International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 5
Number 4
December 2011
483
1 INTRODUCTION
The main objectives of the paper are: to see how the
experimental and numerical calculations of a hydro-
dynamic profile match, to identify the reasons for
which data are not concurring and to also see wheth-
er we can use numerical methods for designing or
pre-designing purposes.
Calculation of hydrodynamic profile belongs to
the engineering field, where we can use three main
directions of investigation: an experimental method,
a numerical method and an analytical method. In our
case, it is very difficult to use the analytical method
because the fluid flow as described by Navier-Stokes
equations has not been yet solved analytically.
Therefore calculating the forces acting on a
hydrodynamic profile can be solved using one of the
two methods mentioned above: the experimental and
the numerical method. The results in this case are
not very precise because in problem statement some
simplifying assumptions, specific to our domain,
have been considered by default. (OANŢĂ, 2009)
Numerical methods most generally used by com-
putational software are: the finite element method,
the finite difference method, the boundary element
method and the finite volume method. ANSYS 13
uses finite element and finite volume method.
Since software using numerical methods for
solving engineering problems of varying difficulty
and providing satisfactory results, have emerged in
the past 15 years, most problems have been solved
by the experimental method. Therefore the approach
proposed in this paper by comparing the two meth-
ods try to present more clearly the physical phenom-
enon investigated and the differences between the
two methods.
To study the coefficients
x
C
(drag coefficient) and
y
C
(lift coefficient), we must remark at first that in
the phenomenon of fluid flow around a wing, one of
physical quantities, i.e. the force (lift force or drag
force), is a variable size depending on the incidence
angle
α
. Therefore, it can be said that the process
under study is a nonlinear one. The
Π
theorem ap-
plies both to linear phenomena and nonlinear phe-
nomena.
Let’s analyze the similarity of the simple nonline-
ar process (one size variable), described by the im-
plicit function (DINU, 1994):
0),,,,,,,,( =Γ
ατρ
pRlcvf
(1)
where the force R, is a function of α :
)(
1
α
fR =
(2)
In relation (1):
ρ - fluid density;
v - fluid velocity;
Γ - velocity circulation,
p - fluid pressure;
Experimental and Numerical Methods for
Hydrodynamic Profiles Calculation
A. Scupi & D. Dinu
Constanta Maritime University
termining the variation of drag force and lift force. Thus, for NACA 6412 profile, we will calculate and com-
pare the changes of values of the coefficient forces mentioned above. The calculation will be done both exper-
imentally in a naval wind tunnel and with a computational fluid dynamics - CFD (ANSYS 13). These
experimental and numerical approaches can be used to study finite scale naval profiles such as the rudder.
484
τ - period of swirl separation;
c
- chord length;
l
- wing span.
Nonlinear dependence expressed by equation (1)
is a curve obtained experimentally. Its equation is
obtained by putting the condition that the power
polynomial has the form:
n
n
kkkkR
ααα
++++= ...
2
210
(3)
and the polynomial should be verified by some ex-
perimental points. The experimental points can be
determined both experimentally and by using a fluid
flow modeling program.
2 WORKING PARAMETERS
We considered a NACA 6412 profile with a relative
elongation 6 with the following characteristics:
− the length of the chord equal to 0.080 [m];
− the wing span equal to 0.480[m].
The profile (Fig. 1) is located in an air stream
with a velocity of 15 m/s. The Reynolds number cal-
culated with formula (4) has the value of 85.000.
υ
cv ⋅
=Re
(4)
where:
v = fluid velocity m/s;
c = chord length m;
υ = cinematic viscosity m
2
/s.
The angles of incidence are (Fig. 1):
- -10
0
÷ 0
0
step 2
0
;
- +0
0
÷ 15
0
step 3
0
;
The forces that are acting upon a hydrodynamic
and aerodynamic profile are: the lift force and the
friction force or force due to boundary layer de-
tachment. These forces give a resultant force R
which decomposes by the direction of velocity at in-
finity and by a direction perpendicular to it. R
x
com-
ponent is called drag force and R
y
component is
called lift force.
R force can also be decomposed by the direction
of chord (component R
t
- called tangential force) and
by the direction perpendicular to the chord (R
n
com-
ponent – called normal force). (DINU, 2010)
Figure 1. General representation of the profile
3 EXPERIMENTAL DETERMINATION OF THE
AERODYNAMIC FORCES
Experiments were made in a naval aerodynamic tun-
nel. Airflow was uniform on a section of 510 × 580
mm.
A tensometric balance was used to determine the
forces acting upon the wing. Results of tests are giv-
en in Table 1.
Table 1. Results of experiments
___________________________________________________
Results R
x
C
x
R
y
C
y
_____________
Incidence angles N N
___________________________________________________
α = -10
0
1.2134 0.2293 -1.80246 -0.3406
α = -8
0
0.8567 0.1619 -1.69714 -0.3207
α = -6
0
0.6620 0.1251 -1.31877 -0.2492
α = -4
0
0.5069 0.0958 -0.95679 -0.1808
α = -2
0
0.4212 0.0796 0.16511 0.0312
α = 0
0
0.4503 0.0851 2.16284 0.4087
α = +3
0
0.6884 0.1301 5.432238 1.0265
α = +6
0
0.9679 0.1829 8.198366 1.5492
α = +9
0
1.4558 0.2751 10.10931 1.9103
α = +12
0
2.0125 0.3803 11.37568 2.1496
α = +15
0
2.7528 0.5202 12.2255 2.3102
___________________________________________________
In Fig. 2 and Fig. 3 we have represented the
graphics of the function C
y
(α) and C
x
(α), respective-
ly.
485
Figure 2. Graphic of C
y
experimentally obtained
Figure 3. Graphic of C
x
experimentally obtained
4 DETERMINATION OF THE AERODYNAMIC
FORCES USING CFD
4.1 NACA 6412 profile
Using Design Modeler v. 13.0, we were able to ac-
curately reproduce the NACA 6412 profile, as repre-
sented in figure 4. Airflow was uniform on a bigger
section 980 × 511 mm.
Figure. 4 Geometric representation of the NACA 6412 pro-
file
4.2 Profile discretization
After the geometric representation of NACA profile,
we went to its discretization, as shown in Fig. 5.
Figure 5. Profile discretization
We discretized the NACA profile in more than 10
million cells, of which 9 million are hexahedrons,
55.000 are wedges, 35.000 are polyhedral, 1500 are
pyramids and only 400 are tetrahedrons. The mesh
has also over 30 million faces and 11 million knots.
4.3 Calculation of the aerodynamic forces
Using Fluent program version 13.0, we set the
boundary conditions as follows:
− The profile is attacked with a velocity of 10 m/s,
under different angles, namely -10
0
, -8
0
, -6
0
, -4
0
, -
2
0
, 0
0
, +3
0
, +6
0
, +9
0
, +12
0
, +15
0
;
− Behind the profile, atmospheric pressure is equal
to 101325 Pa.
− The fluid motion is turbulent with a Prandtl num-
ber equal to 0.667.
− The air density is considered constant and it is
equal to 1.225 kg/m
3
;
− The air dynamic and cinematic viscosity are also
considered constant and are equal to 1.7894×10
-5
kg/ms, 0.0001460735 m
2
/s, respectively;
− The turbulence viscosity ratio is set to 10.
Process has stabilized after 208 iterations allow-
ing us to visualize the values of drag and lift forces
and their coefficients, presented in table 2.
Table 2. Results using CFD
___________________________________________________
Results R
x
C
x
R
y
C
y
_____________
Incidence angles N N
___________________________________________________
α = -10
0
0.4536 0.0857 -1.5145 -0.2862
α = -8
0
0.3606 0.0681 -0.8234 -0.1556
α = -6
0
0.2819 0.0532 -0.4900 -0.0926
α = -4
0
0.2616 0.0494 -0.1756 -0.0332
α = -2
0
0.2529 0.0477 0.1582 0.0299
α = 0
0
0.2683 0.0506 2.1501 0.4063
α = +3
0
0.3402 0.0642 5.3861 1.0178
α = +6
0
0.4604 0.0869 8.0507 1.5213
α = +9
0
0.6160 0.1164 9.4658 1.7887
α = +12
0
0.8447 0.1596 10.4375 1.9723
α = +15
0
1.1043 0.2086 11.3418 2.1432
___________________________________________________
486
In the Fig. 6 and Fig. 7 we have represented the
graphics of the function C
y
(α) and C
x
(α), respective-
ly.
Figure 6. Graphic of C
y
obtained using CFD
Figure 7. Graphic of C
x
obtained using CFD
5 CONCLUSIONS
Comparing the C
y
coefficients values obtained by
experiment and using CFD, we can make the obser-
vation that they are very similar in a the field of the
incidence angles [-2
0
,6
0
]. Also, comparing the C
x
graphic, we remark that the graphics are very simi-
lar, but between the values there are some differ-
ences.
These differences are due to experimental errors
(errors of measurement devices), numerical errors
(rounding errors), and also discretization errors.
Also, the CFD programme doesn’t take into ac-
count the induce resistance in the case of finite span
wings. As a consequence an induce angle α
i
will
appear which thus decreases the incidence angle α.
The alteration of direction and value of velocity
bring about the corresponding alteration of lift force,
which is perpendicular on the direction of stream ve-
locity. (DINU, 1999)
In order to reduce these differences, it is recom-
mended that the object of study be discretized into a
larger number of cells. It is also advisable to leave
out some simplifying conditions, and to impose var-
ious other conditions that simulate reality to a better
precision (e.g. energy equations, air compressibil-
ity).
CFD can replace the experiment within certain
limits, being a good method for pre-designing.
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x
şi C
y
de la model la
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