Propeller Wash Formation

Submerged Propeller Jet

WEI-HAUR LAM†GERRY HAMILL†DES ROBINSON‡

RAGHU RAGHUNATHAN†CHARMAINE KEE‡

†Virtual Engineering Centre, Queen’s University of Belfast

CloreenPark, Malone Road, BelfastBT9 5HN

Northern Ireland

‡School of Civil Engineering, Queen’s University of Belfast

DavidKeirBuilding, Stranmillis Road, BelfastBT9 5AG

Northern Ireland

Abstract: - A high velocity jet can cause seabed scouring in the harbour. This paper presents the behaviour of a submerged propeller jet, which can be divided into the efflux plane, zone of flow establishment and zone of established flow. The semi-empirical equations used to predict the decay of maximum velocities along the flow axis and the distributions of the plane have been reviewed and calculated. These calculated velocities are compared with the LDA measurements and CFD simulation.

Key-Words: - propeller jet, velocity distribution, diffusion, CFD simulation, LDA

1

Nomenclature

BAR is the blade area ratio

Ct is the thrust coefficient

Dp is the propeller diameter

Dh is the hub diameter

n is the number of revolutions per second of the propeller

P is the pitch area ratio

Rmo is the radial distance of maximum velocity of efflux plane

Vo is the efflux velocity

Vmax is the maximum velocity

Vx, r is the velocity at coordinate x and r

x is the axial distance from propeller face

1 Introduction

The size of the ships which navigate in seas and inland waterways is increasing, mainly for economic reasons. A bigger ship needs a bigger thrust force to push it forward. Subsequently a higher velocity propeller wash is induced. The movement of large ships is difficult to control especially when manoeuvring nearby the harbour walls. Hence these ships dock at the same position and navigate the same route when approaching the harbour. The rotation of a propeller produces a wash with high kinetic energy, which results in scouring of the sea bed and damaging the quay structures in a harbour or other docking area.

The problem associated with propeller scour has been documented around the world. A survey by Qurrain (1994) discovered that scouring damage had occurred in 42% of ports in the United Kingdom [1]. In Sweden, Bergh and Cederwall (1981) highlighted the need for repairs caused by erosion at sixteen out of eighteen ports investigated [2]. In France, twenty-nine ports were exposed to propeller induced scouring where the bed velocity of the wash was estimated at 3-4m/s and the erosion was found to reach 0.5 meters per month, Longe et al. (1987) [3]. In Larne harbour, Northern Ireland, scouring has overlain with 250mm diameter cobbles, at a rate of 0.6 meters per year [4].

2 Importances

Bed scour is a function of the near bed velocity, particle size and density [5]. For any given sediment, a critical velocity exists above which the movement will take place. In order to predict the near bed velocity, an accurate prediction of the jet velocity at the exit of the propeller is required. The exit velocity is termed the efflux velocity (Vo). The virtual wash can therefore be used to track the location of any given critical velocity, indicating which areas where scouring will occur. Conversely it will also allow a particle size to be determined, based on the magnitudes of the velocities present in the wash. This will prevent movement and allow an armour layer to be established.

In order to provide an adequate protection system against scouring, an understanding of the velocity distribution within the propeller wash is required. The importance of this situation has been recognised in the United Kingdom by the British Standard Code of Practice for the design of maritime structures, BS 6349 [6]. This code requires the scouring action of propeller jets to be taken into consideration in the design of berth structures. But the code does not a provide method of calculating this scouring damage.

3 Background

A propeller jet can be analyzed globally and locally using the axial momentum theory and blade element method (BEM) respectively. The axial momentum theory can be used to predict velocity and pressure of the upstream and downstream propeller flow, without considering the aerofoil at the rotor. Meanwhile, blade element method is a theory based on dividing the blade up into a large number of elementary strips. Each elementary strip is regarded as an aerofoil subject to a resultant force. The demand for understanding the flow within the rotor is mostly for the purpose ofimproving a propeller performance. A naval architect will analyse the flow globally and locally for this purpose and to investigate the stern vibration caused by a rotating propeller. As a civil engineer, our concern is of the downstream propeller wash, which results in sea bed scour and exposes the quay structure where the wash is impinging. Axial momentum theory is more important in this research.

4 Axial Momentum Theory

The classical analysis method for the global flow region is the axial momentum method, in which the rotor is modelled as an actuator disk and the flow passes this disk without energy losses (see Figure 1). This theory is derived from the concept of conversation of momentum and energy, encompass six core assumptions:

1. The propeller is represented by an ideal actuator disc without thickness in the axial direction.
2. The disc consists of an infinite number of rotating blades, covering the entire disc without space in between.
3. The disc is submerged in an ideal fluid without disturbances.
4. All elements of fluid passing through the disc undergo an equal increase of pressure.
5. The energy supplied to the disc is, in turn, supplied to the fluid without any rotational effects being induced.

The relation between the velocity and pressure profiles is shown in Figure 1. Far upstream of the propeller disk, the pressure and velocity are given by PA and VA. As the flow approaches the disc, acceleration occurs because of the reduced pressure PB on the upstream side of the disc. Energy is supplied to the system as the fluid passes through the disc, and as a result Bernoulli’s equation does not apply between sections B and C. However Bernoulli’s equation may be applied between sections A and B and between sections C and D. The changes in momentum due to the presence of the disc then results in a net thrust on the fluid.

Fig. 1: Axial momentum theory

5 Physical Phenomena

A propeller jet produces a thrust by drawing in water, accelerating it and discharging it when a propeller is rotating. This jet is unlike the other submerged jets because the velocity and shear stresses depend upon the operating characteristics of the propeller and the speed of advance of the ship. The jet velocity entrains the surrounding water and decays with distance from the propeller jet. In this way, the jet expands and the kinetic energy dissipates as diffusion. If the propeller jet is restricted in a confined area such as a waterway or shallow water, the remaining kinetic energy within the propeller jet will cause damage on the bed or banks.

Figure 2 summarized physical jet characteristics suggested by Hamill et. al.. The downstream propeller jet can be divided into two apparent zones; those are zone of flow establishment and zone of established flow. The entrainment starts from the zone of flow establishment, which consists of a symmetry plane along the central flow axis. This symmetry forms two similar profiles with peaked ridges at the central. Later the velocities of these two peaked ridges will decay with distance of the propeller faces along the central axis. The diffusion of the jet is inclined at an angle of 130-150 [7].

Fig. 2: A submerged propeller jet suggested by Hamill et. al.

5.1 Efflux Plane

The exit plane of a propeller flow is called the efflux velocity. This initial plane in front of the propeller is where the velocities within the jet are at a maximum. The predictions of the velocity can be done by using several semi-empirical equations. Knowing the efflux velocity is the pre-requisite to predict the downstream diffusion through these semi-empirical equations.

Theoretical development of equation used to predict the efflux velocity of a propeller wash is based on axial momentum theory shown in equation (1). This equation is widely investigated by several researchers such as Hamill et. al. and Berger at. al..[5]

(1)

Hamill et. al. suggested the efflux velocity is influenced by other propeller characteristics such as blade area ratio and hub diameter of a propeller. The coefficient 1.59 might not be constant. It is changeable based on the propeller characteristics. Hamill proposed equation (2) by replaced the constant coefficient into changeable coefficient based on the propeller characteristics. [5]

(2)

Where Hashmi [8] proposed the coefficient can be calculated using a semi-empirical equation by taking propeller diameter, hub diameter, thrust coefficient and blade area ratio into account (see equation 3).

(3)

5.2 Zone of Flow Establishment

The zone of flow establishment is the region where the jet was divided into two parts by the influence of the rotating hub. Some of the researchers believe the contraction phenomena happened at the exit of the propeller jet. Based on the LDA measurement, it shows no contraction happening at the efflux plane. The velocity profiles of this zone contain two symmetric peaked ridges propagating downstream jet. As the distance from the propeller face is increased, the transverse velocity profile keeps expanding, associated with the decay of maximum velocity. Steward states the zone of flow establishment ranges from the efflux plane to 3.25 Dp [7]. This kind of diffusion can be approximated by using a series of semi-empirical equations (see equation 4, 5, 6, 7). Predicting maximum velocity of a traverse profile is the first step to understand the whole distribution. This maximum velocity at the zone of flow establishment can be predicted using equation (4) [5].

(4)

Hamill proposed two equations to calculate the distribution of the traverse velocity based on the distance form the propeller. For the efflux plane and the region up to 0.5 Dp from the propeller, equation (5) can be used to predict the distribution. For the region where further than 0.5 Dp and within the zone of flow establishment, equation (6) can be used. [5]

(5)

(6)

Where Rmo can be obtained using Berger’s equation (see equation 7). [9]

(7)

5.3 Zone of Established Flow

The fluid from the two peaked ridges will penetrated into the central axis to produce an individual peaked ridge. This zone has been called zone of established flow. The flow velocity will decelerate along the jet with distance from face. The maximum velocity of this zone can be predicted using the Hashmi’s equation (see equation 8) [8].

(8)

The distribution can be calculated using Fuehrer and Romisch’s equation (see equation 9) [9].

(9)

6 Experimental Measurements

A 3D LDA test has been carried out in order to compare propeller jet behaviour with the existing equations. Through the test, the behaviour of a propeller jet can be observed. A 76mm propeller in diameter has been fixed at the shaft and been rotated at 16.67 revolution per second (see Table 1).

Table 1: Propeller Characteristics

A very fine step (25mm) has been used in order to obtain the results. Three sets of measurements has been taken at 0mm from the propeller (efflux plane), at 200mm (zone of flow establishment) and at 400mm (zone of established flow). There are as shown in Figure 3.

Fig. 3: Distribution of axial velocity at 0mm, 200mm and 400mm from propeller.

7 Numerical Predictions

Accuracy of CFD solution is based on the accuracy of theoretical fluid dynamics used; these are based on solving the conservation equation of mass and momentum, which are known as Navier-Stokes equations. These conservation equations are non-linear partial differential. The non-linear characteristic of the partial differential equations means that no method of exact solution exists.

In this case, an unstructured grid was generated using Gambit® 2.1. This unstructured grid is solved using a k- turbulence model and second order discretisation schemesimplemented by the Fluent® CFD package. The simulation results are compared with the calculated values and LDA measurement in next section.

8 Comparisons

The following is the comparison of the maximum velocities of the propeller jet obtained through equation calculation, LDA measurement and CFD simulation. Table 2 shows the prediction of maximum velocity at efflux plane. Equation (2) has been used in calculation. The calculated result shows 4.1% variation if compared with the CFD prediction. For the LDA measurements, it varies 11.5% compared with CFD prediction.After knowing the maximum velocity in a traverse profile, the distribution can be calculated using equation (5). The distributions of the three sets of results are shown in Figure 4.

In the zone of flow establishment, the maximum velocities at 200mm (2.6 Dp) from the propeller are shown in Table 3. The maximum velocity at the first column was calculated using equation (4). The variation between of the maximum velocity obtained from equation and LDA measurement are 17.9% and 14.3% respectively when compared with CFD prediction. The distribution of the traverse is shown in Figure 5.

The maximum velocity at 400mm (5.3 Dp) are compared and shown in Table 4. The plane 5.3 Dp from the propeller face are within zone of established flow, obeying Steward’s suggestion [7] that the zone of established flow started after 3.25 Dp from the propeller face. The equation (8) has been used to estimate the maximum velocity (see Table 4) and the distribution of the traverse can be estimated using equation (9) (see Figure 6). The variation of the calculated velocity and measured velocity are 16.9% and 15.3% respectively compared with the CFD prediction.

Table 2: Axial velocity (Vo)

Table 3: Maximum Axial velocity at 200mm

Table 4: Maximum Axial velocity at 400mm

Fig. 4: Distribution of axial velocity at efflux plane.

Fig. 5: Distribution of axial velocity at zone of flow establishment.

Fig. 6: Distribution of axial velocity at zone of established flow.

9 Discussion

Semi-empirical equations provide a simple way to estimate the velocity of a propeller jet. But these can only provide a rough approximation. The equations used neglect some of the propeller characteristics likes number of blade, pitch and rake angle. But these characteristics directly influence the velocity of the propeller jet.

LDA measurements and CFD simulation do include these propeller characteristics in their investigation. LDA measurements system can provide a better result but the instrument setup is complicated. It requires a good controlled environment such as a hydraulics lab to produce a good result and is impractical in most applications. For example, LDA is not suitable to be used in a narrow area because the instrument needs space to be setup.Besides, the flow needs enough particles to scatter lights becausethe scattered lights will be transformed to be readable velocity values.

CFD is a faster and cheaper way to predict the velocity of the propeller jet compares with LDA measurement. The CFD allows for a wide range of propeller configuration to be analyzed. When using CFD simulation, convergence error, truncation error and round-off error need to be minimized in order to provide a good result.

10 Conclusion

Semi-empirical equations can provide a reasonable result for propeller jet estimation. If a more accurate result is required, CFD or a LDA measurement system can be used. However LDA measurement systems have limited operating environment. The CFD approach can be extended to a wide range of applications. But LDA measurement systems provide an important means of verifying the validity of CFD models.

The accuracy of a velocity prediction of a submerged propeller jet influences the accuracy of the scouring prediction at seabed. This motivatescontinuous research on predicting the velocity of a propeller jet.Future works of this research will focus on using a CFD model to understand the behavior of a propeller jet. The grid resolution, discretisation scheme and turbulence model of CFD model will be adjusting in order to understand the impact on the results.

References:

1