukund, 'Turbulent D ag
R duetion Using Rblets on Supfferitical Al foil t
Tr msonic Speeds', A AA Journal, Vol. 33, No 5, pp
945-947, 1995
Gao Lijin & Zhou Liandfl, '6he N mffical ffudy of
6he h fluenee on 6he Fl w Shucture c msed by
Roughmess of 6he Cylmder', Jo mal of Hydkody amics,
Ser B. to be published
Gao Lijin & Zhou Liandfl, 'The N mffical St dy of
Watff Noise Cmsed by Roughness', 4~ h tffn tional
C mferff cc on Hydkody amics, Y kaham3 Jap m, Sep
2000
A.J. Chor4 'C mputatimal Fluid Mechmics
Seiffted Papers', Academic P ess h c, 1989
Dhg Li & AUen T. Chwang 'Time d mam maly is
of ship-generated waves in habor usmg a fast
hierarchical medhod', ISOPE'97, Hawaii, 1997
Gao Lijin & Zhou Liamdfl, 'N merical Study of 6he
Mech ml m of Watff Noise Gff ffati m usmg the F ff
Vort:x M 6hod', ICHD'98, 1998
L. Greengard & V RokhNn, 'A fast algori6 m for
particle simulati ms', Journal of Computational Phy ics
73, pp 325-348, 1987
P. Koumoutsakos, A. Leonard, F. Pep4 'B mdary
C mditi m fer Viscous Vertex Methods', Journal of
36 1 o 5 io 15 20
XHZ
(b) ~(s)= ~ 5
Fig 11: Watff noise mdff 150 attak mgle
CONCLUSION
The n merical md expffimental remits show 6hat
6he mhodueed mathffmatical roug~mess cm be
cerresponded by 6he real phy ical roug~mess md could
be used as usef I tool in irwestigati m of reduemg noise
The positive mathematical roughmess m kes 6he water
noise e haneed, md a negative mathffmatical
roughness might redua: 6he watff noise (Gao Lidm &
2hm Limd6 2000) How to realize the negative
mathem tical roug~mess m phy ics will be fmthff
st died
REFERENCE
E. Coustols & A.M. SavU, 'Turbulent Skin Fricti m
D 3gR ductionbyActive mdPassiveMems', Spffiai
Course m Skm Friction D 3g R duction, AGARD
R pt. 786, Lond m, pp 8 1 -8 80, Mach 1992
K.S. Choi, 'Nea Wall ffruetmes of a Turbulff t
Bo mday Lay r wi6h Riblets', Journal of Fhid
M - h mics, Vol. 208, pp 417-458, 1989
S. Smmdaram & PR Vrswanath, 'Study m Turbulent
D 3g R dueti m Usmg Rblets on a Flat Plate',
Nati mal Affon mtical L:~, NAL R pt PDEA 9209,
B mgalore, h di3 Nov 1992
E. Comtols, 'C mhol of Turbulff e by Intffnal md
E tffnai Mmipulators', P oeeedings of 4~
Comput tional Thy ics (1994a), Vol. 113, pp 52-61,
1994
P. Koumoutsakos & A. Leonard, 'High-resoluti m
simulati ms of the flow aro md a impulsively started
cylinderusmgvort:xmedhod',J Fl idMech,Vol 296,
pp 1-38, 1995
P. Koumoutsakos & D. Stdels, 'Simulations of the
viscous flow normal to a impulsively stated ad
miformly aceiffated flat pi be', J. Fhid M- h, Vol
328, pp 177-227, 1996
A. Powell, 'cheery of Vortex So md', J. Ac m tic ~ .
Am 36, pp 177-195, 1969
Dr. Ulderico"Paolo" Bulgarelli
Institute Nazionale per Studied
Architettura Navale
Via di Vallerano 139
00128 Rome
Italy
Tel: +39-6-50299-270/222
Fax: +39-6-5070619
E-mail: ~~os3.insean.~t
Esperienze di
Prof. Luis Perez-Rojas
Escuela Tecuica Superior de Ingenieros Navales
Avda Arco de la Victoria S/N
28040 Madrid
SPAIN
Tel: +3491-3367154
Fax: +3491-5442149
E-mail: ~pm cs
Prof. Toshio Suzuki
Osaka University
Department of Naval Architecture & Ocean Eng.
2-1 Yamadaoka, Suita
Osaka 565-0871, Japan
Tel: +8168797579
Fax: +8168797594
E-mail: ~_p
L is Perez Rojas
Escuek Tecnics Superior de in emeros Nsvales
I really con rsmh~e to the mthors for His intere ting
paper that is dewing with s topic, the roughmess, that
need s very deep study as it was stated m 22~d ITTC I
(1) Neve theless, I would lik to indicate some
comment sod questions
The roughmess is represented in this paper by the
f notion o(s) Ed its action is expressed in the
boundary condition, equation (6) of the paper Do the
Abhors thi k fhst this expression is enough for
representing the effect of roughmess ch mgmg the
velocity Ed turbulence distribution near the body
so face as it was stated by Pstel (2)? Do you fhmk
Nat this model is capable of de ~ mg the th ee
roughmess regimes, smely. hyd odynamically
mooch, tr msitiomal Ed full-rough surfaces?
The figure 3 of the paper represents She st mdard no-
slip boundary condition, both figures (a) Ed .1)
seems not verify this condition A e the
measurements done m the experime tal work only
outside the boundary Bye ?
In order to evaluate the validation of the mmmerical
calculation with the experimental work, the
uncertainty assessment must be done as it is indicated
by the Resistance Committee of the ITTC (1), based 4
m the AIAA St mdard (3) In His aspect, has been
done my uncertainty malysis not only in the
experimental data but also in the mmmerical results ?
In the conclusion of the paper, the positive
mathematical roughmess is related with m increasing
water noise what c m conduct to s decreasing water
noise f ough s negative mathematical roughmess
C m it be considered that this negative mathtmati al
roughmess is related to smoother surfaces f m what is
deflnedbythe mthorsssnormal roughmess?
REFERENCES.
I ITTC, 'Report of She Resistmce Committee",
Proceedings of the 22 Intermstiorul Towing Tank
Co ference, Seoul, Kmes & Shmghai, Chime, 1999,
pp 174 -131
2 Pstel, V C "Plow at High Rey olds Nmmber Ed
over Rough Surfaces Achilles Heel of CPD"
ASIDE J. Fluid Er~meenne, Vol. 102, 1995
3 A AA, "Assessment of Wind,Tum I Dots
O A AA, AW~WIlWfU Ul W
Uncertainty" A AA 5-071-1995
AUTHOR'S REPLY
Thsnl.s for ProfessorLuis Perez Rojas's comments
Yes, She qustion (6) can be used to represent
the effect of roughmess as Pstel stated By using
proper so tex Dyers near wall, th model c m
describe deference surface roughness regimes
As Pstel's definition, different y represent
different surface roughmess, which tie I eon me the
strength of the vortex layer near wall So w
c m get the following conclusion that,
hydrodynamically smooth regime:
y+<5 0~o(s)=1 0
h msitiomsl Ed full-rough surfaces:
y+>50~o(s)>1 0
2 One-dbmensiomr1 LDV was used to measure She
hori ontal velocity, which could not get the
velocity m She boundary layer We only
compared She velocity at She points where She
experimental velocities w re achieved
3 E cmse of She time, we haven't made
uncertainty analysis about our mmmerical
method How ver we will do this work latter
The negative mathematical roughmess is not
rented to smoother surfaces th m normal rough
su face The smoother rough su faces
correspond to o < c
