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CONTROL OF THE TURBULENT WAKE OF AN APPENDED STREAMLINED BODY 342
Control of the Turbulent Wake of an Appended Streamlined Body
S.Cordier, L.Descotte (Bassin d'Essais des Carènes, France)
ABSTRACT
Propulsor tests at model scale behind a ship model are faced with the problem that Reynolds number similarity
cannot be met, even if large test facilities are used.
In the work presented we are specifically concerned with the flow similarity over the after part of the hull with and
without appendages. This issue concerns the mean flow into the propulsor (wake fraction) and the powering
characteristics such as shaft speed, thrust and power. When cavitation or hydroacoustic studies are concerned, it also
becomes important to simulate the three dimensional distribution of velocities, and perhaps the turbulent flow properties
in the propeller plane. Several means of altering the flow over the hull in order to simulate Reynolds number similarity
have been studied and tested in different laboratories. Boundary layer blowing has been selected and implemented on a
model tested in the GTH.
The design of this set up is briefly described. Results of LDV measurements are presented which show how the
blowing system modifies the distribution of velocities in a very effective manner. The characteristics of the wakes
generated are analyzed (wake fraction, harmonic content) in particular with respect to the effect of appendages. A method
for analyzing LDV measurements in order to estimate the turbulence in the flow is outlined and applied to the
measurements performed on the after-body. Finally, the effect of the changes in wake on the steady and unsteady
performances of a propeller are presented.
INTRODUCTION
Tests conducted at model scale in naval hydrodynamics are confronted with the problem of Reynolds number
similarity which cannot be met, even if large test facilities are used. This similarity problem requires the use of
extrapolation methods adapted to the different flows: ship resistance and propulsion, flows on lifting surfaces and
propellers, separated flows, sheet or bubble cavitation, vortex cavitation, etc… The variety of difficulties which arise
from the differences in Re is very challenging to the experimental hydrodynamicist. These issues are not easily solved by
CFD either because of the large Re involved (107 to 109) which create numerical problems and the influence of transition
which is not modeled by RANSE codes. Finally, although one can imagine that full scale measurements are the answer to
these issues, the economical cost and technical complexity of performing scientific quality full scale velocity
measurements on a ship have so far reduced these instances to a very limited number with varying degrees of success
(extent, number of components, accuracy).
We focus our attention in this paper on the flow around the hull and more precisely in the propeller disk. Indeed, the
velocity field in this plane determines the volumetric flow rate in the propulsor disk (wake fraction) and the powering
characteristics such as rate of turn of the propulsor, thrust, and power. When cavitation or noise is the purpose of the tests,
then it is important to simulate the 3D dimensional mean flow field and in some instances the turbulence levels in the
wake.
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CONTROL OF THE TURBULENT WAKE OF AN APPENDED STREAMLINED BODY 343
The importance of Reynolds number effects on ship wakes in the range of Re from 107 to 7.107 has been shown in
the GTH by 3D LDV measurements behind a single screw merchant ship form and a twin screw naval ship model using,
in each instance, a single model with flow velocities as widely spread as possible; typically, between 1 and 2 m/s at the
low speed end and 12 m/s, which is the highest speed possible in the large test section of the GTH (L.Briançon-Marjollet
& al., 1995; S.Cordier & al., 1997). These measurements show wide differences in the wake fraction and the three
dimensional features of the wake maps which are due to the changes Re. These have proven useful to correct model scale
towing tank wake maps to full scale wake distributions. More recent work involving the effect of the propeller has shown
how Re effects in the nominal wake are modified by the propeller action.
More recently similar investigations have been performed on a submarine model derived from the SUBOFF shape
and on the twin screw vessel operated by SACLANT (the Alliance). This worked sponsored through a WEO EUCLID
program is focused on evaluating the ability of CFD to capture flow details such as Re and propeller effects.
The motivation in this work was to apply this methodology to submarine work in order to evaluate the Re effects on
bare and appended submarine hull forms.
As far as the wake fraction is concerned, different empirical formulae have been developed for different types of
ships which enable the extrapolation of the model scale effective wake fraction to full scale. These are based on statistical
analysis of families of ships for which reasonably good full scale data is available. For submarines such data bases are
limited in the number of ships and when dealing with novel geometries, empirical methods are of no help. It is therefore
essential to obtain a realistic wake at model scale to determine the full scale design point.
The goal of this work was to develop and demonstrate the effectiveness of a boundary layer control method, to study
the characteristics of the wake of the body at different Re and with different levels of boundary layer control for different
configurations (with or without appendages). Finally, this study focused on the effect of the wake parameters on the
performance of a propeller operating behind this body.
The work was broken down in three parts:
• selection and development of a boundary layer control method using CFD
• design and fabrication of the experimental set up
• tests in the GTH and analysis of measurements (mean and turbulent flow, steady and unsteady forces on the
propeller)
BOUNDARY LAYER AND WAKE CONTROL
Several methods have been imagined and investigated by different authors to reduce the differences in flow field due
to Re non-similarity at model scale. (Lauchle & al., 1983):
• use of a low viscosity fluid such as liquid helium,
• extension of the laminar flow over the body using heating of the body to reduce the width of the wake,
• reduction of the length of the fore part of the model,
• changes in the test section shape in order to modify the pressure distribution and boundary layer development on
the model,
• use of polymers (large molecules) to reduce the thickening of the boundary layer and wake,
• suction of the boundary layer on the body,
• blowing of the boundary layer.
Further examination of these different solutions quickly points to technical or practical difficulties associated with all
these schemes. For example, the use of low viscosity fluid is limiting because it is not suited to the simulation of
cavitation behavior. Furthermore, the size of the models associated with this technique is so small as to be not practical
because of the relative size of existing flow velocity measuring devices. The use of heating for laminar flow is not
practical in terms of model fabrication and its effectiveness is very dependent of the shape of the body. Reduction of the
fore part of the model implies a modification of geometry which is not always compatible with the requirements of the
study. However, when possible, this method is quite practical. Changes in test sections are not practical and not very
effective. The use of polymer requires cleaning of the tunnel after use which is not economically possible. Suction of the
boundary layer requires large flow rates which are difficult to incorporate in a submarine model.
Finally, the possibility of using a blowing system was considered the most practical. This method had previously
been tested with success in a tunnel for the elimination of the wall boundary layer
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CONTROL OF THE TURBULENT WAKE OF AN APPENDED STREAMLINED BODY 344
upstream of a wall mounted fin test set up. Blowing is relatively simple to implement, does not require a change in the
shape of the body. The effectiveness of boundary layer blowing is the injection of small quantities of high momentum
flow along the wall of the body, deep in the boundary layer of the flow. This momentum is transferred through the action
of turbulent shear forces across the boundary layer. After a certain distance, the jet corresponding to the high momentum
flow is diffused so that the velocity profile assumes that of a natural boundary layer. The use of blowing allows the
injection of momentum with a relatively small flow rate which is convenient for integration in a model.
Reynolds Average Navier Stokes (RANS) calculations were performed in 2D axisymetric flow for different slot
positions and slot heights with varying jet velocities. These parameters (figure 1) were adjusted so that the velocity
profiles in the propeller plane were monotonous and corresponded to high Reynolds number velocity profiles. These
calculations allowed the definition of the slot dimensions, and flow rate required to generate the appropriate wake.
Systematic calculations were performed using different sets of parameters (h, Xs, Vj/Vo) and the resulting velocity
profiles were analyzed to identify the best compromise between jet velocity, slot width and position. One constraint in
this optimization was to reduce the flow rate as much as possible so as to reduce the mechanical problems associated with
the integration of the ducting in the model and the support strut. Hence for a given jet momentum required to alter the
boundary layer profile, the jet velocity is increased and the jet slot width is decreased. Then the axial position of the slot is
chosen so that the jet has sufficient time to diffuse and adopt a realistic boundary layer profile. Reducing the slot width is
very effective in accelerating the diffusion of the jet. The compromise was found to be most effective with jet velocity
ratios on the order of 2 and a flow rate coefficient (Cq) of about 1 to 2 percent (Cq=Q/Vo/π/R2).
EXPERIMENTAL SET UP
The tests were carried out in the large test section of the GTH (Grand Tunnel Hydrodynamique) located at the Bassin
d'essais des carènes in Val de Reuil. This test section is rectangular (2m*1.35m), and 10m in length. The maximum flow
velocity in the test section is 12 m/s. The strut which supports the model is attached to the roof of the test section.
Figure 2 shows a schematic of the experimental set up. The model is about 4 m long and 0.45 m in diameter. It is
built in 3 main sections: nose, central section with the blowing system and the tail which houses the propeller drive motor
and the dynamometer. The blowing section forms a 1 mm thick slot around the circular periphery of the body and is set at
a 10° angle with respect to the body surface. The slot is located at about 65% downstream of the nose of the model. The
jet is formed by accelerating the flow from a large settling plenum. This one in turns is supplied with water pumped from
a connection in the tunnel through a flow meter into the strut. The pump was installed as low as possible in the tunnel to
reduce the risks of cavitation. The flow meter is of the venturi type and was specially designed and built for this purpose.
Figure 1: Blowing slot parameters
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Figure 2: Schematic of the blowing section in the experimental set up
The tunnel velocity used throughout these experiments was about 5 m/s and the flow rate on the order of 20 l/s. This
range of parameters allowed the blowing coefficient to be varied from 0 to 2.5% (Cq0=0, Cq1=0.016, Cq2=0.021,
Cq3=0.025). The model can be equipped with different appendages

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CONTROL OF THE TURBULENT WAKE OF AN APPENDED STREAMLINED BODY 345
which are typically found on submarines (sail, deck, dive planes, rudders. The results presented here correspond to two
configurations: bare hull and appended hull (stern dive plane and rudder).
Several types of measurements were performed during several test campaigns:
• 3D laser doppler velocimetry,
• mean thrust and torque on the propeller,
• fluctuating propeller thrust,
• radiated noise,
• pressure fluctuations on the hull.
The measurement of unsteady thrust is useful in evaluating the low frequency excitation of the propeller due to wake
non-uniformity. The results presented here are mostly concerned with the LDV measurements and powering performance.
BLOWING SYSTEM EVALUATION
The blowing system and the behavior of the jet for different flow rates were evaluated during dedicated tests. Some
of the tests were performed to calibrate the pressure drop in the pump loop as well as the flow meter. The behavior of the
jet for different positions downstream of the slot was investigated through measurement of the velocity profile. These
measurements were performed for different jet velocity ratios in the bare hull configuration. The radial distributions of the
measured axial velocity for different flow rates and for different axial positions are presented in figure 3. The data
corresponds to three axial positions: at the jet nozzle exit, in the middle of the after-body and in the propeller plane. z+
represents the distance from the model in mm.
Figure 3 shows how the velocity profiles evolve downstream of the slot from the high velocity jet at the slot exit
which develops a thin boundary layer along the body and a shear layer with the incoming boundary layer (figure 3.a). The
shear forces acting on the jet tend to diffuse the jet, reduce the value of the maximum velocity and increase the width of
the shear layer. Further downstream, the velocity profiles tend to lose the inflection point which corresponds to the
mixing layer between the jet and the upstream boundary layer (figure 3.b). Finally, in the propeller plane, the radial
velocity profiles are monotonous and are similar to the natural wake (Cq=0) (figure 3.c).
Figure 3: Measured radial velocity profiles for 4 blowing flow rate (Vo=5 m/s)
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CONTROL OF THE TURBULENT WAKE OF AN APPENDED STREAMLINED BODY 346
These figures show the effectiveness of this boundary layer control system whereby the radius of the viscous wake
can be changed by a factor of roughly 2 by simply changing the blowing pump velocity. The final wake velocity profiles
with the blowing system active appear to be similar to the velocity profiles obtained naturally.
The profiles on figure 3 show velocity data without blowing (Cq=0) for a tunnel velocity of 5 m/s (Re=3 107) which
corresponds to the natural evolution of the boundary layer and wake. Measurements at 12 m/s (Re=7 107) are also shown
in the propeller disk to illustrate the difference in velocity profiles due to the difference in Reynolds number. Clearly the
range of velocity profiles which can be achieved cover this difference in Re and most likely much larger differences in
Re, i.e. to full scale (Re=109). The advantage of this system is its capability to vary the wake rapidly during a test so that
the sensitivity of the propeller performance to this parameter can be investigated.
Wake fraction
In order to quantify the effect of blowing on the wake, it is convenient to examine the variation of wake fraction as a
function of disk radius. The mean wake fraction is calculated as follows:
Wake fraction without tail planes
Figure 4 summarizes the wake fraction data calculated for 5 values of the radius (20mm, 40mm, 60mm, 80mm et
100mm) based on the measured radial velocity distributions on the propeller plane for 4 blowing conditions at 5 m/s and
without blowing at 12 m/s. The distribution of the wake fraction as a function of the disk radius is similar for the different
conditions which confirms the realistic nature of the resulting wakes. It can be noted that the wake fraction reduces
rapidly as the disk radius is reduced.
Figure 4 shows that significant gains in wake fractions can be obtained using blowing. Hence, at 5 m/s the nominal
wake can be modified by a factor of two and can very easily compensate for the Re effects which could be simulated on
the model by changing the tunnel velocity from 5 to 12 m/s.
Figure 5: Wake fraction as a function of the disk
Figure 4: Wake fraction as a function of the disk
diameter (with tail planes)
diameter (without tail planes)
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Figure 6: Effect of tail planes on the radial distribution of wake fraction

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CONTROL OF THE TURBULENT WAKE OF AN APPENDED STREAMLINED BODY 347
The velocity profile at a blowing coefficient value of Cq1 is sufficient to match the higher Re profile. A slight
difference in profile slope can be identified.
Wake fraction with tail planes
As expected, the presence of tail planes increases the wake fraction giving a relatively linear radial distribution of
wake fraction (figure 5). The shape of the distribution in wake is very similar for all blowing coefficients which shows
that the blown boundary layers have a realistic global effect.
In order to bring to evidence the modification of the wake fraction due to the tail plane, the difference between the
wake fraction with and without tail planes is presented on figure 6. The presence of tail planes results in an increase in
wake fraction for the larger radius. The influence of tail planes on wake fractions is rather constant for all blowing
coefficients with a maximum value of 0.075 at about 0.3 z+/Ro.
EFFECT OF TAIL PLANES ON THE WAKE DISTRIBUTION
In order to analyze in further detail the relative effects of blowing and tail planes, wake maps were performed for the
different configurations. Hence, the effect of tail planes can be identified by subtracting the bare hull velocity profiles
from the wake maps measured with tail planes. This subtraction is performed for the different values of blowing
coefficients. The resulting velocity profiles are shown on figure 7 for Cq0 and Cq2. This figure shows how the tail planes
strongly affect the spatial velocity distribution in the plane of the propeller. The cause of the disturbance, more than the
velocity deficit of the wake of the tail planes, is the presence of the so-called horseshoe vortices which are due to the
radial gradient of upstream velocity which creates a radial gradient of pressure on the thick fins and hence a vortex pair.
The presence of this vortex has for effect to pump high velocity flow in the area behind the fin and to concentrate low
velocity flow between the tail planes.
Figure 8 shows the difference in axial velocity wake maps measured with appendages for two values of blowing (Cq2
−Cq0). The effect of blowing on the wake upstream of the appendages generates a modification of the vortex structure
which develops along the root of the tail planes. The axial vortices are closer to the after-body with stronger velocity
gradients. This difference is hence more important for the inner radii of the wake. If the blowing effect is assimilated as a
Re effect, higher Re will not only reduce the wake fraction but also modify the azimuthal distribution of velocities which
will strengthen the higher harmonics of the wake.
Figure 8: Effect of blowing on the wake with tail planes
(axial component, Cq2−Cq0)
Figure 7: Effect of tail planes—(axial component)
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CONTROL OF THE TURBULENT WAKE OF AN APPENDED STREAMLINED BODY 348
EFFECT OF TAIL PLANES ON THE WAKE HARMONIC DISTRIBUTION
The most effective way of describing the azimuthal variations in wake velocity is to perform a harmonic analysis of
the velocities measured at a given radius. This harmonic decomposition is written as follows:
with:
Vxk amplitude of the kth harmonic of Vx
φk phase of the kth harmonic of Vx
Figure 9 presents the result of this type of analysis for the axial velocity at the radius r/Ro= 19%. The data on
figure 9 is in fact the relative amplitude of the first 4 harmonics of the wake obtained by dividing the amplitudes
measured with blowing (Cq1, Cq2, Cq3) to that measured without blowing (Cq0). The ordinate scale is hence the
amplitude of nth harmonic with blowing divided by the amplitude of nth harmonic without blowing.
Although the wake map data showed some effect of blowing, the harmonic analysis in the form presented here
shows considerable influence of the harmonic content even for minor blowing flow rates (Cq1). The effect on the 3rd
harmonic is considerable since it nearly disappears. The importance of the effect of blowing on the harmonic content is
illustrated on figure 10 where the wake map corresponding to the fourth harmonic is pictured for two values of blowing
coefficient (Cq0 and Cq2). The levels indicated are in m/s for a reference velocity of 5 m/s. For certain values of the
harmonic components, both amplitude and phases of the harmonic are changed. This type of data illustrates how a flow
modification similar to a Re effect can have large influences on the unsteady excitation of a rotor.
TURBULENCE
If the mean velocity distribution (wake) has an effect on the unsteady performance of a propulsor, the turbulence of
this flow can have some importance on the behavior of the hydroacoustic response of the propulsor. It is therefore of
interest to look into the turbulence in the wake and into the way it is affected by parameters such as blowing and propeller
operation. For this purpose, the velocity measurements in the turbulent wake upstream of the propeller disk were
performed using a LDV system in different operating conditions.
Figure 9: Effect of blowing on the harmonic decomposition
Figure 10: Reconstruction of the fourth harmonic of the
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wake for blowing coefficients Cq0 and Cq2

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CONTROL OF THE TURBULENT WAKE OF AN APPENDED STREAMLINED BODY 349
However, turbulence measurements using Laser Doppler Velocimetry are limited in terms of data rates. In the GTH
and using micro bubbles of water vapor and air, the average data rate is in the order of 1 to 2 kHz. This frequency range
represents an average value since the data sampling is a random process which is triggered by the passage of a tracer in
the measurement volume. In the GTH, the time between two consecutive arrival times of tracers follows very closely an
exponential distribution which parameter λ, is equal to the mean sampling rate. This distribution is truncated at high
frequency by the limits of the LDV system. Figure 11 is an example of measured histogram for which the smallest time
between samples is Te=21,333 µs.
Figure 11: Histogram of time between sample arrival times
This type of random sampling precludes the direct use of classical algorithm to estimate the spectral power densities.
Two methods have been considered:
• interpolation methods
• direct autocovariance calculation.
The first method is not reliable and the second one was implemented because it only uses autocovariance
calculations and does not require the estimation of data points between measured points.
The method used relies on the truncation of the actual arrival time to the resolution of the clock of the data
acquisition system. Hence the data is in the form of a regularly sampled signal with missing data points. The spectral
power density of the velocity fluctuations is obtained by the Fourier transform of the autocovariance of this signal. This
method is robust and effective but it is limited in frequency to a value above which the noise in the pseudo signal is larger
than the signal.
Figure 12 presents three examples of turbulence spectra measured in the wake with and without blowing and with
and without propeller. The horizontal line in the plot represents the detection limit of the method.
The results presented here show that the turbulence levels are slightly lower when the blowing system is active and
when the wake is smaller in size. However, when the propeller is operating, the turbulence levels are much lower due to
the acceleration of the flow. This data clearly shows that when turbulence quantities are required, the effect of the
propeller cannot be ignored.
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CONTROL OF THE TURBULENT WAKE OF AN APPENDED STREAMLINED BODY 350
Figure 12: Examples of measured turbulence spectra in the wake.
POWERING PERFORMANCE
The thrust generated by the propeller with different flow rates of the blowing system was recorded. The
configuration tested was the one with the appendages. The trust coefficient, Kt, is plotted against the advance ratio Jtun on
figure 11.
The advance ratio is based on the tunnel speed and hence, does not take into account the differences in wake
fractions due to the viscous effects and blowing. Hence, the curves of Kt exhibit a gradual shift to lower values of Kt as
the blowing is increased which is expected.
In order to asses the effect of wake fraction on propeller performance, the measured nominal wake fractions based on
the LDV measurements were used to correct the advance ratios from a behind condition to an estimated open water
performance J0=Jtun *(1−wn). Figure 12 shows the same values of Kt plotted against a corrected advance ratio. The
collapse of the curves to a single curve is remarkable. Hence, when the measured nominal wake is used to correct the
advance ratio, the resulting Kt values are identical. This shows that although the change in wake due to blowing induces
both complicated changes in the wake structure (axial vortices, etc..) and changes in the radial loading of the propeller,
the nominal wake based on the integration of axial velocities is sufficient to correct the rpm. Inversely, if the propeller
operating point is known at full scale (ship speed and rpm), it is very easy using the blowing device to adjust the wake so
that this operating point can be reproduced at model scale with a realistic wake containing the non-uniformity and the
turbulence content closest to full scale as possible at model scale. The advantage of performing this adjustment is that the
scaling of the frequencies associated with shaft speed will match the full scale values. Furthermore, for cavitation
inception studies, the local cavitation number and the radial distribution of propeller loading will match closely, leading to
more accurate predictions of cavitation inception.
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Figure 12: Propeller thrust as a function of corrected
Figure 11: Influence of blowing on propeller thrust
advance ratio

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CONTROL OF THE TURBULENT WAKE OF AN APPENDED STREAMLINED BODY 351
CONCLUSIONS
A boundary layer control device has been studied and developed based on blowing along the body surface. This
device has been implemented on an axisymetric streamlined body for the purpose of simulating wakes in the propeller
disk with different values of mean wake fraction. This system has been verified to work as expected and to provide
realistic velocity profiles on a bare body. These velocity profiles can compensate for discrepancies in the Reynolds
number of the flow compared to full-scale and it is therefore possible to achieve full scale wake fraction by adjusting the
blowing system flow rate. With this sytel, it is therefore possible to investigate the sensitivity of the propulsor
performance to changes in the upstream wake related to Re number discrepancies.
The effect of the blowing device was studied on the bare hull wake and on an appended wake by studying the
velocity profiles, the radial wake fraction distribution, the wake maps, and the turbulence in the flow. For the latter a
special analysis method has been developed in order to obtain power spectra of the turbulence.
The data shows a strong influence of the upstream velocity field on the perturbation caused by tail planes which
appears in the velocity field and the harmonic decomposition. On the other hand, the turbulence levels do not seem to be
strongly affected by the blowing levels. However, it is clear that the propeller action is responsible for a large decrease in
the turbulent levels.
After this study oriented towards the qualification of this system, it has been found to provide an effective answer to
the need for a variable wake test set up. It has therefore been used for the design of submarine propulsors where the
advance ratio and the distribution of circulation plays a key role in the precise estimation of the noise of the propulsor.
REFERENCES
Briancon-Marjollet L., Cordier S., Laurens J-M., Raulo J., “Effect of wake scaling on the prediction of propeller cavitation”, CAV'95, Deauville,
France, May 1995
Cordier S., Legrand F., Pinard J-C., “Hull and shaft wake interaction”, Propeller and Shafting 1997, September 1997
Pinard J.C., “Etude expérimentale et numérique du sillage en am ont d'une hélice” Thèse ECN, 1997 High Reynolds Number Flows Using Liquid and
Gaseous Helium, Springer-Verlag, J.Russell Editeur Viscous Drag Reduction in Boundary Layers, Progress in Astronautics and Aeronautics,
Vol 123, AIAA, D.Bushnell et J.Hefner, editeurs.
Lauchle G., Gurney G., “Laminar Boundary Layer Stability on a Heated Underwater Body”, Technical Memorandum, Applied Research Laboratory,
PSU/ARL-TM-83–157, Janvier 1983.
Jessup S., Remmers K., et Berberich W., “Comparative cavitation performance evaluation of a naval surface ship propeller”, ASME 1993, Cavitation
Inception, pp 51–62
Nobach H., Müller E., Tropea C., “Efficient estimation of power spectral density from laser Doppler anemometer data”, Experiments in Fluids 24,
(1998) 499–509
Ramond A., Millan P., “Mesures couplées LDA—Fils chauds, et traitement des signaux LDA”, 5ème Congrès Francophone de Vélocimétrie Laser,
Rouen.
the authoritative version for attribution.

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CONTROL OF THE TURBULENT WAKE OF AN APPENDED STREAMLINED BODY 352
DISCUSSION
M.L.Billet
ARL/Pennsylvania State University
USA
The authors have performed an interesting experiment where they used a wall-jet on a streamlined body to control
the mean wake ingested by a downstream propeller. This has provided some insite into modelling higher Reynolds
number flows in reference to powering performance. However, the incoming wake into the propeller for this streamline
body is also controlled by the afterbody adverse pressure gradient and interactions with the appendages.
The resultant mean velocity profiles at different Reynolds number are appropriately similar. However, the lower
Reynolds number wall-jet case is still a wall-jet, although complicated by the afterbody geometry and propeller. The
distribution of the turbulent energy throughout the boundary layer cannot be appropriately similar (see Wygnanski, Katz,
and Hover (1). The turbulence data is not complete in this paper and the measurement method needs some clarification.
Have the authors made measurements of the RMS, means and length scales for the cases tested?
As discussed by the authors, the spatially nonuniform flow and the temporal variations are of primary concern for the
propeller inflow. For this reason, ARL Penn State has utilized shorter models and in some cases screens are added to the
nose of the body to generate the predicted mean wake. However, the issue of turbulent energy distribution and flowfield
harmonic content as a function of Reynolds number remains a critical issue for cavitation and hydroacoustic performance.
Hydroacoustic performance is very sensitive to flow features and many studies have shown this relationship. Two
interesting experiments that relate appendage wake features to noise have been conducted by ARL Penn State and
Brookfield and Waitz (2).
Two experiments to investigate blowing from the trailing edge of an appendage have been conducted at ARL Penn
State. The wind tunnel experiment of a control-surface-like appendage showed the ability of trailing-edge blowing to
generate a momentumless wake, for a nonlifting, three-dimensional airfoil. At an angle-of-attack of ten degrees, a
completely momentumless wake using trailing-edge blowing could not be generated, because of the asymmetry of the
original wake. A dual-slot configuration for adapting trailing-edge blowing to a lifting foil was then evaluated. In a
second experiment, trailing-edge blowing on five stationary struts located upstream of a five-bladed fan was incorporated.
With a total flow rate through all the blowing holes equal to 0.7% of the flow rate through the fan itself, significant
reduction in the radiated noise at the blade-passing frequency and its integer multiples was demonstrated. The reductions
ranged from 15–24 dB for the first four harmonics and from 3–9 dB for the next three harmonics. Brookfield and Waitz
(2) have had similar success using trailing-edge blowing on rotor blades upstream of stator blades in a high-bypass-ratio
fan stage. They approximately filled in the momentum deficit in the rotor wakes, reducing the amplitudes of the first two
wake harmonics by 70–85%. The resulting stator unsteady loading was reduced up to 10 dB at the blade-passing
frequency.
REFERENCES:
1. Wygnanski, Katz, and Hover, “Applicability of Scaling Laws to the Turbulent Wall Jet,” Journal of Fluid Mechanics, 234, pp. 669–690, 1992.
2. Brookfield, J.M. and Waitz, I.A., “Trailing-Edge Blowing for Reduction of Turbomachinery Fan Noise,” Journal of Propulsion and Power, Vol. 16,
No. 1, pp. 57–64, January-February 2000.
AUTHOR'S REPLY
In our paper, figure 3 shows the evolution of the mean axial velocity profiles from the jet nozzle exit to the propeller
plane in the bare hull configuration. Four blowing flow rate were tested (Vo=5 m/s). Furthermore, measurements at 12 m/
s were also shown in the propeller disk to illustrate the difference in velocity profiles due to the difference in Reynolds
number.
Figure 3 showed that:
• the velocity profiles with the blowing system active appear to be similar to the velocity profiles obtained naturally,
• the blowing covers the difference in Re between 5 m/s (Re=3 107) and 12 m/s (Re=7 107). The range of velocity
profiles which can be achieved seems to correspond to full scale Reynolds Number (Re=109).
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CONTROL OF THE TURBULENT WAKE OF AN APPENDED STREAMLINED BODY 353
Measurements of RMS were also performed for all the cases but were not shown in the paper. The radial
distributions of the measured RMS axial velocity are presented below in the propeller plane. z+ represents the distance
from the model in mm and R the radius of the body.
RMS curves show some differences in the blowing effect area.
Radial distributions of the measured RMS axial velocity in the propeller plane for 4 blowing flow rates (Vo=5 m/s)
DISCUSSION
Michael B.Wilson
David Taylor Model Basin, Carderock Division, NSWC
This is an interesting investigation and implementation of a slot blowing boundary layer control concept aimed at
manipulating the velocity distribution of a model scale turbulent wake at the plane of the propeller. The criterion of
success should be the degree of accuracy of the simulation of the main features of a full scale turbulent wake. The
approach taken here hinges on the range of control of the nominal wake fraction.
Checks on the workability of this approach are based on test results over a very limited range of model Reynolds
numbers: 3×107 to 7×107, not even a full decade. As mentioned in the paper, the target full scale Reynolds number is O
(109). It is also noted that the testing must have been carried out in relatively high temperature water, since the kinematic
viscosity value inferred from the stated Rn-values and the model dimensions indicates that the water tunnel water must
have been at around 39 deg C. One wonders whether this Rn range is perhaps too small for good accuracy control in light
of the inherent uncertainties of the experimental process. For example, in Figure 4 of the paper, the curve of measured
wake fraction wn for the tunnel velocity 5 m/s and Cq0 is essentially the same as the curve for tunnel velocity 12 m/s (at
Cq=0), and only slightly different from the curve for light blowing at Cq1. The relative trends for the Cq0 and Cq1 curves
actually change character with respect to the nondimensional distance (z+)/R0. Has there been an attempt at an uncertainty
analysis for the determination of the wake fraction with the present scheme?
There is no question that at the higher Cq values, the variation of the measured u/V0 has the general appearance of a
higher Reynolds number boundary layer and wake velocity pattern. It is likely that at a higher blowing rate the distance
between the slot and the propeller should be somewhat larger than at lower blowing rates so that the flow mixing and
diffusion mechanisms have enough time for the velocity distribution to settle into the desired configuration. Are there test
results that deal with this issue?
A real practical question is what is the actual appropriate target wake velocity distribution at full scale. Also, can the
full scale wake be simulated at the model scale with a jet blowing flow rate that does not produce a distorted velocity
distribution within the region of interest. It is suggested in the paper that this could be the case, but it is not demonstrated
here.
Some comments and questions in the nature of practical testing issues come to mind:
• The slot blowing around the periphery of the body will affect the test section ambient pressure and its spatial
distribution in the vicinity of the stern and propeller. This pressure would be used in the calculation of the
cavitation number. Was the magnitude of this influence measured?
• The blowing jet will also influence the distribution of the local surface pressures over some length of the body.
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Altered pressure distributions will affect the measurement of net hull forces in a water tunnel experiment. Has
this effect been explored?
• The cross section area blockage of the model body in the 2×1.35 m test section is 5.9%, which is pretty low.
Nevertheless it would be useful to know if there are present any notable interaction effects or unwanted
secondary flows involving the narrow circular jet in the presence of the test section wall boundaries.

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CONTROL OF THE TURBULENT WAKE OF AN APPENDED STREAMLINED BODY 354
• How would this boundary layer control concept work with the body at an inclination angle to the oncoming
stream?
AUTHOR'S REPLY
The Reynolds number is based on the model length. Typically Reynolds number effects on ship wakes can be shown
in the GTH in the range of Re from 107 to 7.107, which corresponds with flow velocities between 1 and 2 m/s and 12 m/s
(highest speed possible in the large test section of the GTH).
In our case the model is 4.4 m long. The water tunnel temperature was at around 24° during the tests. Then the range
of model Reynolds numbers was: to .
All tests were performed with the same model and the same blowing system. The blowing section forms a 1 mm
thick slot around the circular periphery of the body and is set at a 10° angle with respect to the body surface. The slot is
located at about 65% downstream of the nose of the model. As explained in the paper, the characteristics of the slot were
found to be the best compromise between jet velocity, slot width and position in order to minimize the flow rate as much
as possible and to obtain monotonous velocity profiles in the propeller plane.
This optimization was performed with 2D Reynolds Average Navier Stokes (RANS) calculations.
In the paper, we concluded that the range of velocity profiles which can be achieved with blowing covers differences
in Re between model and full scale (Re=109) for the bare hull configuration. It is more difficult to conclude with the
presence of tail planes. The full scale wake distribution in not well known in this case.
The maximal blowing case (Cq3) represents only 0.15% of the test section flow rate. Then we assumed that the
blowing system have no influence on the tunnel parameters (pressure, velocity).
It's true that the blowing jet changes the local surface pressures and then the local friction downstream of the slot.
However we did not measure the hull resistance since this set up is dedicated to hydroacoustic experiments.
The boundary layer control concept can work with a 10° angle inclined body with respect to the upstream flow.
However this experimental configuration has not been investigated yet.
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