Simplified Prediction of Propeller
Inflow/Outflow Properties
A HydroComp Technical Report
Report 129
Overview
There are
certain instances where an understanding of propeller inflow and
outflow properties can be applied to the initial selection of
propeller parameters. Two such instances are for the selection
of counterrotating propellers and the design of propeller ducts
(nozzles).
Figure 1 illustrates
the flow of the water “jet” through the propeller disk. This simplified
approach relies on the wellused massflow (or momentum) methodology
. As the mass of the water is accelerated through the propeller
disk to a higher velocity, the Bernoulli effect causes a corresponding
reduction of the diameter of the jet. The velocity and diameter
of the jet at points along the propeller axis can be found with
the equations shown below.
Figure
1. Propeller Jet InflowOutflow Properties
[SNAME, Principals of Naval Architecture]
Equations
Item 
Equation 
Variables 
Comments 
Thrust
loading coefficient 

T
= openwater thrust
A_{0} = propeller disk area
V_{A} = advance velocity 
Make
sure all units are compatible. 
Ideal
efficiency 

C_{T}
= thrust loading coefficient 

Overall
velocity factor 

η_{i}
= ideal efficiency 
This
provides a way to estimate the overall change in velocity
from inflow to outflow. 
Local
velocity multiplier 

c =
curve shape coefficient
x = distance from propeller (in diameters, positive aft) 
This
provides a way to estimate velocities at specific axial
locations. The “c” coefficient typically equals 34, with
one reference using 3.3 as a representative value. 
Local
jet velocity 

V_{A}
= advance velocity
k = local velocity multiplier
a = overall velocity factor 
This
is the local jet velocity at any location (X) along the
axis. 
Local
jet area 

V_{A}
= advance velocity
a = overall velocity factor
A_{0} = propeller disk area
V_{X} = local jet velocity 
This
is the local jet sectional area at any location (X) along
the axis. 
Local
jet diameter 

A_{X}
= local jet area 
This
is the local jet diameter at any location (X) along the
axis. 
Wake
Fraction and Scale Correction
It is important
to note that the wake fraction generally includes the velocity
profiles described in Figure 1. The prediction of effective wake
fraction is derived by comparing the thrust loading in a circulating
channel to that found behind the hull during a selfpropulsion
test – and solving for the corresponding velocity that would produce
the measured thrust. In both cases, the jet will exhibit flow
constriction and increases in local velocity. In other words,
the V_{A} described above is the wellknown V_{A}
which is equal to V(1w).
Model and
fullscale propeller loadings will act differently, however, causing
a slightly different distribution of the flow. The use of a wake
fraction scale correction is a recommended step in all performance
predictions.
Influence
of the Hub
One of the
initial components of this simplified methodology – the thrust
loading – depends on the relationship between thrust, velocity
and the area through which the water passes (i.e., the disk area).
If the hub gets to be sizeable, as might be the case for a controllablepitch
or counterrotating propeller, it may be appropriate to reduce
the propeller disk area to be equal to the area outside of the
hub.
For example,
a conventional propeller with a hub of 18% of the diameter will
only cause about a 3% reduction in disk area, but a 35% hub reduces
the disk area by more than 12%.
