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Ser.B, 2007,19(1):121-126

EXPERIMENTS ON HYDRODYNAMIC INTERACTION BETWEEN 3-D OVAL AND WALL*

SUN Ke, SHENG Qi-hu, ZHANG Liang, LI Feng-lai College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China, E-mail: sunke@hrbeu.edu.cn (Received September 26, 2005; Revised September 15, 2006) ABSTRACT: The boundary hydrodynamic interaction of a 3-D oval body was experimentally surveyed for different cases. The regression method was employed to find the experimental formulae of hydrodynamic coefficients relating to the attack angle, clearance to wall, and moving speed. The mechanism of interaction was discussed. The experimental results show that there exists a lifting effect, similar to wings in flow. The lifting effect is remarkable. The boundary hydrodynamic interaction of the small aspect ratio model is almost linearly dependent on the attack angle, but the effect of the moving speed of the body on the hydrodynamic coefficients is very small. The effect of clearance is related to the geometric shape. The boundary hydrodynamic interaction always enhances the lifting effect if the clearance is small. KEY WORDS: hydrodynamic coefficient, model experiment, boundary interaction, oval 1. INTRODUCTION

The hydrodynamic interaction among bodies in fluid flows is of great importance in some engineering applications, such as, the collision between floating ice and offshore structures, the encounter of two ships, the high speed movement of underwater vehicles [1], the near-sea flight of WIG vehicles, and so on. Hence the prediction of hydrodynamic interaction is of basic significance. Experimental research is necessary because of the complexity of this phenomenon.

For the head encounter movement of two marine vessels in rectangle section canals, O’Dea and Fisher [2] and Cohen and Beck [3] presented some experimental results. For simulating the environment

of the Panama Canal, SSPA [4] investigated the interactions of ships with the plane bottom of the inclined side of the canal. Kazi, Chwang, and Yates [5] reported the results of the hydrodynamic interaction tests between a floating cylinder and a fixed cylinder, where six different moving cylinders with circular, square, and rectangular cross-sections, with varying length- width-ratio were examined. Alam et al. [6], measured the dynamic interaction of two circular cylinders in a tandem arrangement, in uniform flow, in a wind tunnel at the Reynolds number Re = 6.5 × 104. Kumar [7, 8], studied the ground effect of wings. Zhan et al. [9], studied the force exerted on a near-wall circular cylinder. Zhang et al. [10], surveyed the boundary hydrodynamic interaction of a 2-D oval body. However, experiments on the boundary hydrodynamic interaction of a flat body with blunt ends have been seldom seen.

In this study, the boundary hydrodynamic interaction of a 3-D small width–length ratio body is investigated. A symmetric oval body is examined to avoid the influence of irregular shape effects on the measurement. The mechanism of boundary hydrodynamic interaction of 3-D is elucidated. 2. MODEL TESTS

The models of an oval-section rotor and a flat body were employed to survey the hydrodynamic interactions between the model and the wall. The dimensions of the rotor model were L × B × H = 1120 mm × 160 mm × 160 mm, and those of flat model L ×

* Biography: SUN Ke(1978-),Female, Ph. D.

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B × H = 1120 mm × 346 mm × 160 mm. The flat body was structured in the following way: splitting the rotor model along the axial surface, and connecting the two parts with a column. The wall consisted of a wood plate with the dimensions L × B = 3000 mm × 1500

mm. The breadth–length ratio is defined as LB

λ = .

The experiment was carried out in a towing tank. The temperature of the water was T = 19.3oC, the density of water ρ = 998.255 kgm-3, the kinematic viscosity . The geometrical, kinematic, and dynamic similarities were ensured in this experiment. The model was fixed on the towing vessel with a rigid bar. The balance was placed in the model and was waterproofed by soft material. The weight of the model was adjusted to keep the gravity and buoy balanced. The clearance between the model and the wall could be adjusted by special tools.

6 2 11 0466 10 m s.ν −= × −

Fig.1 Coordinate system

The hydrodynamic forces for the cases with

different clearances, speeds, and attack angles were measured in this experiment. The hydrodynamic forces exerting on the model, moving in unbounded flow, were also measured for reference [11]. A model-fixed, right-hand, coordinate system was adopted here. The axial planes were three symmetric planes of the model. The X-axis was along the longitudinal direction and pointed ahead. The angle between the X-axis and the moving direction was defined as the attack angle α . The Z-axis was along the vertical direction and pointed to the wall (see Fig. 1). The hydrodynamic force acting on the model was taken as (X, Y, Z) and the moment as (MX, MY, MZ). However, only X, Z, and MY were significant. The moment, component MY, was replaced by M for convenience. The force (or moment) coefficients were defined as follows:

The longitudinal force coefficient:

LBU

XC X2

21 ρ

= (1)

The vertical force coefficient:

LBU

ZCz2

21 ρ

= (2)

The moment coefficient:

BLU

MCM22

21 ρ

= (3)

3. EXPERIMENTAL DATA

Experimental results show that the hydrodynamic coefficients at different speeds (but with the same attack angle and clearance) are very close, which means that the hydrodynamic coefficients mainly depend on attack angle and clearance. Figs. 2 - 7 indicate that the hydrodynamic coefficients depend linearly on the attack angle, except in the case where the flat model is very close to the wall. So it is assumed that the hydrodynamic force can be expressed as

20 1 2( ) ( ) ( ) ,xC X h X h X hα α= + +

2

0 1 2( ) ( ) ( ) ,ZC Z h Z h Z hα α= + +

20 1 2( ) ( ) ( )MC M h M h M hα α= + + (4)

where the nondimensional clearance, hhL

= , and the

unit of attack angle is radian. By using the curves for the hydrodynamic coefficients versus the attack angle, all the hydrodynamic derivatives at different clearances can be calculated. The nondimensional clearance h varies from zero to infinity and is not suitable to be directly analyzed. Hence an arc tangent transformation is introduced as follows:

hKh 1tan2 −=′π

(5)

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where K is a constant depending on the model shape. The hydrodynamic derivatives can be given as

follows. (1) For the rotor model: the constant K = 20, and

the coefficients are

3 20 ( ) 0.0125 0.01817X h h h′ ′= − + −′

′

0 00162 0 02169. h .′ − (6a)

3 21( ) 0 29598 0.3139Z h . h h′ ′= − + +

0 08855 0 34938. h .′ − (6b)

4 3

0 ( ) 0.0753 0.0142Z h h′ ′= − + −h 20.0899 0.0341 0.0092h h′+ − (6c)

3 2

0 ( ) 0.0056 0.0031M h h′ ′= − + +h

′

′ +

2′ −

′ +

0.0035 0.0006h′ − (6d)

3 21( ) 0.36918 0.082788M h h h′ ′= − + −

0.57278 0.24807h′ + (6e)

02221 ==== MZXX (6f)

(2) For the flat model: the constant K = 10, and

the coefficients are

3 20 ( ) 0.08668 0.15309X h h h′ ′= −

0.10169 0.08071 h′ − (7a)

4 30 ( ) 0 3425 1.0231 1 1162Z h . h h . h′ ′ ′= − + 0 (7b) 5265 0 0913. h .′ +

3 2

1( ) 1.1099 3.5643Z h h h′ ′= −

3.7336 2.3522h′ − (7c)

4 30 ( ) 0 1915 0 3735M h . h . h′ ′= − + −′

′

20 2618 0 0785 0 0016. h . h .′ ′+ − (7d)

3 21( ) 0.1809 1.0688M h h h′ ′= − + −

1.3309 0.9790h′ + (7e)

02221 ==== MZXX (7f)

4. ANALYSIS OF EXPERIMENTAL RESULTS

The experimental results show that the hydrodynamic coefficients mainly depend on the attack angle and the clearance. 4.1 The influence of attack angle

Figs. 2 - 7 exhibit the experimental data for the flat body (U4-B), and the rotor body (U4-C), in different states. The experimental results show that the hydrodynamic coefficients depend linearly on the attack angle except the case where the flat model is very close to the wall. The longitudinal coefficient varies slightly when the attack angle changes. When the attack angle is positive, the vertical force coefficient is negative and the moment coefficient is positive. It means that a lifting force perpendicular to the moving direction exists when the attack angle is not zero, even if the model surface is pointless. The focus of lifting force is defined as

dddd

M

fZ

C

x Cα

α

= − (8)

The focus of rotor model is 0.486- 0.60, and

that of flat model is − −

−0.45- 0.49. Different from the 3-D airfoil, the focus of the model is at or in front of the body.

−

Fig.2 Experimental data for a flat body in unbounded flow 4.2 The influence of clearance

Figure 8 gives the longitudinal force, coefficient CX, for the two models, at different attack angles. It shows that CX is always negative, and its strength increases when the model is close to the wall.

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Fig.3 Experimental data for a flat body with hL

= 0.21

Fig.4 Experimental data for a flat body with hL

= 0.075

Fig.5 Experimental data for rotor body in unbounded flow

Fig.6 Experimental data for rotor body with hL

= 0.21

Figure 9 shows the vertical force coefficient CZ

for the two models at different attack angles. When the attack angle is zero, the model is in a nonlifting state. In this case, the vertical force coefficient is relatively small. The experimental results show that there is positive vertical force acting on the flat model

when hL< 0.08, which increases with decreasing

clearance. It means that the wall attracts the flat model.

However, the case for the vertical force coefficient of the rotor model is more complicated. It becomes

negative when 0.075hL< . The result is doubtful

because the value of CZ may be as large as the measuring error.

Fig.7 Experimental data for rotor body with hL

= 0.075

Fig.8 Comparison of CX for two models

Fig. 9 Comparison of CZ for two models

When the attack angle is not zero, there is lifting

force acting on the model. The lifting force is proportional to the attack angle. Its value changes with the clearance at the same attack angle. Different models have different rules according to their breadth–length ratio. For the rotor model, the breadth–length ratio is very small, The lifting force

approaches its smallest value at hL

= 0.21. For the

2-D model [10], the lifting force always linearly

increases (hL

> 0.22) when the clearance becomes

small. For the flat model, the lifting force keeps

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constant if hL

> 0.21, and increases when clearance

becomes small if hL

< 0.21.

Fig.10 CZ for rotor, flat, and 2-D models at α =5° 4.3 The influence of breadth–length ratio

Figures 10 and 11 give the comparison of CZ at the attack angles　α = 5° and 5° for the rotor, flat and 2-D models. It shows that there are different changing rules for the hydrodynamic coefficients of different models with their breadth–length ratios. The hydrodynamic coefficient increases with the increase of breadth–length ratio, The lifting effect can be characterized by the slope of the curve for C

−

Z versus

α , that is, by dd

Zz

CCα

α= − . The lifting effect is

enhanced with increasing and breadth-length ratio.

αZC

Fig.11 CZ for rotor, flat, and 2-D models atα = 5°

The breadth–length ratio also influences the

hydrodynamic interaction of the body and wall. For the rotor model, the hydrodynamic interaction is linear with the attack angle in the whole region. For the flat model, the hydrodynamic interaction has some nonlinear characteristics when the model is very close to the wall. For the 2-D model [10], the hydrodynamic interaction has different properties. The blocking effect is very strong at extremely small clearance. The clearance between the 2-D model and the wall is

similar to a flow tube. When the breadth of tube is very small, the viscous force is relatively large, so the resistance is considerably large, and the pressure in the tube is very high, so the model is repulsed by the wall. However, the clearance between the 3-D model and the wall is open on all sides. The water can flow freely in any direction, especially in the small breadth–length ratio model, where the blocking effect is very small and can be ignored. 5. CONCLUSIONS

The experimental result shows that the boundary hydrodynamic interaction of the 3-D oval-section model with a small breadth–length ratio depends on the attack angle, clearance, and geometry of the model. The following conclusions can be reached:

(1) The lifting effect is apparent for the 3-D oval-section model, which is enhanced with the increase of the breadth–length ratio.

(2) The experiments show that for the Reynolds number Re = 2.5 × 105 – 1 × 106, the hydrodynamic coefficients do not vary with moving speed. In other words, the hydrodynamic force is proportional to the square of the moving speed.

(3) The resistance of the model increases when the model approaches the wall. The resistance coefficient of the flat model is larger than that of the rotor model.

(4) The vertical force coefficient and moment coefficient are proportional to the attack angle. When the attack is positive, the vertical coefficient is negative and the moment coefficient is positive. It means that a lifting effect exists. The attack angle’s focus of vertical force coefficient is at the head of model.

(5) When the attack angle is zero, the flat model

is attracted by the wall at a small clearance (hL

<

0.08), the attracting force increases with decreasing clearance, but the vertical force acting on the rotor model is very small. When the attack angle is not zero, the value of the vertical force coefficient depends on

the clearance. If hL

> 0.21, the lifting effect of the

rotor model is weakened when the model approaches the wall, but that of the flat model remains constant. If hL

< 0.21, the lifting effects for the two models

become stronger when the models approach the wall. (6) The boundary hydrodynamic interaction of

the 2-D model with a small breadth–length ratio is quite different because of the difference flow types in clearance. Dislike the 2-D oval model, the blocking effect of the 3-D model is too small to be accounted

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for. The boundary hydrodynamic interaction is almost linearly dependent on the attack angle, except in the case of a flat model with an extremely small clearance.

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