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

ABSTRACT: The calculation of a hydrodynamic profile for a fluid that flows around mainly consists in de-

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.