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Design of an Advanced Waterjet William A. Facinelli (AM)
Honeywell Tempe, Arizona Alan J. Becnel (M) John G. Purnell CDI
Marine Systems Development Division Severna Park, Maryland and
Robert F. Blumenthal ANSYS CFX El Dorado Hills, California
ABSTRACT State-of-the-art computer programs have been used to
design a waterjet for marine propulsion applications. The design
was accomplished in an iterative process between a potential-flow
design code and a fully viscous, three-dimensional computational
fluid dynamics analysis program. These tools were first directed at
the evaluation of three options: a single rotating blade row plus a
stator; a rotating blade set consisting of main blades and splitter
blades, plus a stator; and two co-rotating blade rows (an inducer
and a kicker) plus a stator. In the second step of the design
process, the single rotor/stator concept was optimized to maximize
the efficiency while matching a given design point. The resulting
design is predicted to have much improved cavitation performance
compared with a design accomplished with older techniques. Other
advantages are reduced weight, shorter length, and lower
manufacturing cost.
1. BACKGROUND ON THE COMPUTER
METHODS
Rotors for waterjets have previously been designed with the
assumption of free-vortex radial blade loading. This loading
distribution simplifies the design process, because it means equal
energy input to the flow at each radius and a uniform axial
velocity in the exit jet. However, it results in rather long axial
blade lengths for the hub sections. In order to reduce weight and
volume, and increase hydraulic efficiency and therefore thrust, it
was desirable that a non-uniform radial blade loading
be used for the new design. The use of non-uniform radial blade
loading required changes to the basic design and analysis methods
and computer programs.
The first program used in the design process was the preliminary
design code WJOPTIM. This spreadsheet-type program was used to
match the pump to the inlet and nozzle. For the purpose of the
design of this new waterjet, it was improved to account for
non-uniform blade loading. Inputs to the program included desired
cavitation margin, fluid vapor pressure, velocity at the pump inlet
(assumed uniform for this purpose), inlet hub-to-tip radius ratio,
and nozzle loss coefficient.
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Outputs consisted of the pump flowrate and head rise, rotational
speed, shaft torque, exit hub-to-tip ratio, and derived quantities
such as pump efficiency.
The second program was an EXCEL Simplified Streamline Curvature
macro SLC that was used in conjunction with WJOPTIM to determine
the blade loading pattern. Inputs consisted of the number of
streamlines to evaluate, pump efficiency, shaft power, rotational
speed, inlet and exit radius ratios, relative amounts of turning at
hub, middle, and tip, axial velocity at the inlet, and fluid
density. The output was in the form of two tables, the first giving
the velocity and pressure distribution at the blade inlet, and the
second giving the blade velocity triangles along each streamline
through the rotor or stator.
The third program used in this design was a streamline curvature
code, PLOTSCMD. The code was modified to accommodate non-uniform
blade loading, and a diffusion factor subroutine was added to check
for flow separation at all radii. The inputs to this program were
the upstream inflow information, the flow-turning schedule from
macro SLC, and the hub and shroud geometry of the pump. PLOTSCMD
then predicted the velocity and pressure fields for the unit. In
this manner, the impact of various hub, shroud, and component
lengths and geometries can be evaluated.
The designs were checked for problems such as static pressure
below vapor pressure at some location. An example output from
PLOTSCMD is shown in Figure 1.
The blade shapes were generated using TURBOdesign-1, an inverse
design code developed by Advanced Design Technology of the U.K.
that is based on the potential flow equations. TURBOdesign-1 allows
the designer to control the blade surface pressure distributions by
specifying the chordwise blade loading at different radii.
Secondary flows in the blade passages can also be minimized with
the correct blade loading distributions. These features of
TURBOdesign-1 allow the designer to develop high efficiency designs
with very high suction specific speeds. The hub and shroud contours
and radial blade loadings generated by the other programs were
input to TURBOdesign-1, along with the assumed blade section
profile, thickness distribution, and number of blades. For each
type of rotor considered, a computational grid was prepared such as
the one shown in Figure 2. The results from this code were the
blade shape definitions and surface static pressures, which were
checked for possible cavitation regions.
Figure 1 Example Streamline Curvature Results for Static
Pressure
X (inch)
R(inch)
0 10 20
-5
0
5
10
15
20Pst
(ft)98.1491.9285.7079.4973.2767.0560.8354.6248.4042.1835.9729.7523.5317.3111.10
4.88-1.34-7.56
-13.77-19.99-26.21-32.42-38.64-44.86
Rotor Stator
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Figure 2 - Example TURBOdesign-1 Grid
A linear stress analysis was performed for each blade design.
Boundary conditions restricting transla-tions were applied at the
nodes corresponding to points on the hub. Loads applied included
the pressure dis-tribution on the blade, obtained from
TURBOdesign-1, and centrifugal loads at the given rotational speed.
The material properties for 15-5 stainless steel were also used.
The predicted radial deflection of the blade tip was compared with
the assumed tip gap of about 0.050 inch. Also, the maximum and
minimum principal stresses on the pressure and suction sides of the
blade, respectively, were compared with the allowable values for
the material.
Viscous effects in the pump section were predicted using
CFX-TASCflow, a Computational Fluid Dynam-ics (CFD) program widely
used in pump applications. CFX-TASCflow employs a conservative,
finite-element based control volume method and a pressure-based
coupled solver for solution of the discretized Navier-Stokes
equations. This code has been successfully used to predict
turbomachinery performance for nearly two decades. In particular,
it has been shown to accurately model cavitation effects. In this
application, the program was used to analyze a single blade row, or
several blade rows in combination usually via a Stage Interface
approach. The Stage Interface is a means of coupling blade rows
together that are in different rotational frames of reference
(e.g., a rotor-stator) by circumferentially averaging pressure and
velocity but maintaining spanwise gradients. This interface is
especially useful for allowing multiple blade rows to be modeled by
using just a single blade in each blade row. Mass, momentum and
energy are fully conserved across the interface, even for blade
rows with significantly different pitch ratios.
1.1 Preliminary Rotor Design
The programs just described were first used to produce a
preliminary design of each of three rotor types:
1. A single rotor with seven equally sized blades
2. A single rotor with four main and four splitter blades
3. An inducer with four blades followed by a kicker with eight
blades.
The numbers of blades were chosen based on the experience of the
authors with similar pump designs.
The preliminary design process is shown in Figure 3. First,
program WJOPTIM was used to define the diameter and operating
conditions. The results of this analysis are listed in Table 1.
Then the design programs (SLC, PLOTSCMD, and TURBOdesign-1) and the
stress analysis code were used in an iterative manner with
CFX-TASCflow for each type of rotor. The resulting rotor designs
are shown in Figure 4, and the predicted characteristics are given
in Table 2.
Table 1 Diameter and Operating Conditions
Pump diameter (in) 23.0 Rotational speed (rpm) 1113.9 Torque
(ft-lbf) 6181.6 Flow rate (ft3/s) 101.98 Water density (slugs/ft3)
1.9905
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Figure 3 Rotor Preliminary Design Process
Figure 4 Preliminary Rotor Designs
Table 2 Rotor Trade Study
Type Description Rotor efficiency Head rise (ft of water)
Relative weight (lbs)
Blade stress at root (ksi)
1 Single rotor 0.937 101.3 0 13.0 2 Main + splitters 0.932 97.9
-6.5 14.0 3 Inducer + kicker 0.937 102.3 -12.5 24.4/15.7
The cavitation predictions from CFX-TASCflow are shown in Figure
5. For each Type, the CFD code was run with decreasing values of
inlet total pressure, and therefore decreasing amounts of net
positive suction head (NPSH) at the inlet to the model. At each of
these points, the predicted head rise across the rotor was noted.
The head rise at each point was divided by the head rise at a high
inlet pressure to arrive at the non-
dimensional value for the vertical axis in Figure 5. As one
looks from right to left in the Figure, the bump in head rise and
subsequent roll-off are characteristics of cavitation onset.
Consideration of the Table 2 results suggested no clear winner
among the three Types studied. All of the options offered high
efficiency, good cavitation performance, and acceptable stress
levels.
Determine operatingconditions usingWJOPTIM
Run SLC,PLTSCMD, andTURBOdesign forthe Type 1 rotor
Run CFX-TASCflow for theType 1 rotor
Run SLC,PLTSCMD, andTURBOdesign forthe Type 2 rotor
Run CFX-TASCflow for theType 2 rotor
Run SLC,PLTSCMD, andTURBOdesign forthe Type 3 rotor
Run CFX-TASCflow for theType 3 rotor
Compare rotorresults
Performlinear stressanalysis
3 times
Performlinear stressanalysis
2 times
Performlinear stressanalysis
2 times
Type 1 (Single rotor with seven blades) Type 2 (Single rotor
with four main andfour splitter blades)
Type 3 (Inducer + kicker)
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Figure 5 Cavitation Predictions From CFX-TASCflow for the Three
Types 1.2 Preliminary Stator Design
A stator was designed via a process similar to what was used for
each of the rotors. For this purpose, the exit velocity
distribution as a function of radius from the preliminary Type 1
rotor was used at the stator inlet boundary in the CFX-TASCflow
runs. A picture of this eight-bladed design is shown in Figure 6.
The head loss across the stator was estimated to be two feet of
water.
Figure 6 Preliminary Stator Design
A compact pump design was achieved in part by
making the stator integral with the nozzle of the waterjet. This
feature is illustrated in Figure 7 for the preliminary stator
concept.
Figure 7 Integral Stator/Nozzle (With Straight
Exit Section for the CFD Model)
0.980
0.985
0.990
0.995
1.000
1.005
20 30 40 50 60 70 80 90 100Net positive suction head (ft)
Hea
d ris
e w
ith c
avita
tion/
Hea
d ris
e at
hig
hN
PS
H (w
ithou
t cav
itatio
n)
Type 1Type 2Type 3
Inlet condition: NPSH=40 ft
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1.3 Final Rotor Design
In an effort to reduce the rotor weight, decrease the
manufacturing cost, and improve the efficiency, the Type 1 rotor
was chosen for optimization. In particular, the number of blades
was reduced from seven to five. Iterations between the design
programs and CFX-TASCflow were done with these goals in mind.
match the design point increase the efficiency maintain a margin
above vapor pressure
throughout the blade keep the blade stresses low. A final run
with the rotor blade alone was done
using the complete inlet velocity profile shown in Figure 8,
which had been obtained previously for a specific waterjet inlet.
In this case a 360 model of the rotor blade was set up and run in
CFX-TASCflow. The resulting rotor is shown in Figure 9.
The final rotor design was also analyzed for cavitation
performance to obtain results like those shown in Figure 5. The
predictions were compared with those for another rotating group
designed with older techniques. This comparison is shown in Figure
10. Clearly, the new design should be much more resistant to
cavitation. 1.4 Final Stator Design
In order to be further away from a multiple of the number of
rotor blades, and to decrease the weight and cost, the stator blade
count was reduced from an initial ten to eight. The final stator
design was verified by a run of CFX-TASCflow using a
rotor-plus-stator stage model. Some results from this run are shown
in Figure 11. 2. PARAMETRIC STUDY/DESIGN OF
EXPERIMENTS
Certain simplifying assumptions were made in the process of
designing the rotor. First, the tip clearance was held at 0.050
inch. Second, the surface was assumed to be hydrodynamically
smooth. Also, no analysis was done of the effect of blade
deviations caused by manufacturing inaccuracies. In order to have a
robust blade design, a parametric study which included a design of
experiments (DOE) was accomplished. Implementation of different
clearance
and roughness values in the CFD model was straightforward.
Assessment of manufacturing toler-ance effects was done by defining
a profile parameter as shown in Figure 12. Variation of the blades
in this manner was essentially a check for the effect of small
changes in incidence angle.
Figure 8 Inlet Velocity Profile
Figure 9 Final Rotor Design
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Figure 10 Cavitation Predictions from CFX-TASCflow for an Older
Design and for the New Rotor
Figure 11 Results From Stage Analysis
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1.00
1.01
20 30 40 50 60 70 80 90 100Net positive suction head (ft)
Hea
d ris
e w
ith c
avita
tion/
Hea
d ris
e at
hig
hN
PS
H (w
ithou
t cav
itatio
n)
Type 1 - 5 bladesBaseline
Inlet condition: NPSH=40 ft
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Figure 12 Profile parameter definition
The matrix of parameter variations and the predicted rotor
efficiency values from the CFX-TASCflow runs (for the rotor alone)
are given in Table 3.
Table 3 Parametric Study Table
Run Radial
Clearance (in)
Profile (in)
Surface Finish
(Micro-in)
Rotor Efficiency
(Design) 0.05 0.00 0.0 0.940 1 0.05 -0.03 20.8 0.937 2 0.15
-0.03 13.3 0.920 3 0.05 0.03 13.3 0.938 4 0.15 0.03 20.8 0.918 5
0.1 0.00 17.1 0.928 6 0.05 -0.03 125.0 0.924 7 0.05 0.03 125.0
0.923
The results of this analysis imply that the rotor efficiency is
highly sensitive to tip clearance and surface finish, but
insensitive to the profile parameter, at least over the range of
0.030 inch. This information suggests that the clearance be held as
tight as possible (without encouraging tip rub) and that the finish
be as smooth as economically feasible. 2.1 Off-design
Performance
An analysis of the advanced waterjet was done to predict
off-design performance. Three runs of CFX-TASCflow were done with
the stage model of the final pump design, in which the flow rate
was 10% below, 5% above, and 10% above the design value. The
results in terms of overall pump efficiency are shown in Figure 13.
As indicated in the figure, the calculated efficiency depends upon
where the exit plane is positioned. When the exit plane is at the
model exit, the efficiency includes the nozzle losses as well as
stator losses. One additional source of losses, when using the exit
plane to calculate the overall efficiency, is related to the
boundary conditions applied along the jet boundary in the nozzle
computation. To model the jet downstream of the nozzle, the
location of the free surface must be determined. CFX-5 has the
capability to perform free surface calculations, and was used to
model the flowfield downstream of the nozzle exit. As
Figure 13 Predicted Off-Design Performance
.030"
.030"Stacking line at
trailing edge
102
0.86
0.87
0.88
0.89
0.90
0.91
0.92
0.93
90 95 100 105 110 115Flowrate (ft3/s)
Pum
p E
ffici
ency
TASCflow, 1 inch past stator
TASCFLOW, model exit
Design flow rate
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shown in Figure 14, the jet boundary was then specified in
CFX-TASCflow using a slip wall boundary condition with the location
of the free surface based on the CFX-5 solution. Because of slight
differences
between the CFX-5 and CFX-TASCflow models, pressure and velocity
gradients were observed in the CFX-TASCflow solution on the jet
boundary that would not be present on a constant-pressure free
surface.
Figure 14 Meridional View From Stage Model Including Exit
Jet
3. CONCLUSIONS
This project demonstrated how a combination of fluid
dynamics-based design programs, a stress analysis code, and a
flexible CFD analysis tool can be used to optimize a waterjet pump.
CFX-TASCflow was also used in a parametric study on clearance,
incidence angle, and surface finish for the rotor. An
off-design
analysis implied that the pump efficiency will drop only about 1
point over the useful speed range of a typical marine vehicle.
This rotor/stator/nozzle design is compact, lightweight, and
easy to manufacture, and its predicted cavitation performance is
much better than that of an older design.
Streamlines colored bymeridional velocity
Slip Wall Boundary Condition
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