|
Items in cart [0] |
Questions? Call 888-624-8373 |
| Copyright © 2009. National Academy of Sciences. All rights reserved. Terms of Use and Privacy Statement |
Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter.
Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.
OCR for page 284
Propulsor Design Using Clebsch Formulation
C Dai, R Miller (Naval suTface Warfare Center, Carderock Division, USA),
M Zengeneh, C Yiu (University College London, United Krngdom)
ABSTRACT
A three dimensional invense design
method is presented for the design of marine
propulsors This method makes use of the
Clebsch representation of the rotational part of the
ve ocity held for modeling both the bound vorticity
of blade surfaces and the free stream vor city
The blade shape is detemmined by imposing the
flow tangency condition for a given loading
specihcation This technique is demonstrated
here for the design of a ducted pod propulsor
operating in a unifomm stream and a ducted
propulsor mounted on the tail of an axisymmetnc
body operating in a shear onset Row For the case
of ducted propulsor design, both mixed and axial
flow conhqurabons are presented to demonstrate
the use of mixed flow concept for cavitation
perfommance improvement
INTRODUCTION
The problem of propulsor design has
aroused considerable the reheal interest for over
half a century For examp e, the lining line [1 ] and
limbo surface theories [2] [3] have advanced to a
stage that they are routinely used in propulsor
design in the last three decades Particularly, in
the area of open screw propeller design, the
classical approach of lifting line and limbo surface
in conjunction with the notions of thnust deduction
and wake fraction has been proven to be a very
reliatie approach to the propulsor design problem
Recent y there has been a strong interest in the
internal r r ducted types of propulsor The internal
type of propulsor is mainly refe red to as a waterjet
propulsor Both waterjet and ducted types of
propulsors were conceived and developed in the
latter part of 19th century The resurgence of
interest in the internal and ducted propulsors is
mainly due to the fact that there is better
understanding of both physical phenomena and
design issues related to those types of propulsors
For example the hull and propulsor interaction
can contribute positively to the waterjet
hydrodynamic performance [4] The ducted
propulsor has long been recognized for its ability
to improve cavitation perfommance and sustain
higher loading near the tip region Historically, the
ducted propulsor design is based on the princip e
of potential flow [5] in the last decade, efforts
have been made to couple Euler or Navier Stokes
solver with a limbo surface code for the ducted
propulsor designs [6], [7] and [8] The procedure
has been used very successfully in the situation
which involves simple throughnow geometry or
the onset shear is weak Another approach that
has been taken in the last 3 decades in the design
of internal or ducted propulsors is the use of
streamline cu vature methods for throughtlow
analysis and a semi emp ncal method of meanline
design for blades [9] Despite the fact that the
streamline cu vature method can handle the
throughtlow with the blading ehect more ethcienf y
than the EuierAihbng surface approach the blading
design is relatively weak and it has to rely on
experience and the experimental database
With increased demand for high
perfommance propulsor, a design method, based
on a high order physical model which can account
for maul bole stages, shear flow and fully three
dimensional effect is needed An inverse design
method based on the idea of Clebsch
decomposition of theveocity held has been
successfully developed in [10] for unifomm how and
vortex free loading conditions Subsequently, the
method has been applied successfully to
turbomachinery designs [11] it has also been
used to demonstrate its potential for ducted
propulsor design [12] [13] The work to further
develop the inverse design method as part of code
enhancement and verihcabon processes is
described in this paper Several improvements
and new design capabilities were incorporated in
the existing code so it can be more ehectivey
used for propulsor design The new features
include addibon of three dimensional boundary
layer calculations arbitrary blade planfomm layout
foraccrmmodatirn of rake and skew, and a new
OCR for page 285
mixing plane f ml u at a1 to account for dose
spacing between stages This paper will address
the fundamental foundation of the present
approach and three design examples will be
presented as illustrations The the reheal part of
the presentation is to identity the basic concept
and the key features of the method The idea of
using mixed flow for cavitabon imprrvem ent will
also be demonstrated in one of the examples
THEORETICAL FORMULATION
The usual method of expressing the
ve ocity vector held is to express it as the gradient
of a scalar potential bus the cur of a vector
potential, which results in the Hemlldtzs
decomposition An alternative way is to dehne all
potentials as scalarvariables and Clebsch in 1859
introduced such dehnibon for the case of
isentropic fluid how as follow:
y(x,t) = V ¢(_,t) + kgx,t)V x(_,t)
(1)
where V ~ is the potential part of v and XV X is the
rotabonal part of v All vector qualities are in bold
with underscores it is interesting to observe that
y is detemmined uniquely by a set of potenbals but
not vice versa This unique proper y of the
Clebsch representation enables modeling of
different voracity types for a propulsor now in this
work the Clebsch variables are used to model
bound and trailing vortices associated with blade
loading and the onset shear ehect
The voracity vector is defined by taking
the curl of velocity and it can be written as
(=V\(x,t)xVxgx,t) (2)
It is clear frrm (1) blat the voracity lines lie on
the surfaces of constant X and X Furthermore,
it satishes Kelvin's theorem exact y by taking the
divergence of (2) One can also observe from
(2) that both X and X have to satisfy the
c ndihrns that
6.V~ x,t)=0
and
'7X x,t) =0
(4)
(3)
In the propulsor flow problem the Clebsch
representation of the bound and the trailing
vortices can be identified with the loading and
the geometric parameters of the trading design
One logical choice for X and X is the blade
circulation and the nommal vector to the blade
surface The bound circulation around the blade
section is related to the circumferential averaged
swirl ve ocity around the axis of rotation and the
hrst Clebsch potential can be defined as
X=r vc =rH/2x (5)
where H is the blade number and E is the blade
circulation The trade surface can be
represented by the wrap angle of the blade
geometry and the second Clebsch potential can
be defined as
x=r(x,r,8)=8 f(x,r)
(6)
where f is the wrap angle and x r and 8 are the
c- lindn~al coordinates of the prr blem The
bound and the trailing vortices can then be
defined as
lob = Vrv~xVr)6(r)
(7)
where 3(r ) is the periodic delta function about r
and it can be written as [14]
3(r ) :: exp
N=1 - ~
(8)
The free stream voracity can also be modeled by
selecting a different set of Clebsch potentials
The momentum equation for an in. isad and
incompressible fluid can be expressed as
VH=p(wxt)
(9)
where H is the total head, w is the relative
ve ocity and p is the fluid density it can be seen
frrm (9) that the vo~baty vector lies on the
surface of Bernoulli surface Therefore the hrst
Clebsch potential to m c de the free stream shear
can be identhed as the total head H The
second Clebsch potential requires a time scale
representati on i n order to m ake the vorti a ty
dehnition The deft function [15] provides such
representation and is consistent with the overall
scheme of the fommulabon The drip function
can be interpreted, as the bme required for a
fluid particle to trove hrom a reference position
to reach a particular point in the nc :: he d and it
can written as
OCR for page 286
Y=i(w.d3)!(w._) (10) streamshearv rba es issimplythemean
f ( 1, and it can be written as
where 3 is the distance along the stream surface
frrm the reference position Taking the cross tv = V H x V ~ (15)
product of (9) with V ~ and making use of a
vector identity, it can be shown that and
~y=VHxV~ (11) fbisthemeanof(7)
Appropnate Clebsch potentials for both blade
effect and free stream shear effect have been
identified and can be applied to the propulsor
flow modeling The velocity held has to satisfy
continuity condition by taking the divergence of
(1) and setting to zero,
Van= EVER V\.Vx
(12)
If the circumferential component of the ve ocity
he d is represented by generalized Fourier
series, then one can write
V = V + ~ ., (r x) exp ~ n$, Or [0, 2.. H]
11=1 - K (13)
where v is the zero hammonic or the
circumferential mean velocity component and
., (r x) is the or mplex periodic components of
veocitybeld verbarandstarrepresentmean
and periodic components respectively The
above Fourier series representation of
circumferential components can also be applied
to the potential functions as depicted in (12)
The result is a system of equations that governs
each harm oni c or m ponent of the velocity h eld
that must satisfy continuity The circumferential
m ean or m ponent wil I be exam ined hrst before
the periodic components will be evaluated The
mean .eoaty can be represented better by
considering the axisymmetric stream hunchon
instead of the potential functions because of the
convenience in implementing blockage and
thickness effect in the formulation Furthemmore,
the stream function satishes continuity by
dehnition and it explicit y re ates to the voracity in
the flow held By dehnition the axisymmetnc
stream function V can be written as
V V = ( f b By) ·ec
(14)
where V 2 ,5 the Lap Dean operator in the r x
plane e is the unit vector in the circumferential
direct on fib and Embark the circumferential
averaged components of the blade and free
Sb = Oryx Vr
(16)
since the mean of the periodic delta function is 1
[14] The periodic components of the velocity
he d can be evaluated by solving the Fourier
components of ¢, X and X The periodic
component of the bladevorticity can Rewritten
as
fib- =( Vrv~x Vr )(6(r) 1) (17)
where(0(r ) 1) is S'(r ), the hrst order de vabve
of saw tooth function [14] Therefore the
periodic components of velocity due to blade
vortiaty that satishes (17) can be written as
ye = S(r ) V r via (18)
and from [14], S(r ) can be expressed as
S(r ) = :: ( i/ nH) exp ~ no
N=1 - ~
(19)
The penodicveocity components due to free
stream shear can be represented by the
Clebsch potentials H and ~ as follow:
ye =( H+H*) V( ~ + r*) H V .(20)
where Hi' and Rae are the complex Founer
call ponents of H and ~ It can be seen from
(20) that the periodic velocity of free stream
shear consists of cross product terms and they
can be expanded as
y · = H V r~ + Hi' V r~ + Hi' V ~ (21)
(18) and (21) presents the Clebsch
representation of complex penodicveloaty
com ponents induced by the blade vr rtcity and
the free stream vorticity The Clebsch potentials
as specified in (18) and (21) can be substitute
direct y into (12) The resultant equation for the
nth order of the complex Fourier component can
be written as
OCR for page 287
V 2q~n ~ = imp nrf/(nH) V 2 r Vc
( Vr via. Vf)ioxp nut
( H v2 Ann + V H · V an )
( HE v2 ~ + V HE eV ~ )
:=1 - N _ H ~ Vat ))
The present code only models the
circumferenbal mean of shear effect and fully
three dimensional shear effect will be
investigated in the future Two auxiliary
equations are required to solve for H and ~ it
can be seen frr m (9) that the total pressure
convects along the re ative velocity, i e
w.VH=0
and from (3) that
VH. VHxVr)=0
(23)
(24)
Hotll H and ~ are decomposed into the
circumferenbal mean and periodic components
in (23) and (24) and the Fourier components of
both H and ~ can be calculated from the
resultant relative velocity An addibonal
condition is required in order to solve for the
blade geometry f for a given loading r via The
flow tangency condition is required and it can be
expressed as
_b -Vf = 0
(25)
where Wb = ( W + W )/2 and w and w are
the upper and lower surface velocibes r n the
blade (14), (22), (23), (24) and (25) constitute
the complete set of equations that are required
to be solved for the design calculation of a
propulsor system The boundary conditions for
(14) are very straightforward since the inflow
condition is specified and the solid boundaries
are simply lines of constant V The boundary
conditions for (22) are no penetration condition
on the solid boundary For the multi stage
propulsor design problem i M S solved for
individual blade row where inflow boundary
condition for downstream Made row is specified
by the solution frrm the upstream blade row
The periodic components are assumed to vanish
far downstream (22), (24) and (25) are
hyper olic set of equations and initial cc ndbc us
are required to start the integration The
equations need to be solved in an iterative
manner subject to the blade loading and
boundary conditions specified Another
advantage of the present fommulabon is that the
Kutta condition at the blade trailing edge is
satished exact y and the trailing wake geometry
can be computed as part of the overall solubon
The pressure jump across the blade surface can
be shown [10] to be
p p = 2x/H(~wb.V r V)
(26)
It is obvious from the above equation that the
kutta condition can be imposed explicitly by
specifying V r v ~ to be zero at the trailing edge
Furthermone, the germetry of the trailing vortex
sheet due to the force vortex loading distribution
can be computed as part of the overall solubon
The set of equations and the boundary
conditions are cast in body htted coordinates
and solved by unite difference technique with a
mulbgnd algorithm for quicker convergence
ALGORITHM DESCRIPTIONS
The present code was originally
developed at University College London (UCL)
It was vended and further enhanced at Naval
Surface Warfare Center Carderock Division
(NSWCCD) so that it can be used for practical
propulsor design The code can perfomm
inverse blading design for a given body and duct
geometry Upstream inflow velocity and static
pressure distributions must be preach bed The
blade loading is specified by prescnlzn3
span ::lse swirl velocity distribubons at the
leading and trailing edges of the blade rows
The code has two modes of blade design with a
given duct and body geometry The hrst mode
is to design the blades according to the given
loading and duct geometry in this case, the
mass nc :: rate is a calculated parameter The
second mode is to design for a given mass nc ::
rate and the load distnbubon will be scaled
accordingly to achieve the required mass nc ::
rate for a heed duct and body geometry The
second mode also allows vanabon of duct
geometry by increasing or decreasing duct
radius for a heed load distribubon A
generalized load distribution algorithm has been
incorporated so that different chordwise load
distnbubons can be specified along different
streamlines The new capability enables hne
tuning in blade design which is partculary
useful for Made section design near the end:. all
OCR for page 288
region in the original code, the duct can also be
designed with an inverse mode by specif ng the
target surface velocity distribution on the duct
inner surface and the duct lower contour shape
will be calculated The solubon may not always
guarantee a unique solution A direct approach
is taken in this work for the duct design The
lower surface of the duct was detemmined
through design iteration using the streamline
curvature method frr the throughtlow
calculations The mater advantage of the
streamline curvature approach is relative quick
evaluation of the impact of duct shape on the
throughtlow solution before the detailed Lade
design A thickness fomm is added to the lower
duct surface to dehne the duct shape The duct
geometry can be perturbed during the blade
design cycle to affect the duct pressure
distnbubon The approach is extremely effective
and robust for practical design applications A
brief discussion on the ducted propulsor design
will be given in the next section and fdlowed by
three design examples
DESIGN CONSIDERATIONS
An internal or ducted propulsor consists
of a rotating impeller operating inside a casing or
duct with stationary vanes for swir cancellation
so that loss of rotabonal energy in the slip
stream can be reduced or eliminated Stabr nary
vanes can also serve the purpose of supporting
the duct in contrast to an internal propulsor,
such as a waterjet, which is inside the hull, a
ducted propulsor is usually external to the hull
An integrated hull pn~l)ulsor design can also
lead to a potenbal improvement in powering
performance by mat Rig use of p sibve
interaction effect between the hull and the
propulsor The intent here is not to give a
detailed account of propulsor design, but to
highlight the important design considerations in
the process in the ducted propulsor design the
domain of interest is the region of the hull where
the propulsor will be located The shaping of the
hull and the location of the propulsor relative to
the hull are the host considerations in the design
cycle Once they are sets ed, the flow path
inside the propulsor needs to be defined This is
an extremely important step in the whole design
process For an axisymmetnc vehicle the now
path will be defined by specifying the Irwer duct
surface and the shape of the hull where the rotor
and stators are mounted The me dirnal
shaping" of the internal passage of a ducted
propulsor defines the "environment" where the
rotor operate The next step is to perform a
tradeoff study in temms of different perfommance
requirements Mass flow rate and rpm are the
hrst order design parameters that will dictate the
overall size and perfommance of the unit Once
the major size, design conditions, passage
geometry are decided through an iteration
process, the anal step will be the Bade design
Two mater global design decisions need to be
made in the beginning of the blade design
process They are the planfomm of the Made
layout which indudes the skew rake chord and
thickness distributions and the it ad d stnbuf on
The specihcation of load distribution is critical in
the success of propulsor design The prescribed
load distribution should be such that all adverse
effects i e flow separabon and cavitabon can be
avoided or delayed Obviously, one will seek a
load distribution that gives the most eDhcient
blade perfommance subject to the constraints
The issue can be more crmdex if the acoustic
performance becomes an integral part of the
consideration Flexibility in the load distribution
is dehnitely a requirement for any advanced high
performance propulsor design
There are other issues in the design that
will affect loading prescriptions For example, a
mixed flow passage geometry will induce an
additional secondary flow component due to
streamline curvature The vorticity generated by
the boundary layer on the lower surface of the
duct interact with the up of the blade and can
signihcantly affect the loading charade sacs
near the up region These physical phenomena
away from the surfaces may have a signihcant
impact on the Made design process Presently,
Reynolds Averaged Wavier Stokes Solver
(RAMS) can predict the above mentioned effect
with fairly good results it is shil notvery time
and cost ehectve to incorporate RAMS in the
design iteration RAMS is used only to analyze
selected design candidates Use of RAMS as
analysis tool in propulsor design has been
proven to be very effective However it is highly
desirable to incorporate in the love se design
mode as much physical phenomena as possible
The be Eat is that the candidate design for
RAMS analysis should be very close to the best
comprc mised design The Clebsch approach
provides a base for incorporation of of her ehects
during the design calculation The secondary
flow is intrinsically captured using the fully three
dimensional fommulation Theoretically, the
boundary layer developed on the lower surface
of the duct can also be modeled in the
OCR for page 289
circumferential averaged sense. The tip gap
effect can also be simulated using this model.
The planform geometry can also affect the
loading distribution and if properly chosen, can
help the loading distribution.
A word on design optimization may be
appropriate to conclude this section. When one
thinks about design, one must consider the way
that will give the "best design" within the given
resources and constraints. The Clebsch based
inverse design method provides a theoretical
background for the development of a toolbox for
practical propulsor inverse design. The ultimate
goal is to find shapes, which perform "optimally"
during the mission of the vehicle. This is truly a
multi-disciplinary optimization (MDO) problem.
The propulsor not only has to satisfy
hydrodynamic requirements, but also structural
and sometimes acoustic requirements. From
the total ship system level, the propulsor also
has to be compatible with the power plant and
the ship layout. Furthermore, the effect of
propulsor on stability and maneuvering also
needs to be considered in the design cycle. It
was noted earl ier that there is strong i nteraction
effect between propulsor and hull. It is
imperative that both propulsor and hull be
considered as an integrated part of each other
during the design process. This makes the
design, not only multi-disciplinary, but also multi-
component. Despite major advances made in
optimization and computation techniques,
human experience and knowledge cannot be
overlooked. Optimization tools should be used
in the context of assisting designers in making
design decisions during the design cycles.
Sometimes they may even reveal areas that the
designer never considers before. Yet, a proper
framework needs to be established to make
optimization part of a toolbox that complements
designer's knowledge.
DESIGN EXAMPLE 1 - DUCTED POD
PROPULSOR
A ducted pod propulsor was designed
by the use of inverse design technique. A grid
structure of the computational domain is shown
in Figure 1. A grid sensitivity study was
performed to ensure the grid size used in this
computation is sufficient for the convergence of
the solution. It was found that thrust, torque and
the maximum difference in wrap angle are all
within 0.03°/O by reducing the grid size by half
and a quarter in both x and r directions
LL
respectively. The wrap angle is defined as the
angular position of the camber surface. The
ducted pod is a post swirl propulsor operating in
the uniform stream with axial velocity equal to
unity. A post swirl system is one with a rotating
rotor forward of the stationary vanes. All
geometric dimensions are normalized by the
inlet diameter of the duct. All velocities are
Figure 1 Grid Structure for the Pod
norm al ized by the f ree stream velocity. The
pressure is non-dimensionalized by the free
stream dynamic head. The code can design the
whole propulsor, which includes the duct, the
hub and all the blade rows simultaneously. No
blockage or thickness effects are modeled in this
example. No empirical loss models are
incorporated at this time. The effect of blade
load distribution was illustrated in this example.
The design was constrained by the overall size
of the unit and the hub shape. The flow path is
very much restricted by the imposed geometric
constraints. The result is a highly accelerated
flow path that results in a jet velocity ratio of
approximately 1.8. The stacking positions for
both rotor and stators are at the leading edge of
the blades. Only the zero harmonic or the
circumferential averaged design calculations
were performed to evaluate different blade load
distributions. The zero harmonic solution is
equivalent to the infinite blade solution where
the blade to blade effect is ignored. The fully
three dimensional blade design will be
performed once the load distribution is selected.
A free vortex (constant r Vie distribution along the
span) loading distribution was specified initially
as a baseline. The net pressure distribution on
the blade surface and the pressure distributions
on both suction and pressure sides are shown in
Figures 2, 3 and 4. It seems that the load near
the rotor hub region is too high. The absolute
tangential velocity is even greater than the
rotational speed of the rotor at the rotor hub.
OCR for page 290
This is undesirable not only for the possibility of
flow separation, also for the potential of early
cavitation on the suction face near the hub. The
r Vie distribution was revised so that the hub was
unloaded. In the second calculation, a force
vortex load distribution with a linear distributed
r Via was prescribed. The hub r Vie was set to
two thirds of the tip r Vie. The resultant pressure
distributions are shown in Figures 5, 6 and 7.
1 25 _
1 _
In 75
n ~
0 25
I,1,,,,1,, ,,1,,,,1,,,,1 ,, ,,1,,,,1, ,, ,1 ,,,,1,, ,,1, ,,
-1 -0 75 -0 ~ -0 25 0 0 25 0.5 0 75 1 1 25
X
CPNON
O. 1 S7955
0.110948
0.08S9S01
0.0559124
0.0298947
0.002877
0.0241407
0.051 1584
0.0781751
.105194
0.1S2212
.159229
.185247
0.21S2Ei5
0.2~0282
Figure 2 Net Pressure Distribution with Free Vortex Loading 1 95
0 2 ~ .
it, I, ,, ,1,, ,, I,, ,, I,,, ,1,,, ,1,, ,, I,,, ,1,,, ,1 ,, ,, I,,,
-1 -0 75 -0 ~ -0 25 0 0 25 0 ~ 0.75 1 1 25
Figure 3 Pressure Distribution with Free Vortex Loading for
the Pressure Side
1 96~
0 25 ~
CPNON
0.505
0.521145
0.475225
0.4S1 304
0.S85S84
0.S41 454
0.29554S
0.251 52S O 2 ~
0.20570S
0.151782
O. 1 15852
0.0719415
0.02702 1S
0.0 17899
n n~o~n~
~ I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I
-1 -0.75-0.~-0.26 0 0.~S 0.S 0.75 1 1.25
CPNON
0.4SS108
0.S82827
0.SS2545
0.2822ti5
0.2S1 984
0.18170S
0.1S1422
0.0811 4~
o.oso8595
0.01942 14
0.0597024
0.1 1998S
.170254
0.220545
0.27082ti
Figure 4 Pressure Distribution with Free Vortex Loading for
the Suction Side
1 25 _
.. ..
>0.7~
0.s
0 25
.. .... ................ ,,, I,,,, I,,,, I,,,, I,,,, I,,,
-1 -0 75 -0 ~ -0 25 0 0 25 0 ~ 0 75 1 1 25
Figure 5 Net Pressure Distribution with Force Vortex Loading
n ~
0.25
I,1,,,,1 ,, ,,1,,,,1,,, ,1 ,, ,,1,,,,1, ,, ,1 ,,,,1,,,,1, ,,
-1 -0 75 -0 ~ -0 25 0 0 25 0 ~ 0.75 1 1 25
CPNON
0.5~0Ei5
0.521145
0.475224
0.4S1 S04
0.S85S84
0.S41 45S
0.29554S
0.251 52S
0.205702
0.151782
0. 115852
0.0719415
0.0270212
0.0178991
.0528194
Figure 6 Pressure Distribution with Force Vortex Loading for
the Pressure Side
I,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
-1 -0 75 -0 ~ -0 25 0 0 25 0 ~ 0 75 1 1 25
Or
rid
CPNON
0.4SS108
0.S82827
0.SS2545
0.2822ti5
0.2S1 984
0.18170S
0.1S1422
0.0811 41
0.0S08ti
.019421
0.059702
0.1 1998S
.170254
0.220545
0.27082ti
Figure 7 Pressure Distribution with Force Vortex Loading for
the Suction Side
The effect of hub unloading is clear by
comparing the pressure distributions depicted in
Figures 2 to 7. The negative pressure peak and
the adverse pressure gradient near the rotor root
region have been greatly reduced. The effect on
powering is very small. The force vortex loading
resulted in less than 1 percent reduction in
propulsive efficiency as compared that with free
vortex loading. The force vortex load
distributions for the entire blade is shown in
Figure 8.
1.2 _
CPNON
0.1 S7955
0.110948
0.08S9S01
0.0559124 n n
0.0298947 U . O
0.002877
· 0.0241407 n
0.0511 584
0.078 1 751
0.105194
0.1S2212
0.1 59229
0.185247
0.2 1S255
0.2C10282
04
lo
X
Figure 8 Blade Load Distributions for Rotor and Stator
OCR for page 291
The blade geometry was updated iteratively
during the velocity computation cycles until
convergence. The convergence criterion was
set to be the maximum relative change in wrap
angle less than 0.05°/0. The convergence
history for this computation is shown in Figure 9.
It can be seen from Figure 9 that the blade
shapes converge very rapidly in the first 4
iterations.
0 1 2 3 4 5
BLADE ITERATION NUN BER
6 7
Figure 9 Blade Shape Convergence History
The full three-dimensional computation
was performed for different numbers of
harmonics to ensure convergence. 16
harmonics were computed for less than 0.5 °/0
relative change in averaged wrap angles.
Pictures of the blade shapes for the rotor and
the stator are shown in Figures 10 and 1 1. The
red is the mean and the blue is the three
dimensional designed blade shapes. A
maximum change of 7°/0 in wrap angel between
the circumferential mean and the three
dimensional solution was noted.
An,
LEADING EDGE
LEADING EDGE / ~ TRAILING EDGE
Figure 11 Stator Blade Shape
The major differences between the
circumferential mean and the three dimensional
solution seems to occur near the trailing edge of
both rotor and stator.
Q ~
1 ~
c3 n
-051
-'1
-1 ~
~ —,, \
TRAILING EDGE
—~ nilfT IIDO~ ~11~1 AL
1 _ ~
_,
Figure 12 Pressure Distributions for Duct and Hub
The pressure distributions for the duct
and the hub are shown in Figure 12.
The net thrust contributions from the duct and
hub can be computed by integrating the
pressure distributions. It is interesting to note
that the contributions from the hub and the duct
lower surface very much cancel each other and
the duct upper surface contributes
approximately 16% of the rotor thrust. The
vanes also contribute 18% of the rotor thrust.
The next two design examples show the
effective use of mixed flow concept for cavitation
improvement if manipulation of loading is not
adequate for desired improvement in cavitation.
DESIGN EXAMPLE 2 - AXIAL PRESWIRL
A preswirl propulsor is defined as a
Figure 10 Rotor Blade Shape ducted propulsor with a set of preswirl stators in
front of the rotor. The preswirl stators ahead of
OCR for page 292
the rotor blades induce a swirl distribution as the
onset loading to the rotor blades. This can
effectively cancel the swirl produced by the rotor
and reduces the rotational energy loss in the
slipstream. The penalty paid is the additional
drag due to negative thrust that the stators
produce. In this and the next example, a
Preswirl propulsor is designed for a given
axisymmetric body. The stern for this example
is a tapered cone and the flow path is straight
conical. Despite the fact that the flow is not
strictly axial, this case is called axial preswirl.
The incoming velocity at the inflow plane is not
uniform because of the boundary layer
developed on the surface of the body. The
boundary layer thickness can be of the order of
the duct inlet diameter because of rapid
pressure recovery near the stern region. A
notional body with a tapered stern is def i ned for
this design example. The length scale for this
and the next design example is the radius of the
body. The velocity scale is the vehicle speed.
Pressure is normalized by the free stream
dynamic head. All design calculations
converged according to the criterion mentioned n
in the last example. The grid structure for this
design computation is shown in Figure 1 3.
Of
0 4
0 3
Figure 13 Grid Structure for the Axial Preswirl
The inflow meridional velocity
distribution is shown in Figures 14. There is no
upstream tangential velocity component at the
inflow plane. The loading distributions for both
the rotor and stator are shown in Figure 15.
Notice that the blades are approximately 70°/0
more loaded at the tip as compared with that at
the hub. The resultant pressure distributions on
suction and pressure sides and the net pressure
distribution are shown in Figures 16, 17 and 18.
O .g:
n is
O BE
no
1
_
_1-:
5
.~
l l l l l l l l l l
0.O 0.7
on ~ =
l l l l l l l l l l l l l l l l l l l l
OH O9 1 1 1
Figure 14 Inflow Meridional Velocity Distribution
a ~
n r;
n ~
Figure 15 Loading Distributions for the rotor and stator
CPNON
0.173783
0.142552
0.11 1S2
0.080088B
0.0~88574
0.01 7Ei259
- 0.01 3ti05E
- 0.0~48371
-0.076OE86
-0.1073
- 0.138532
o. 1ti9753
- 0.200995
-0.232225
- 0.2ti3458
Figure 16 Net Pressure Distribution for Axial Preswirl
1
Jo.
04
0 3
0 2
CPNON
0.220904
O. 18525e
0.15 1E08
0.115951
0.0823 13
0.047d553
0.0130 177
- 0.02 1E3
- 0.05fi2777
- 0.0909254
- 0.125573
- O. 1b0221
- 0. 19~8E8
- 0.2295 1E
n CAM PA
Figure 17 Pressure Side Pressure Distribution for Axial
Preswirl
OCR for page 293
Ott
no
0 3
0.2 _
CPNON
0.~57~81
0.~7
- 0.~172
- 0.10~
-0.13~1S
- 0.1750~
-0.21Z31g
- 0.24Eti7
- 0.~2
- 0.~1371
- 0.~7721
0.~72
- 0.~04=
0.~5773
- 0.~31 =
Figure 18 Suction Side Pressure Distribution for Axial
Preswirl
The pressure distributions for the duct and the
body are shown in Figure 19. Lowest pressure
occurred on the suction face of the rotor blade
near the tip region. This design constitutes the
baseline design and improvements are sought
for cavitation performance. Further
improvements can be made to the axial design
by further refinement in load distributions and
relaxing the design requirements. The intent
here is not to optimize the present design, but to
demonstrate the idea of mixed flow in propulsor
design for cavitation performance improvement
under the same design requirements. Figure 1 9
shows the pressure distributions on the duct
upper and lower surfaces and on the stern
surface. The duct slightly accelerates the flow
and produces a net thrust equivalent to
approximately 50°/O of the rotor thrust. The
stators produce a negative thrust approximately
equal to 10% of the rotor thrust and part of the
stern i ncl uded i n the com putation produces a
drag of approximately 18% of the rotor thrust.
0.~5 ~
O.5
_w
. UPPER Pliant
_1
L33WER. DUCT
/ '__~
EO [of
Figure 19 Pressure Distributions for the Duct and the Body
for the Axial Preswirl
Pictures of the rotor and stator blades are shown
in Figures 20 and 21. The red and blue layouts
represent the circumferential mean and the full
three dimensional design solutions. The three
dimensional correction to the mean solution
tends to increase the pitch at the tip and to
reduce the pitch near the hub for the rotor blade.
The three dimensional solution tends to reduce
the camber and increase the pitch along the
entire span.
Figure 20 Pictorial View of Rotor Blade for the Axial Preswirl
TIP
HUB
LEAD1~5 EDGE
Figure 21 Pictorial View of Stator Blade for the Axial Preswirl
The next example is to explore the concept of
mixed flow for improving cavitation performance
and compare the design results with the axial
preswirl.
DESIGN EXAMPLE 3 - MIXED FLOW
PRESWIRL
The notion of mixed flow is not new.
Mixed flow turbomachinery has been designed
and used in various applications for many years.
Turbomachines can be categorized into three
OCR for page 294
major configurations and they are the axial flow,
mixed flow and radial flow machines. The
selection of different configurations is mainly
dictated by the operation requirements. For
example, an axial machine is usually
characterized by high mass flow rate and low
head. On the contrary, a radial flow machine is
applicable for high head and low mass flow rate
application. The mixed flow configuration
contains features from both axial and radial and
it occupies the middle of this design spectrum.
Most of the marine propulsors can be
characterized as axial flow machine. Use of the
mixed flow unit provides the flexibility in the
design space to address the load limits of axial
flow machine. The main idea can be illustrated
from the Euler's turbomachinery equation, which
can be written in the differential form as follow:
OH = m.~( r Vie
(27)
where co is the rotational speed. If one assumes
that the total head across the blades for both
axial and mixed flow units are almost the same,
then one can write
Cl) / cl)m = [jig r m V`3 my / ~` r a —V a' (28)
The superscripts a and m represents axial and
mixed flow. Consider the change along a
differential distance As on the stream surface,
(28) becomes
a / alum ~ r m ([j Via m / [js)+ V`3 tar lbs))l
~ r (6 Vie I bs)+ Vie tar lbs)) (29)
The stern shape has been modified to
accommodate the mixed flow design. As it was
mentioned, the flow path design is an important
part of the entire design process. It requires
design iterations between flow path design, and
the blade design. In this case, the flow path
design is mainly the design of the stern and the
duct. This example mainly demonstrates the
mixed flow concept and no attempt is made to
"optimize" the entire stern/propulsor design. The
com putational grid for the design com putation is
shown in Figure 22.
to 1 2
Figure 22 Grid Structure for The Mixed Flow Preswirl
The mass flow rate and the rotational speed for
the mixed flow design is same as that for the
axial design. The load distributions for the stator
and the rotor are shown in Figure 23. The
cavitation inception depth is improved by 50°/O
relative to that for the axial preswirl. The effect
of mixed flow enables load reduction relative to
the axial preswirl and hence an improvement in
cavitation performance.
O.
For the moment, the rotational speed ratio is
assumed to be unity. For an axial configuration,
fir a /6s is zero or in the previous design °
example, it is negative. The mixed flow
configuration has a positive fir m /6s and it can be
concluded by inspection of (29) that loading for
the mixed flow is less as compared with that for
the axial. (29) enables one to study the effect of
differences in rotational speeds between the
axial and mixed flow on the relative changes in
loadings and the geometry from an axial
configuration to a mixed flow configuration. A
notional mixed flow propulsor design is
presented here to illustrate the use the present
design code for such propulsor design and to
show the potential gains in performance as
compared with that for an axial unit. The body
configuration and the inflow conditions are the
same as the previous axial preswirl example.
03
. 03 04 05 OG 0~-
-o.oo~o~
-0.0180~
-0.0271 10
-0.0381
-0.0451
-0.05~1
-0.06
-0.07
-0 0813
-0.0003
-0.00
-0.10
-0.~
-0 12~17
- O. 13~
Figure 23 Loading Distributions for Mixed Flow Propulsor
Stator and Rotor
OCR for page 295
The computed pressure distributions on the
pressure and suction surfaces of the blades and
the net pressure distributions are shown in
Figures 24, 25 and 26
07
0 2
O G
0.5
>04
03
.......
. . . .
CPNON
1.~1 2
1.~01 1
1.31411
1.1401
0.~20~
0.016005
0.650001
0.~4087
0.31 80~
0.152079
- 0.01~245
-0.17~28
-0.3~32
- 0.5110
-0.07704
~ I , , , 1 1 1 1 ' ' I
o
0.5
1
Figure 24 Net Pressure Distributions for Mixed Flow Preswirl
0 7
O G
0.S
04
I
0.6
CPNON
0.71 go 15
0.005377
0.~ 154
0.377002
0.254154
O. 150427
0.03~ 1
0.0770~5
0. 1007~
0.304524
0.418252
0.53 10~
0.545737
0.750475
0.8732 12
1
Figure 25 Pressure Side Pressure Distribution for Mixed
Flow Preswirl
07
O G
0.5
03
CPHON
o.~so~
0.~ 19
o.
0.11
- 0.00 13
- 0.12~02
-0.~19
0.~
-0.~54
- 0.00~71
-0.~30~
0.~05
-0.~03
- 1.091
- 1.21~5
1 1 1
to
0.5
rat
1
Figure 26 Suction Side Pressure Distribution for Mixed Flow
Preswirl
The pressure distributions for the duct and the
stern are shown in Figure 27.
1
or
-or.
UPPER BIDET it ~ \,
81~
1
X
Figure 27 Pressure Distributions for the Duct and Stern
The duct and the stern axial forces as a
percentage of rotor thrust for the mixed flow
Preswirl is different from that for the axial
preswirl. The net force acting on the duct is
almost zero. The part of the stern included in
the computation produces a positive thrust of
approximately 25% of the rotor thrust and the
stators produces a negative thrust of
approximately 25% of the rotor thrust. Pictures
of the blade shapes are shown in Figures 28
and 29. The red and blue layouts stand for the
circumferential mean and the full three
dimensional design solutions.
TRAILING ED5E TIP
Figure 28 Pictorial View of Mixed Flow Preswirl Rotor Blade
OCR for page 296
TRAILINGi EDGE
LEADING EDGE
Figure 29 Pictorial View of Mixed Flow Preswirl Stator Blade
The circumferential mean and the three
dimensional solutions are surprisely close.
There are some minor differences in wrap
angles near the tip and hub region. The two
solutions agree with each other on most parts of
the blade surfaces. Computation was also
performed for a rotational speed 30°/0 less than
the basel i net An i m provem ent of 1 2% i n
cavitation inception depth relative to the axial
preswirl was obtained. Mixed flow concept as
applied to propulsor offers a way of improving
cavitation performance. There are other issues
that may require further study before mixed flow
concept can be fully developed. Three-
dimensional effects are more prominent in mixed
flow design as compared with that for axial flow
design. Flow passage geometry becomes more
important in mixed flow design and the blade
load prescriptions may require new set of
guidelines as compared with that for axial
design.
CONCLUSIONS
A new approach to the three
dimensional blade designs for marine propulsors
has been presented. Traditionally, the propulsor
design relies on the use of experimental data
and experience of a designer to compliment the
use of analytical tools. The present approach is
of no exception. Experience and test data
continue to play an important role. With the
advances in computational fluid dynamics,
Reynolds Averaged Navier-Stokes solver
(RANS) starts to play an important role in the
design cycle. Gradually, it may even replace
some of the experiments for design validations.
Presently, RANS still has its own limitations in
terms of turnaround time, gridding issues and
turbulence modeling. It is extremely important
that a designer understand the limitations of the
tools in terms of physical models and the
numerical accuracy. In general, design codes
are much faster running as compared to RANS
codes and they are easier to couple with
algorithms for design optimizations. Therefore it
is highly desirable to have a design code based
on a physical model that can offer three-
dimensional modeling and less assumptions. In
the case of propulsor design, the ability to model
free stream shear and its interactions with the
blading is important, the effect of multiple blade
rows on each other and their interactions with
nearby boundaries such as duct and body are
equally important. The use of Clebsch
potentials in modeling bound vorticity of blades
and the free stream vorticity proves to be an
effective way of approaching the propulsor
design problem. It addresses the consistency of
a single formulation for the free stream shear
and multi-stage blade-rows interactions problem.
The code can further be enhanced to capture
additional flow physics such as distortion of
Bernoulli surfaces and tip gap flow. It also offers
relatively quick turnaround time so it can be
used for design optimization problems. Three
design examples are given in this paper. The
pod propulsor design is for a heavily loaded
blade design. The effect of different loading
distributions on blade design was demonstrated
in the pod example. A notional mixed flow
preswirl propulsor is designed to demonstrate
the use of Clebsch method. Comparisons were
made to a baseline axial preswirl design.
Significant improvement in cavitation
performance can be obtained. The mixed flow
concept offers opportunity for performance gains
but it also poses a more difficult design problem.
The tortuous flow path as compared with that for
an axial unit offers great design challenges to a
designer. The stern/propulsor interactions can
be more complex. The effect of secondary flow
on blade design is more important. The duct
lower surface boundary layer development is
quite different as compared with that for an axial
flow. Its interaction with the rotor tip gap and
effect of flow passage geometry on the tip gap
physics is still unclear for mixed flow propulsor
design. Consideration of propulsor design can
no longer be considered as a separate entity in
the design of any vessel. The propulsor has to
be part of a total system in ship design where
commonality in both design and performance
parameters with other subsystems must be
identified. With more stringent design
requirements for the future ship propulsors, it is
OCR for page 297
imperative to use optimization at both system
and detailed design levels
Acknowledgement:
The work described in this paper was
performed by the Propulsion and Fuild Systems
Department of the Hydrpmechanics Directorate,
Carderock Division, Naval Surface Warfare
Center The work was sponsored by the Oh ce
of Naval Research, Mechanics & Energy
Conversion S&T Division (OUR 333)], under the
Advanced Propulsons Task of the FY00
Submanne HM&E Technology Program
(PE0602121N) Dr Peter Majumdar initiated the
project Dr. Edwin Rood has provided the
support for the both inverse design technique
development and the mixed flow concept study
The authors would like to thank both Dr.
Majumdar and Dr. Rood for their interests and
support during the course of this investigabon
REFERENCES:
1 Lerbs, H W " Moderately Loaded propellers
with a Finite Number of Hlades and an
Arbitrary Distribution of Circulation ",
Trans SNAME, Vol 60, pp 73 123, 1952
2 Hrockett, T E " Lifting Surface
Hydrodynamics for Design of Rotating
Hlades ", Proceedings of the SNAME
Frweller 81 Symposium, pp 357 378,
Virginia Heach, VA, 1981
3 Greeley D S and Kerwin J E " Nun al
Method for Propeller Design and Analysis in
Steady Flow ", Trans SNAME, Vol 90,
pp415 453, 1982
4 McMahon,J F,etal "VMPWaterjetTest
Results ", Naval Surface Warfare Center
Carderock Division Hwlnxllecllamcs
Directorate Research and Development
Report, NSWCCD 50 TR 1999/015, April
1999
5 Morgan, W H " Theory of Annular Airfoil
and Ducted Propeller 4'h Symposium on
Naval HvdrodVnamics, pp 151 197,
Washington, D C 1962
6 Dai, C M, Gonski, J J and Haussling H J
" Computation of an integrated Ducted
Propulor/Stem Fe fqmlam e in Axisymmetric
Flow ", Fmceed~n 15 of the SNAME
Propeller,Shafbnq '91 Symposium, pp 14 1
14 12, Virginia Heach, VA, 1991
7 Kerwn J E, Keenan D P. Hladk, S D
and Diggs, J G " A or upled
Viscous/Potential Flow Design Method for
Wake Adapted, Multi Stage, Ducted
Propulsors Using Generalized Geometry ",
Trans SNAME, Vd 102, pp2 1 2 28,1994
8 Renick D H " An Analysis Procedure for
Advanced Propulsor Design " Master of
S ci ence Thesi s M assacll usetts I nsti tute of
Technolonv, May 1999
9 McHnde, M W " The Design and Analysis
of Turbomachinery in an incompressible,
Steady Flow Using the Streamline Curvature
Method " Technical Memorandum TM 79
Fe 1nsvl. area State University, February,
1979
10 Tan, C S. Hawthorne, .'! R. McCune, J E
and Wang, C " Theory of Blade Design for
Large Deflechons",Trans ASMEJ of
Engineering for Gas Tur ines and Power
Vol 106, pp 354 365, 1984
11 Zangeneh, M, Goto, M, and Takemura, T "
Suppression of Secondary Flows in a Mixed
Flow Pump impeller by Application of 3D
Invense Design Method Part1: Design and
Numencal Validation " Trans ASME J of
Turbomachinery, Vd 118, pp536 543,
1996
12 Zangeneh,M and R adds M E "AThree
Dimensional Method for the inverse Design
of Manne Ducted Propeller Hiding ",
Proceedings of the SNAME
ProPell errs oaf b no '94 Svmoosium, 1)1) 7 1
7 11, Virginia Heach, VA, 1994
13 Yiu, K F C and Zangeneh, M " On the
Simultaneous Design of Blade and Duct
Geometry of Marine Ducted Propulsons",
Joumal of Ship Research, Vol 42, Number
4, 1)1) 274 296, 1998
14 Lighthill M J " An introduction to Fourier
Analysis and Generalised Functions"
CamDndqe Universitv Press, Cambridge,
1967
OCR for page 298
15 Lighthill, M J " Drift" J Fluid Mech Vol 1'
pp 3153 1956
OCR for page 299
J. E leer .. u.
Msssachusetss institute of Tech ol on:
USA
The mthors have provided m extremely mterestmg Ed
valustlepaper onthe topic of propulsorhyd odynsmics
While the Clebsch t:3rmu 1~n on has been applied to s lim ited
extent to She li eld of turbomachmery since the 1 950's, it
represents s new Ed u familiar approach to m my of us in the
field of me me propulsor design
Regardless of She specific hyd odynsmic fommulstion which is
used, I believe thst it is essential to provide designers with
computatiom~l tools thst will enable them to evaluate
propulsor slterrurtives as rapidly as possible The problem of
developing s duly optimum design for s single, open propeller
is hard enough, but one now has to deal with mm mill, multiple
blade-row, ducted propulsors of the types illu trsted in the
paper in my opmion, the focus of She mfhor's research is
therefore w 11 directed
The mthors are aware of parallel research thst I have been
involved in, as indicated by Heir references [7] Ed [5] Our
objective has been to develop s fast Ed versatile
design Wry sis method by combining s lifting-su face
representation of the blades with either maxisymmetric
RANS or Euler solver The mfhors characteri e this approach
as successful " in the situation which invol Uris sim /e
th roughJL w geometry, o r The om et shear k weak " That
comment is certainly valid in She se of earlier Ifftmg-surface
codes thst were lim ited to cylind ical flow geomeh y, Ed for
which no provision was made for the ma en on of the
propulsor with s s oni 91 i flow How ver, neither of these
lim itations mph to the methods cited in References [7] Ed
[5] Could the mfhors comment on thi ?
While the Clebsch decomposition results in s very different set
of equations to be solved, I am curious as to whether or not
this approach is actually different fi om our coupled Lifting-
Su face/Euler scheme [5] m terms of underlying flow physics
In either case, the b la de forces are introduced mto He
th oughflow solver by morns of the ... u I velocity, as
indicstedinthe mfhon E mation (5) in rh mfhor'scsse,the
fact that the blade forces are concentrated at discrete mgular
locations is h mdled by s Fourier represem3n on in the mgular
du ection, while in our method it is h mdled explicitly in the
Iffting-surface computation
While the latter approach adds comp lexity to the process, He
local velocities on the blades are computed du ectly I note thst
the mthor's repo t Nat 16 harmonics m the Fourier
decomposition of She blade flow is sufficient for convergence
for the cases presented How ver, These w re all for ducted
propulsors with zero tip gap, where blade-toblade variations
might be expected to be small Have She hors exam med the
convergence of Heir medhod for m open prop her, where the
effect of blade mmmber is greater? I also could not find the
blade mmmber repo ted for the mthor's examples it would be
useful if this i tannin on could be provided
One possibly fundamental difference 1 en en the methods is
thst we make She as lampoon at the outset thst the vo ti 91
interactionbetw endhepropulsor Ed maxisymmehici flow
remains axisymmetric, while the mfhor's method c m treat the
fully f ee-dimensiom~l inrerscrise probl m f ough s Fourier
representation m She mgular coordinate
I have l en concerned about whether this sssumption is
justified le. Ed .. 95 ah rel ore very Interested in the findings of
Kiowas Ed Choi, presented at fi is same co ference They
developed s special unsteady, 3-D Euler solver, which .. 95
coupled with s propeller lifting-su face code While She latter
code has She lim itstion of con t mt reams flow geomet y, it is
suitable for testing the difference between She effective wake
predicted by the steady version of then Euler solver Ed She
time-a verage of the results obtained with Heir unsteady solver
Such s comparison is show in Section 5 5 of Heir paper, with
the conclusion thst She differences between the two memo ds
are extremely mall
The mfhors have presented results for m exh emely Interesting
variety of propulsor t pes I wouldbe very interested in
making comparative calculations, Ed believe thst others
m ight have She same interest Would the mthors consider
posting the geomeh ies, cu culstion dish ibutions Ed pressure
dish if urions on the web to enat l qu mtihtive comparisons?
AUTHOR'S REPLY
We w mt to fib mk Frofessor Kerwin Ed Dr S mchezCajs few
their cements We would like to start by mew ring Frofessor
Kerwin's questions Fropulsor design is indeed 9 complex task
that involves m my performance rent m em em s Ed constraints
Different propulsor types Ed their inrerscrions with bull
fu ther complicate the design problem We totally a? e wifih
Frofessor Ke win's commentthat designfoods need to be fast
enough so the designers c m evaluate different propulssr types
Ed explore design space in m efficient meaner The
computational model based on the Clebsch Fommubtion is
extremely fast bee mse of its mmmerical 1 oilman on of
decomposing 9 th ee-dimffnsionsl problem into 9 series of
two-dimensionsl calculations
Use of potential flow models in propulsor design requires the
k owledge of effective wake Ed th ust deductions The use of
either sxisymmetric RA!dS or Eid r Salvers wifih 9 Lifting
Su—-. e Code that Frofessor Kerwin Ed his colleagues have
developed represents 9 hybrid approach in solving the give
wake / thrust deduction problem The propulsor is modeled as
m sch stor disk in the sxisymmetric part of the computation
A iterative process is required to relate the effective i flow to
the design cu cu he on The procedure has been demonstrated
to be very effective to mod hng flow passage that free stream
vorticity is restively week Ed is mainly com cted by the
background potential flow in the situation where thef ow
passage may have important effect of redish ibuting The onset
OCR for page 300
vorticity such that She vorticity may not be small in ce thin
region of the flow passage he on -l l shear Assumption ma.
not be valid mdbkding designhas to take into account She
distortion of the free stream vo ticity due to blade deflection
The Clebsch fommubtion provides s theoretical framework
that is not rein limed to the w ok shear as mmption
In principle, the Clebsch formulation represents s design
theory based on ire -isc id rotation theory model it c m be
degenerated to s special case that is equivalent to She
Euder/Liftmg Surface Model by only accounting for the shear
in the zero harmonic solution We have not pe formed s
simulation for m open propeller md are pkmomg to perform
such simulation in the future The convergence properties for
the openpropeller wil l definitely be e- chatted
In regard to Dr 5 mchezCsjs's comment on She large hub
design The Clebsch formulation does not make use of the
image m odel that potential flow m od is ha ve to use The use
of mgukr momentum as design variable does not impose my
constraints on She large hub boundary The challenge for the
large hub design is merely the question of prescribing good
losdmg dish ibution for such design application
Representative terms from entire chapter:
propulsor design
