Submerged Propeller Jet
WEI-HAUR LAM† GERRY HAMILL† DES ROBINSON‡
RAGHU RAGHUNATHAN†
CHARMAINE KEE‡
†
‡
Virtual Engineering Centre, Queen’s University of Belfast
Cloreen Park, Malone Road, Belfast BT9 5HN
Northern Ireland
School of Civil Engineering, Queen’s University of Belfast
David Keir Building, Stranmillis Road, Belfast BT9 5AG
Northern Ireland
http://www.vec.qub.ac.uk/members/weilam/
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
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, twentynine 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
1
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
of improving 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,
2
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].
13 o-15o
Zone of flow establishment
Zone of established flow
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]
Vo  1.59nD p Ct
Vo  nD p Ct
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).
 Dp 
  
 Dh 
0.403
Ct 1.79 BAR 0.7 (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].
 x 
Vmax

 0.87
D 
Vo
 p

BAR
4
(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]
Vx ,r
Vmax
(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)
V x ,r
Vmax

1  (r  Rmo )
 EXP  
2 1
( Rmo )
 2
2


 (5)



(r  Rmo )
1
 EXP  
21
( R )  0.075( x  R p )
 2 mo





2
(6)
Where Rmo can be obtained using Berger’s equation
(see equation 7). [9]
3
Rmo  0.67 R p  Rh
7 Numerical Predictions
(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].
x
 0.097


Vmax
Dp

 0.638 EXP
Vo


(8)
The distribution can be calculated using
Fuehrer and Romisch’s equation (see equation 9)
[9].
Vx,r
Vmax
2

r 
 EXP 22.2  
 x  

8 Comparisons
(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
Propeller diameter, Dp
76mm
Hub diameter, Dh
15.24mm
Thrust coefficient, Ct
0.4
Blade area ratio, BAR
0.47
Rotation speed
16.67 rev/s
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
along flow axis
flow). ThereLDA
aremeasurements
as shown in
Figure 3.
1.60
Axial velocity (m/s)
1.40
1.20
1.00
0mm
0.80
200mm
0.60
400mm
0.40
0.20
0.00
-0.20 0
20
40
60
80
100
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 nonlinear
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 schemes implemented by the
Fluent® CFD package. The simulation results are
compared with the calculated values and LDA
measurement in next section.
120
Radial distance from propeller axis (mm)
Fig. 3: Distribution of axial velocity at 0mm,
200mm and 400mm from propeller.
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.
4
Table 2: Axial velocity (Vo)
Equation
LDA
Vo (m/s) 1.27
1.36
Variation 4.1%
11.5%
CFD
1.22
-
Table 3: Maximum Axial velocity at 200mm
Equation
LDA
CFD
Vmax
0.99
0.72
0.84
(m/s)
Variation 17.9%
14.3%
Table 4: Maximum Axial velocity at 400mm
Equation
LDA
CFD
Vmax
0.49
0.5
0.59
(m/s)
at efflux plane
Variation Distribution
16.9% of axial velocity
15.3%
1.60
Axial velocity (m/s)
1.40
1.20
1.00
CFD
0.80
LDA
0.60
Equation
0.40
0.20
0.00
-0.20 0
10
20
30
40
10 Conclusion
50
Radial distance from propeller axis (mm)
Distribution of axial velocity at 200mm-plane from
Fig. 4: Distribution ofpropeller
axial velocity at efflux plane.
Axial velocity (m/s)
1.20
1.00
0.80
CFD
0.60
LDA
Equation
0.40
0.20
0.00
0
20
40
60
80
100
120
Radial distance from propeller axis (mm)
Fig. 5: Distribution
of axial velocity at zone of flow
Distribution of axial velocity at 200mm-plane from
establishment.
propeller
0.70
Axial velocity (m/s)
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 because the 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.
0.60
0.50
CFD
0.40
LDA
0.30
equation
0.20
0.10
0.00
0
50
100
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 motivates
continuous 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.
150
Radial distance from propeller axis (mm)
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
References:
[1]
Qurrain, R. , Influence of the sea bed
geometry and berth geometry on the
hydrodynamics of the wash from a ships
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University of Belfast, Northern Ireland,
1994.
[2]
Bergh H. & Cenderwall K., Propeller erosion
in harbours, Bulletin No TRITA-VBI-107,
Hydraulics Laboratory, Royal Institute of
5
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
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6