The Influence of the Wake Model
on Induced Velocities in the
Pro-peller Plane
J.C. MouIijn and G. Kuiper Report No. 1028-P
PROPCAV'95, Newcastle upon Tyne, U.K. 16th - 18th May 1995
TU Deift
Paculty of Mechanical Engineering and Marine TechnologyShip Hydromechanics Laboratosy Deift University of Technology
PROPCAV' 95
An International Conference on Propeller Cavitation to celebrate 100 years of Propeller Cavitation Research16th -18th May 1995
Newcastle upon Tyne
United Kingdom
Edited by
E J Glover
GHGMitchell
Department of Marine Technology The University Newcastle upon Tyne
lilT
Penshaw Press
The Influence of the Wake Model
on
Induced Velocities in the Propeller Plane
Nomenclature
loading coefficient T/(D2pV) D
non-dimensional circulation F/(2IrRUR)
J
thrust coefficient T/(pn2D4) n
geometrical propeller pitch R
radiai coordinate propellers surfaçe
wakes surface T
reference velocity [V + (2irnø.7R)2]°5 i
advance velocity
principal value velocity at the jth
element of the n0 approximation of Va,Vr
the wake
axial coordinate X
the point at the trailing edgç where X
a trailing vortex starts
angle of attack ß
induced pitch angle
wakes pitch angle F vorticity vector
length of the th element
CT G KT
P
r Sp SW (JR Va 1/cn aJ.C. Moulijn'
G. Kuiper2
Deift Uñiversity of Technology
2 MARIN, Wageningenand Deift University of Technology
Abstract
The trailing vortices from a lifting line propeller model are aligned with the
flow in the wake. Both bound and trailing vortices are discretized. The calculated
location of the trailing vortices is compared with experiments and the agreement
is good. The effect of wake alignment on the induced velocities and on the loading
distribution of the propeller is investigated. This effect is compared with the
effect of linearization of the bound vortices on a mean helical plane. For light to
moderately loaded propellers the effect of wake alignment on thrust is found to be
limited (approx. 4 percent). On skewed propellers the linearization of the bound vortices becomes important,
propeller diameter
advance coefficient Va/(nD) propeller revolutions per second propeller radius
vector of collocation point to a point
on singularity surface
thrust
principal value velocity induced velocity
onset flow velocity
axial, radial, tangential and
rotational(Vt/T) velocity
vector to a line vortex (streamline)
the mt nodal point of the th
approximation of the wake onset flow pitch angle geometrical pitch angle circulation
i
Introduction
The computation of propeller performance is generally done using potential flow formu-lations. The effects of viscosity and rotation of the flow are thus ignored, at least locally in the neighbourhood of the propeller.
It is convenient to distinguish between the propeller design problem and the analysis problem. In the design problem the pressure distribution on the blades is prescribed both in radial and chordwise directión and the geometry of the blades is calcu1ated In the analysis problem the geometry of the propeller is given and the pressure distribution is calculated.
Since the disturbance of the incoming flòw by the propeller blades is relatively small,
the boundary condition on the propeller blade can be linearised. This allows the sep-aration of the effects of camber and thickness. The design problem is thus reduced to the determination of the pitch- and camber distribution for a given distribution of the loading. The analysis problem is thus reduced to the calculation of the loading distri-bution from a given camber/pitch distridistri-bution. The loading can be expressed in both cases by a singularity distribution consisting of vortices or dipoles. In this paper the lifting line approach has been used, which means that all bound vortices in radial direc-tion are taken together as a single lifting vortex. A main problem in the formuladirec-tion of
design and analysis methods is the location of the propellers wake. The. wake consists of
vorticity, shed from the blades. This vorticity is transported by the flow and therefore should be aligned with the flow in the wake. The flow in the wake is, however, also determined by the location of the vortici:ty and the wake structure is therefore part Of the sol.ution. The problem has to be solved iteratively. Since the solution of the wake structure requires lông computations, several assumptions regarding the location of the vorticity in the wake have been used.
In lifting line propeller design the induction factors defined by Lerbs [1.] are generally
used. In this approach the vorticity in the wake is located on helical lines of constant radius and with a prescribed pitch. The pitch of the trailing vortices is generally taken as the induced pitch in the propeller plane 2irrianf3(r)', as shown in Figure 1.
According to Burrill [2] propellers with minimum energy loss in the wake have a
radially constant pitch of the trailing vortices in the ultimate wake. This is a condition
for the radial loading distribution for optimum efficiency. This feature can be used in the analysis of an existing propeller. Assuming that good prope1'1rs are not far from this condition, the pitch of the wake is oftenly taken constant over the radius. In that case only one parameter, the mean induced pitch, describes the wake structure;
A good approximation for the pitch angle is the mean geometrical pitch angle ß, which is known in the analysis problem. This is done in the lifting surface program
AÑPRO of MARIN, which is used later in this paper. The pitch angle /3 can also be used as a starting value for further iterations.
A well known and more refined wake model is that of Kerwin and Lee [3], who assumed that the trailing, vortices would roll-up into a single vortex within a given. distance behind. the blade. The point where all trailing vorticescame together Was called
Figure 1: Velocity Diagramof a Blade Section
the' roll-up point and its location was defined by an angular and a radial (slipstream contraction) coordinate and the pitch of the tip vortex. At the roll-up point all trailing vortices were assumed to have been rolled-up into a tip vortex for each blade and one single hub vortex. The radius of the tip vortex downstream of the roll-up point and the pitch of the tip vortex was taken constant. The transitional wake between the blades and the roll-up point consisted of lines connecting the trailing edge with the roll-up point. This model contains five parameters instead of one. All parameters were chosen on an empirical basis.
Greeley and Kerwin [4] developed a more sophisticated wake model whichwas
im-plemented in the design method P'BD-lO. They split the wake in a transition and an ultimate wake. The ultimate wake was the same as in [3], but the pitch was aligned with
the flow. The transition wake consists of a number of discrete vortices. Their radial position is prescribed from an interpolation between the hub and the outer radius. The pitch of the vortices in the transition wake is roughly aligned with the flow in an iter-ative procedure which converges rapidly. Unfortunately, the pocedure was not stable. The calculated geometry depended on the number of discrete trailing vortices in the transition wake. However, calculations using 9 vortices trailing from each blade were in
good agreement with measurements of Min [5I
Hoshino [6] also splits the wake in a transition and an ultimate part. In the ultimate wake the radial position of the vortices remains constant. The pitch of the ultimate wake is constant in axial direction, but varies in radial direction. its contraction and pitch follow from empirical formulas that are based on flow measurements. In the transition wake the radial and angular position.are obtained by means of linear interpolation from the trailing edge to the ultimate wake.
Glover [7] used slipstream deformation in a lifting line design program. From the radial loading distribution and the helicoidal wake the induced velocities in the wake are calculated. These induced velocities are used to deform the the wake by integrating the slope of the total velocity. Finally the velocities induced in the propeller plane by the deformed trailing vortices are calculated using induction factors for vortex elements.
The use of induction factors for the deformed wake assumes that the elements of the trailing vortex are part of a helicoidal line with constant radius. The error may be significant just behind the propeller where the contraction is largest. The calculation scheme amounts to a first iteration in the adaptation of the trailing vortex location to the local fiow Calculations with and without deformation of the wake showed that the wake deformation had 'a significant effect on the radial loading distribution of the designed propellers.
Maitre and Rowe [8] did calculations with a panel method and a wake which was fully adapted to the flow iteratively. They found a significant difference in pitch of the trailing vortices over the radius. This difference remained in the final wake. It agrees
qualitatively with the results of Glover in that the radial loading distribution is affected by the wake structure.. 'In the present paper a wake alignment procedure quite similar to the iterative method of Maitre and Rowe is used. The wake is fully aligned to the flow in an iteratie procedure.
The wakes of DTRC propellers 4119, 4381 and 4383 have been calculated. Propeller 4119 is a three bladed propeller having no skew and rake. It has been used in extensive measurements by Jessup [9]. Propeller 4381 and 4383 are five bladed propellers. They are two of a systematic series designed by Boswell [10]. In this series skew was varied while the load distribution was kept the same. Propeller 4381 has no skew, and propeller
4383 has an almost linear skew distribution up to 72 degrees at the tip. Boswell reports
a significant delay of cavitation inception with increasing skew. Because sheet cavitation
usually begins at the blade tips, the propeller tip of skewed propellers might be loaded
less heavily than was designed.
-The alignment procedure will be presented. -The aligned wake geometries of
pro-pellers 4119 and 4381 will be compared to measurements of Jessup [9] and Min [5]. The wake measurements of Jessup are considered the most accurate available. The
conse-quences of the linearisation of the boundary condition on the propeller blade and the
effect of the wake alignment on the induced pitch angle ß are investigated. These effects
are translated into effects of propeller loading and radial load distribution. The effect
of skew is also considered.
2
The wake alignment procedure
Two more or less equivalent boundary conditions can be used on a trailing vortex sheet: - the shed vorticity is convected by the flow according to Helmholtz's theorem,
no pressure jump occurs across the vortex sheet.
The first condition has been applied in a time simulation model. This alignment
proce-dure might also be used in unsteady problems, butup to now it has only been formulated
for the steady case The computational effort of this model is too large for any useful
The second condition is used in a faster iterative alignment procedure. This
proce-dure can only be used in steady problems.. In a steady flow free vorticity is convected (according to Helmholtz's theorem) along streamlines,so the shed vorticity can be
mod-elled by a steady vortex sheet. This. free vortex sheet cannot bear, any forces, so the pressure at both sides of the sheet should be the same. The pressure jump p across a
vortex sheet can be expressed as follows:
(1) is the vorticity vector, and l is the 'principal value velocity at the trailing vortex sheet:
Jf
Ts
+-.v.JJ
3TdS+
(2)w.here S, is the propellers surface, S,, is the wakes surface, and is the onset flow velocity due to advance and rotation of the propeller. The thickness of the blades and the hub has been neglected. Because and V are non-zero, they should have the same direçtion to avoid a pressure jump.
The vortex sheet is modelled by a number of discrete line vôrtices. Each line vortex must coincide with a streamline based on the principal value velocity. The differential equation of a streamline reads:
dX1 dX2 dX3
di
.v1
v2v31ç1
Integration and rearrangement of (3) leads to:
Idi
Jo is the point at the trailing edge where the trailing vortex starts. Because i7 depends on the trailing vortex wake geometry an iterative procedure is applied:
n+i+J:
xn -.dI
(5)
The line vortex is divided into a finite number of straight line vortex elements, so this
integral can be 'approximated by a summation over m elements:
rnn
1Xo+I1T1
¿X1 (6)¿K is the length of the jth element. This process is illustrated in Figure 2.
The trailing vortex wake has been discretized into a finite number of straight line elements. The velocity induced by each element has been calculated by means of
Figure 2: The Iterative Wake Alignment Procedure.
the velocities induced by all separate elements. The self-induced velocity of an element has been be omitted.
The curved vortices are divided into a finite number of straight line vortices, so the
trailing vortices have to be truncated at a finitedistance behind the propeller. Theerror
in the induced velocity in the vicinity of the propeller due to this truncation vanishes if the truncation ismoved downstream. However the truncation might influence the calcu-lated wake geometry and so the calcucalcu-lated flow around: the propeller. If the perturbation
velocity is relatively small compared to the onset flow ve1ocity, the approximation of the
wake near the truncation will be reasonably accurate. J that case the truncation of the vortices is allowed. Some calculations to .check this assumption have been performed.
In order to start the iterative procedure (6) an approximation of the wake is needed. This can be an approximation by vortices following the onset flow..
Necessary conditions for convergence of the iterative procedure are: small perturba-tion velocity, and applicaperturba-tion of cylinder coordinates, if cartesian coordinates are used
and IX+l
- X
is large due to summation over the elements i to m - 1, the velocityV is not a good approximation of V,, so the procedure will not converge. If cylinder
coordinates are used the velocity is expressed in terms ofan axial (Va), a radial (Vr) and
a rotational (VO vt/r) component. In that case the onset flow velocity is everywhere
the same (va = Va., V,. = O,, V = 2irn), so this par,t of the velocity V14 is always
approxi-mated exactly. Probably the perturbation velocity is approxiapproxi-mated in a better way too. Anyhow the iterative procedure appears to cnverge. if cylinder coordinates are used. If the perturbation velocity is large because the vortex strength of the vortices is large, or discrete vortices are positioned close to each other, the iterative procedure also fails. The demand of small perturbation velocity restricts the application of this alignment
procedure to moderately loaded propellers. If some special arrangements hike combining
vortices in roll-up regions are made, good results for heavily loaded propellers might be obtained.
lifting bound vortex 15 Q 10 Q Q (3
Figure 3: Modelling of the Bound Vorticity.
-
propeller 4119.-L propeller 4381
propeller 4383
non-lifting bound vortex
3
The Geometry of the Aligned Wake
The wake of the DTRC propellers 4119, 4381 and 4383 have been calculated. For the calculation of the wake geometry the radial circulation distribution is needed. For
pro-pellers 4381 and 4383 the circulation distribution as calculated by the MARIN program ANPRO was used, and for propeller 4119 a circulation distribution calculated by the MIT program PSF-lO (from literature) was used. The radial circulation distributions are presented in Figure 4.
The the wake of propeller 4119 as calculated by the alignment program is given in Figure 5. For convenience the wake f just one blade is shown, but the Figure is a
free-vortex
.2 .4 .6 .8 lo
nR
Figure 4: Radial Circulation Distribution of DTRC Propellers
The iterative procedure is embedded in a computer code. In this computer code the bound vorticity is represented by one discrete lifting vortex and a number of nonlifting vortices connecting the lifting vortex to the trailing vortices which start at the trailing edge of the propeller blade (see Figure 3). The lifting vortex is situated at the blade reference line, and a non lifting vortex coincides with the pitch helix.
Figure 5: Lateral view at the wake of propeller 4119.
result of a three bladed model. The pitch variation of the wake over the rádius is clearly visible: the pitch of the trailing vortices at the inner and outer radii is much smaller than the the pitch of vortices trailing from intermediate radii. At the outer radii some
roll-up of the vortices occurs.
The calculated wake of propeller 4119 is compared to measurements of Jessup [9] in Figure 6. These measurements of propeller wakes by Jessup are considered to be the most accurate available. Although the modlling by discrete vortices can never represent the complex structure of the real wake, the global position of the wake is approximated
very well. It is the global position of the wake that has an important effect on the
induced velocities in the propeller plane and on the propeller loading.
The calculated position of the tip vortex is defined as the mean position weighted by the vortex strength of the discrete vortex lines that
are part of the tip vortex. A
discrete vortex line joins the tip vortex at some axial .distance after the propeller when its radiai position is larger than that f the local the tipvortex. This causes the mean tip vortex to be not very smooth.
In the Figures 7 and 8 the radial and angular positions of the tip vortex are compared to measurements of Jessup [9] and Min [5]. The contraction of the thus defined tipvortex seems to be underestimated by the program. The angular position of the wake corresponds very good. This angular position is directly related to the pitch of the wake. Kerwin and Lee [3] found from systematical variation of pitch and contraction of the wake, that pitch has a major effect on the propeller loading, while contraction was less important.
4
Linearisation on the Propeller Blades
A.part from simplifications of the wake another simplification which is often made in propeller calculations, is the linearisation of the boundary condition on the propeller blades surface. In many lifting surface programs like ANPRO the boundary condition
52.50 27.50 24.40 301 I 287 Angle (Dog.) X/RQ .328 259 -Aa/ (V/RI C0.4TCUR VALUES In 2.000E+1 2 l.SOOEnoi 3n I.000EsOI 4n 5.000E+00 5 e -S.00aE00 6 e -t.000E+01 7 n -1.00E+0I O n -2.000EsOl 9 I -4.000E+0I -Wa, (V/RI CONTOUR VALUES j n 2.000EI0I 2 e I.SOOE+01 3 n 1.0000+01 4 n 5000E.O0 5 n -2.5000+00 6 n -5.600E+Oo 7n-1.0000+02 I -2.5000+01 9 -2.0000+01 10 n-4.0000+01 266 252 238 224 Angle )Deg.l
Figure 6: The Radial and Angular Position of the Wake at x/R
= 0.328 and x/R =
0.951 as Measured by Jessup (Contour Values of Vorticity in Pitch Direction) and as Calculated by the Wake Alignment Programm (The Circles Indicate the Vortex Strength of the Discrete Vortices).at the camber surface (zero velocity normal to this surface) is fulfilled at a mean pitch surface. The singularities are also located on the mean pitch surface instead of on the camber surface. Figure 9 illustrates this linearisation in a sectional cross plane. In this plane the camber and mean pitch surface reduce to a camber and mean pitch line. This linearisation is allowed when the distance between the camber line and the mean pitch line is small.
Skew is defined as a translation of the propeller blade section along the actual pitch line. Due to this definition, and because skewed propellers often havea strongly varying
pitch, the distance between the camber line and themean pitch line of skewed propellers
202.50
'-84.40
64.40
propeller 4119
i :oo
Figure 8: The Angular Position of the Tip Vortex
can be large. Then the linearisation of the boundary condition on the blades surface is questionnable.
An indication'of the effects of this linearisation is obtained using the model outlined in Figure 3. When the blade is linearised all singularities are located on the mean pitch surface. In the non linear case t:he singularities are located on the true geometrical pitch surface which is located very close to the camber surface because camber is usually
small.
The induced velocities are calculated at points situated at the lifting bound vortex (see Figure 3). This lifting bound vortex is not a straight line when the propeller is
measxed by Jessup asic. 17 voroces .95 - csic. 9 voilices __. r__ .90 - - -. .85 .4 i/R propellèr 4391 .6 .8 10 1.00 ---_ --.-_ measured by l9n cac. 17 vorces calc.9vorbces 5:oroces 90 .4 1.0 oiR
Figure 7: The Radial Position of the Tip Vortex
propeller 4119 o .4 .6 .8 10 propeNer 4381 400 asic. Il vocices 350 measured by Jesaup -, 300 C 250
mean pitch line
prescribed velocity direction at mean pitch line
camber line
Figure 9: Linearisation of the boundary condition on the propeller blades surface skewed, so it induces a non-zero velocity to itself. Because a curved discrete line vortex contains a so called logarithmic singularity, this self-induced velocity is not defined. If the lifting vortex line is divided into straight line vortex elements, the self-induced velocity is defined by excluding the element containing the singularity. However, this velocity will not converge if. the number of discrete elements is enlarged. Only if the number of elements is the same, and the local shape of the lifting vortex does not change too much due to the linearisation, the induced velocities in different situations
can be compared. A more consistent analysis should be performed using a lifting surface
method.
5
The Investigated Conditions
in order to study the effects of wake alignment and linearisation of the propeller blade on the induced velocities in the propeller plane and the propeller load distribution, the following three conditions will be investigated:
The bound vortices and the vortices of the wake are all located on a helical plane having a constant pitch. This pitch is chosen to be the mean geometrical pitch of the propeller. This situation corresponds to the model used in lifting surface programs like ANPRO. It will be referred to as the.fully linearised condition. The bound vortices are located on the geometrical pitch plane, while the trailing vortices are located on a helical piane. with constant pitch, just as in the first situation. In this case the trailing vortices start at the trailing edge of the blade. This situation will be indicated as condition with a linearized wake.
The bound vortices are located on the geometrical pitch surface, while the trailing vortices are aligned with the flow.. This condition will be indicated as the aligned wake.
When the results of the first and second conditions are compared the effect of the linearisation of the propeller blades is found. Comparison of the results of the second and third condition gives the effect of the wake alignment.
ne -. aligned wake
O-0 linear wake
fully lineanzed
"S
N
ne-. eligned wake O-e linear wake
' fully lineanzed
nR
Figure 10: Induced Pitch Angles of Propellers 4381 and 4383
All conditions have been investigated for DTRC propellers 4381 (no skew) and 4383 (72 degrees skew).
6
Induced Pitch Angle and Load Distribution
In Figure 1 the velocity diagram for a propeller blade section has been presented
pre-sented. This Figure shows that the induced pitch angle /3 has a direct effect on the angle of attack a of the propeller blade section, and therefore on the loading of the blade section. Small variations in ß are significant, because the angle of attack a is much smaller than fi. To show the relevant variations in /3 these are expressed in the angle ß
-
9. In the comparisons the advance ratio of the propellers, and thus the angle fi, does not vary.In Figure 10 the ang1s ß
-
@ of the different conditions are presented for propellers 4381 and 4383. From this Figure it is clear that the effect of linearisation of the boundarycondition on the blade of the unskewed propeller 4381 is small. The effect of the wake model is much more impOrtant.
For the skewed propeller 4383 the linearisation of the blade causes an important difference of the induced pitch angle. The effect of the linearisation of the wake of propeller 4383 is similar to the effect of the linearisation of the wake of propeller 4381.
The effect of the wake model and the linearisation of the boundary condition on the propeller blades has been expressed above in a variation of ß
-
/3. The effect on the calculated load distribution of the propeller cannot directly be calculated because the wake alignment program was developed as a design method. In that case the loading is fixed and a change in /3 results in a correction on the propeller pitch ß. However, when the propeller pitch is' corrected for the variation in ß-
ßj, an analysis with the lifting surface program ANPRO provides an approximation of the effect on the propeller loading and load distribution. In Table 1 this approximation of K at design J = 0.889of propellers 4381 and 4383 at the three different cases is presented. The difference in K of 3% to 4% due to. the linearisation of the wake is quite relevant. The error due to the linearisation of the blade is negligible for the unskewed propeller, but for the skewed propeller it is about 6% of K. The linearisation of the propeller blades of
1.0 proplôr 4381 propeller 4383 10 0 .2 .4 .8 O .2 .8 nR .8 15 10 a o 15 10 5, O .5.
Table 1: The effect of the linearisation of the boundary condition on the blade and the alignment of the wake on K.
propeller 4381 propeller 4383 50 1.00 .75 .25 0' o
/
/
I
Jo-c
o 1.0 0/
/
. -fully linearizedo-c linear wake - aligned wake
'S.
'---4 alIgned wake-fully linearized
r/A
Figure 11: The Effect of the Linearisation of the Boundary Condition on the Blade and the Alignment of the Wake on the Load Distribution of Propellers 4381 and 4383. skewed propellers is questionable.
The effect of the wake model and the linearisation of the propeller blades on the radial distribution of the circulation is presented in Figure 11. The load distribution of propeller 4381 does not change much due to either the linearisation of the boundary condition on the blades or the alignment of the wake. The load distribution of propeller 4383 is affected significantly. The linearisation of the boundary condition on the blades
is the most important. The load of the blade tip is
overestimated in both the fullylinearised and the non-aligned wake cases. This might be a factor in the the delay of cavitation inception of skewed própellers as reported by Boswell [10].
7'
Conclusions
The present method to align the flow is straightforward and relatively simple. The cal-culations were carried out on a SUN Sparc station 1 (computational speed is comparable
case 4381 4383 fully linearised 0.219 0.211 linear wake 0.219 0.198 aligned wake 0.211 0.192 1.00
/
.75 .50 fully Inearized linear wake .25 - -, aligned wake .2 .4 .6 .8 10 4 L s o .0-. linear wake - fully linearized
-4 a-a alIgned wake - linear wake '-' aligned wake - fully linearized
4 a' 'S
o
B--. Ilnearwake-fully lInearIzed
-4 a--0 aligned wake . linear wake
.2 .4 .6 .8
10 0 .2
.4.6
10o .2 .4
nR
to a 486 PC). The tizne ino1ved in one alignment iteration was of the order of 15
mm-utes for propeller 4119 (9 trailing vortices, length of wake 3.3D). The induced velocities in the propeller plane converged within about 5 iterations. On a faster machine these calculations can easily be carried out on a routine basis.
The results of Propeller 4119 indicate that the calculations agree very well with measurements. This is particularly true for the radial pitch distribution. of the trailing vortices. The reduction of the pitch of the trailing vortices, as discussed by Dyne [1 1] is confirmed. The contraction shows larger discrepancies.. This is partly due to the fact that the definitionofthe outer radius of thevake can vary. The effect of this discrepancy
on the propeller loading is considered to be small.
The calculation of the wake alignment still requires a significant effort. To see if that effort is worthwhile the calculations of propellers 4381 and 4383 were carried out. The wake alignment causes a decrease of the propeller thrust of some 4 percent. In itself this is not very large. Errors in the representation of viscous effects are probably similar in magnitude. This is certainly true for programs with a fully linearized approach, where the location of the singularities deviates from the pitchline of the blade sections. In case
ofskewed propellers the error due to linearization of the blades becomesmore significant
than the effect of wake alignment.
The present results are for a few propellersonly and it is not possible to generalize the results. Both propellers 4381 and 4383 are lightly loaded (with a thrust coefficient
CT 0.7). The propeller used by Clover [7] e.g. had a thrust coefficient C' of 3.3. The
effects of wake alignment will increase with the loading.
Propeller 4381 is a common type of propeller, with a maximum pitch ratio of 1.35. At the tip the pitch ratio is 1.03. This is a moderately unloaded tip. In commercial
propellers the tip loading will generally be higher. It is expected that in those cases the
effect of wake alignment will remain about the same.
Propeller 4383 is not only skewed, but also, has a more strongly reduced pitch at the tip. This is generally done to counter the increased tip loading due to skew. The wake
alignment procedure indicates that the ti.p loading on a skewed propeller is overestlmated
when no wake alignment is used. So on skewed propellers the actual tip loadingmay be
smaller than designed.
This effect is particularly strong when the linearization of the blade is important. In those cases the tip loading is significantly increased due to the linearization and the actual tip loading may be significantly smaller than designed This problemmay confuse
the effect of skew on cavitation inception, where skew delays cavitation inception in the tip region. It is possible that the origin of the decrease is,, at least for
a part, caused y
errors in the calculation of the tip loading.
Further calculations on heavily loaded propellers' are required to assess when the wake alignment is necessary for a proper calculation of the loading 'and 'the loading distribution. For Navy propellers, which are always lightly loaded, the effect is limited. For those propellers, which often have a strongly reducçd pitch at the tip in combination with skew, the hnearization of the blades gives larger errors
References
[1] H.W. Lerbs, "Moderately Loaded Propellers with a Finite Number of Blades and an
Arbitrary Distribution of Circulation", Trans. SNAME, Vol.60, 1952.
[2] L.C.Burrill, "On Propeller Theory", Inst of Eng. and Shipb. in SEOTH, 1947. [3] J.E. Kerwin, C.S. Lee, "Prediction of Steady and Unsteady Marine Propeller
Per-formance by Numerical Methods", Trans. SNAME, Vol.86, 1978.
[4] D.S. Greeley, J.E. Kerwin, "Numerical Methods of Propeller Design and Analysis
in Steady. Flow", Trans. SNAME, Vol.90, 1989.
[5] K.S. Mm, Numerical and Experimental Methods for the Prediction of Field Point
Velocities Around Propeller Blades", M.I.T. Department of Ocean Engineering
Re-port 78-12, Cambridge, Mass., June 1978.
[6] T. Hoshino, "A Surface Panel Method with Deformed Wake Model to Analyse
Hy-drodynamic Characteristics of Propeller in Steady Flow", Mitsubishi Technical Bul-letin No.195, 1991.
[7] E.J. Clover, "A Design Method for the Heavily Loaded Marine Propeller", Trans.
RINA, vol.116,1974.
[8] T.A. Maitre, A.R. Rowe, " Modeling of Flow around a Marine Propeller using Potential Based Methods", Journal of Ship Research, Vol.35, 1991.
S.D. Jessup, "An Experimental Investigation of Viscous Aspects of Propeller Blade Flow", Thesis, The Catholic University of America, Washington D.C., 1989. R.J. Boswell, "Design, Cavitation Performance and Open- Water Performance ofa
Series of Skewed Propellers", NSRDC Report 3339, 1971.
G. Dyne, "On the Efficiency of a Propeller in Uniform Flow", Trans RINA, 1993.
