Identification of the Key Parameters for
Electric Waterjet Intake Optimization
Joint project with Kongsberg Maritime

Master’s thesis in Naval Architecture & Ocean Engineering

Lleo De Ribot Grau
Nuttarat Vichanphruek

DEPARTMENT OF MECHANICS & MARITIME SCIENCES
CHALMERS UNIVERSITY OF TECHNOLOGY
Gothenburg, Sweden 2022
www.chalmers.se

www.chalmers.se




Master’s thesis in naval architecture & ocean
engineering

Identification of the Key Parameters for Electric Waterjet Intake
Optimization

Lleo de Ribot Grau
Nuttarat Vichanphruek

Department of Mechanics and Maritime Sciences
Division of Marine Technology

Chalmers University of Technology
Gothenburg, Sweden 2022



Identification of the Key Parameters for Electric Waterjet Intake Optimization
Lleo de Ribot
Nuttarat Vichanphruek

© Lleo De Ribot, Nuttarat Vichanphruek, 2022.

Master’s thesis 2022:65 [Ask Study administrator for correct number]
Department of Mechanics & Maritime Sciences
Division of Marine Technology
Chalmers University of Technology
SE-412 96 Göteborg
Sweden
Telephone: +46 (0)31-772 1000

Cover:

Typeset in LATEX, template by Kyriaki Antoniadou-Plytaria
Printed by Chalmers Reproservice
Gothenburg, Sweden 2022

iv



Identification of the Key Parameters for Electric Waterjet Intake Optimization
Joint project with Kongsberg Maritime
Nuttarat Vichanphruek
Lleo de Ribot
Department of Mechanics & Maritime Sciences
Division of Marine Technology
Chalmers University of Technology

Abstract
Waterjets are commonly used in high-speed crafts because they have better propul-
sive efficiency compared to conventional marine propellers at high speeds. Nowa-
days, electric propulsion has been developed worldwide. This brings up the possibil-
ity of doing more research on how it can affect the hydrodynamic performance of the
waterjet propulsion system. The main objectives of this project are to optimize the
waterjet intake, which can maximize the overall system performance, and to inves-
tigate the hydrodynamic performance of the entire system when some constraints
can be modified due to waterjet electrification. During this research, finding the
system performance curve, the effect of extending pump-intake connection study,
the effect of shaft removal study, rim-driven impeller study, and intake optimiza-
tion are carried out. The results show that the intake design and the rotor driving
method are directly related to the system efficiency because the inflow to the pump
is significantly affected by the intake shape and the shaft. The impeller and the
intake should be designed together to match the blades with the specific wake field.
To achieve a better inflow to the pump, the key approaches are to lower the intake
height and extend the cylindrical part of the intake ahead of the impeller.

Keywords: Waterjet, Optimization, Computational Fluid Dynamics (CFD), STAR
CCM+, Capture Area, CAESES, Parameterized geometry, Wake field, Pump Per-
formance.

v





Acknowledgements
First of all, we would like to thank Arash Eslamdoost for supervising and guiding
our thesis project from his excellence and dedicated career in the Hydrodynamic
field. For many valuable discussions at his office, and especially for the time he
dedicated on teaching us, not only work-wise, also towards our future careers.

We would also like to thank Kongsberg Maritime, specially to the Kristinehamns
research center team, Marko Vikström, Reima Aartojärvi, Rickard Gustafsson,
Markus Lindholm and Göran Grunditz. Thanks for sharing their knowledge with
us and for such a great welcome during our study visit to the Kongsberg maritime
research center.

Special greetings to all our classmates for joining us during our journey, enriching
and being part of our academic training, as well as for much-appreciated support.
Finally, a well-deserved acknowledgment to family and friends.

Nuttarat Vichanphruek and Lleo De Ribot, Gothenburg, July 2022

vii





Acronyms

CFD Computational fluid dynamics
CAD Computer-aided design
ITTC International Towing Tank Conference
MRF Moving reference frame
NURBS Non-uniform rational B-spline
RANS Reynolds-Averaged Navier-Stokes
SST Shear Stress Transport
WJ Waterjet

ix





Nomenclature

A Area, [m2]
D Diameter, [m]
g Gravitational acceleration, [m/s2]
h Height, [m]
H Pump head, [m]
η Efficiency
L Length, [m]
M̂i Momentum flux
n Normal vector
ν Fluid viscosity, [Pa·s]
ϕ Flow rate (non-dimensional)
ψ head rise (non-dimensional)
θt Start tangential angle
P Pressure, [Pa]
Q Mass flow rate, [Kg/s2]
ρ Fluid density, [Kg/m3]
R Radius [m]
τ Torque, [Nm]
T Thrust, [N]
Tw Wall shear stress
V Velocity , [m/s]
w Width, [m]
ω Angular velocity of impeller, [rpm]
y+ Wall distance (non-dimensional)
ξva Pump inflow uniformity
ϕp Perpendicularity
Va Axial velocity, [m/s]
Vt Tangential velocity [m/s]

xi



xii



Contents

Acronyms ix

Nomenclature xi

List of Figures xv

List of Tables xix

1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Project Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Literature review 5

3 Theory 9
3.1 Characteristic Velocities in a Waterjet . . . . . . . . . . . . . . . . . 9
3.2 Control Volume of the Waterjet Unit . . . . . . . . . . . . . . . . . . 9
3.3 Capture Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.4 Head Rise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.5 Momentum Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.6 Waterjet System Performance . . . . . . . . . . . . . . . . . . . . . . 12
3.7 Impeller Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.8 Flow Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.9 Tip Clearance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.10 Meshing Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.10.1 Prism Layer Mesher . . . . . . . . . . . . . . . . . . . . . . . 15
3.10.2 Trimmed Mesher . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.10.3 Advancing Layer Mesher . . . . . . . . . . . . . . . . . . . . . 16

4 Methods 17
4.1 Parametric Geometry Generation . . . . . . . . . . . . . . . . . . . . 17

4.1.1 Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.1.2 Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.1.3 Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.2 Pump Geometry and Characteristics . . . . . . . . . . . . . . . . . . 22

xiii



Contents

4.3 Set up the CFD simulation . . . . . . . . . . . . . . . . . . . . . . . . 23
4.3.1 Computational Domain Generation . . . . . . . . . . . . . . . 23
4.3.2 Physics model . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.3.3 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . 25
4.3.4 Pump modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.3.5 Mesh generation . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.3.6 Post processing . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.4 Capture area extraction . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.5 CAESES coupled with STAR CCM+ . . . . . . . . . . . . . . . . . . 29

5 Verification and Validation 31
5.1 Set up of AxWJ-2 validation simulation . . . . . . . . . . . . . . . . . 31
5.2 Validation Results of AxWJ-2 pump . . . . . . . . . . . . . . . . . . 33

6 Optimization Study 37
6.1 Original intake geometry . . . . . . . . . . . . . . . . . . . . . . . . . 37
6.2 Verification and Mesh sensitivity analysis . . . . . . . . . . . . . . . . 38
6.3 System Performance Curve Set up . . . . . . . . . . . . . . . . . . . . 39
6.4 System Performance Curve Results . . . . . . . . . . . . . . . . . . . 40
6.5 Extending Pump-Intake Connection Set up . . . . . . . . . . . . . . . 44
6.6 Extending Pump-Intake Connection Results . . . . . . . . . . . . . . 46
6.7 Shaft Removal Set up . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
6.8 Shaft Removal Results . . . . . . . . . . . . . . . . . . . . . . . . . . 50
6.9 Rim-driven Impeller Set up . . . . . . . . . . . . . . . . . . . . . . . 54
6.10 Rim-driven Impeller Results . . . . . . . . . . . . . . . . . . . . . . . 55
6.11 Intake Optimization Set up . . . . . . . . . . . . . . . . . . . . . . . 57

6.11.1 Objective definition . . . . . . . . . . . . . . . . . . . . . . . . 58
6.11.2 Intake height . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6.11.3 Cross section . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

6.12 Intake Optimization Results . . . . . . . . . . . . . . . . . . . . . . . 60
6.12.1 Intake height . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.12.2 Cross section . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
6.12.3 Shaft Removal study for the best design . . . . . . . . . . . . 68

7 Discussion 71
7.0.1 System Performance Curve . . . . . . . . . . . . . . . . . . . . 71
7.0.2 Extending Pump-Intake Connection . . . . . . . . . . . . . . . 71
7.0.3 Shaft Removal . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
7.0.4 Rim-driven Impeller . . . . . . . . . . . . . . . . . . . . . . . 72
7.0.5 Intake optimization . . . . . . . . . . . . . . . . . . . . . . . . 72

8 Conclusion 75

9 Future Work 77

References 79

A Appendix 1 I

xiv



List of Figures

3.1 Characteristic velocities of a waterjet (Bulten, 2006b) . . . . . . . . . 9
3.2 Control volume of the waterjet Unit . . . . . . . . . . . . . . . . . . . 10
3.3 Capture area geometry - ITTC Method . . . . . . . . . . . . . . . . . 10
3.4 Capture area geometry - CFD Method . . . . . . . . . . . . . . . . . 11
3.5 Waterjet head rise sketch . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.6 Impeller velocity and force components . . . . . . . . . . . . . . . . . 13
3.7 Boundary layer flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.8 Risk of separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.9 Tip Clearance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.1 Geometry Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2 Design Parameters of an Intake duct. Huang et al. (2019) . . . . . . . 18
4.3 NURBS Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.4 Cross-Section Variation . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.5 Engine Curves for cross-section variation . . . . . . . . . . . . . . . . 21
4.6 Reference curves for cross section transition . . . . . . . . . . . . . . 21
4.7 AxWJ-2 pump from John Hopkins University . . . . . . . . . . . . . 23
4.8 Rotor and Stator regions . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.9 Computational Domain . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.10 Computational Domain (side view) . . . . . . . . . . . . . . . . . . . 24
4.11 Computational Domain (Zoom in) . . . . . . . . . . . . . . . . . . . . 24
4.12 Mesh refinement regions . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.13 Volume meshes of Intake, Stator and Rotor. . . . . . . . . . . . . . . 28
4.14 Mesh Section representation . . . . . . . . . . . . . . . . . . . . . . . 28
4.15 Sections representation . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5.1 Experimental setup of the AxWJ-2 pump . . . . . . . . . . . . . . . . 31
5.2 Setup of the AxWJ-2 pump in STAR CCM+ . . . . . . . . . . . . . . 32
5.3 y+ values for the AxWJ-2 pump at V1 = 5.711 m/s . . . . . . . . . . 33
5.4 Head rise vs volumetric flow rate . . . . . . . . . . . . . . . . . . . . 33
5.5 Comparison between measured and simulated head coefficient . . . . 34
5.6 efficiency vs volumetric flow rate . . . . . . . . . . . . . . . . . . . . . 34
5.7 numerical uncertainty study for the AxWJ-2 pump . . . . . . . . . . 35

6.1 Original intake design . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
6.2 numerical uncertainty study for the computational domain . . . . . . 39

xv



List of Figures

6.3 y+ values for the rotor and stator regions at mass flow rate of 961.9
kg/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

6.4 y+ values for the intake and hull bottom regions at mass flow rate of
961.9 kg/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

6.5 System performance curves . . . . . . . . . . . . . . . . . . . . . . . . 42
6.6 Comparison between impeller and stator torque . . . . . . . . . . . . 42
6.7 Capture area from eight different mass flow rates . . . . . . . . . . . 43
6.8 streamtube at mass flow rate of 761.9 kg/s . . . . . . . . . . . . . . . 43
6.9 Streamline for the mass flow rate of 561.1 kg/s and 961.9 kg/s . . . . 44
6.10 Pump-Intake connection length variation . . . . . . . . . . . . . . . . 45
6.11 Pump-Intake connection length variation . . . . . . . . . . . . . . . . 45
6.12 Without intake setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
6.13 Efficiency vs intake connection length . . . . . . . . . . . . . . . . . . 46
6.14 Pump Inflow Uniformity and Perpendicularity vs intake connection

length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
6.15 Thrust and Torque vs intake connection length . . . . . . . . . . . . . 47
6.16 axial velocity vs intake connection length . . . . . . . . . . . . . . . . 48
6.17 Vt/Va vs intake connection length . . . . . . . . . . . . . . . . . . . . 49
6.18 absence of shaft simulation domain . . . . . . . . . . . . . . . . . . . 50
6.19 absence of shaft simulation domain (perspective view) . . . . . . . . . 50
6.20 Efficiency vs mass flow rate between shaft-existing and shaft removal 51
6.21 Torque and Thrust vs mass flow rate between shaft-existing and shaft

removal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
6.22 Head plot vs longitudinal position between shaft existing and without

shaft conditions at 801.6 kg/s . . . . . . . . . . . . . . . . . . . . . . 52
6.23 Axial velocity at the pump upstream cross section comparison be-

tween shaft-existing and shaft removal . . . . . . . . . . . . . . . . . 52
6.24 Vt/Va at the pump upstream cross section comparison between shaft-

existing and shaft removal . . . . . . . . . . . . . . . . . . . . . . . . 53
6.25 Axial velocity field at the pump upstream cross section for the mass

flow rate of 641.3 kg/s . . . . . . . . . . . . . . . . . . . . . . . . . . 53
6.26 Pressure contour plot of the mass flow rate of 641.3 kg/s . . . . . . . 54
6.27 Head plot vs longitudinal position with different mass flow rate con-

ditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
6.28 Rim driven pump (no tip gap) . . . . . . . . . . . . . . . . . . . . . . 55
6.29 Efficiency vs mass flow rate between having tip gap and no tip gap . 55
6.30 Torque and Thrust vs mass flow rate between having tip gap and no

tip gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
6.31 Axial velocity field at the pump upstream cross section comparison

between having tip gap and no tip gap . . . . . . . . . . . . . . . . . 56
6.32 Vt/Va at the pump upstream cross section comparison between having

tip gap and no tip gap . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6.33 Vt/Va at the stator start cross section comparison between having tip

gap and no tip gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6.34 Intake height variation . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6.35 Effect of start tangential angle (θt), while wt = 3 and farea = 1 . . . 59

xvi



List of Figures

6.36 Effect of weight top (wt), while θt = 45◦ and farea = 1 . . . . . . . . 59
6.37 Effect of area adjust factor (farea), while θt = 45◦ and wt = 3 . . . . . 60
6.38 Thrust-over-Torque vs intake height . . . . . . . . . . . . . . . . . . . 60
6.39 Surface Uniformity and Perpendicularity vs intake height . . . . . . . 61
6.40 Thrust and Torque vs intake height . . . . . . . . . . . . . . . . . . . 61
6.41 axial velocity vs intake height . . . . . . . . . . . . . . . . . . . . . . 62
6.42 Vt/Va vs intake height . . . . . . . . . . . . . . . . . . . . . . . . . . 62
6.43 Sensitivity analysis of start tangential angle top . . . . . . . . . . . . 63
6.44 Sensitivity analysis of weight top factor . . . . . . . . . . . . . . . . . 63
6.45 Sensitivity analysis of area adjust factor . . . . . . . . . . . . . . . . 64
6.46 Intake cross section Optimization . . . . . . . . . . . . . . . . . . . . 64
6.47 Intake shape comparison (Perspective view) . . . . . . . . . . . . . . 65
6.48 Intake shape comparison (Side view) . . . . . . . . . . . . . . . . . . 66
6.49 Intake shape comparison (Top view) . . . . . . . . . . . . . . . . . . 66
6.50 Intake shape comparison (Bottom view) . . . . . . . . . . . . . . . . 66
6.51 Axial velocity at the pump upstream cross section comparison . . . . 67
6.52 Vt/Va at the pump upstream cross section comparison . . . . . . . . . 67
6.53 Streamline for the original intake to the rotor . . . . . . . . . . . . . 68
6.54 Streamline for the optimized intake to the rotor . . . . . . . . . . . . 68
6.55 Axial velocity at the pump upstream cross section comparison be-

tween shaft-existing and shaft removal conditions . . . . . . . . . . . 69
6.56 Vt/Va at the pump upstream cross section comparison between shaft-

existing and shaft removal conditions . . . . . . . . . . . . . . . . . . 69
6.57 Streamline for the optimized intake without shaft to the rotor . . . . 70

A.1 Cross section optimization execution script . . . . . . . . . . . . . . . I

xvii



List of Figures

xviii



List of Tables

4.1 Profile Design Parameters . . . . . . . . . . . . . . . . . . . . . . . . 18
4.2 Cross-Section Design Parameters . . . . . . . . . . . . . . . . . . . . 20
4.3 The main particulars of the AxWJ-2 waterjet pump . . . . . . . . . . 22
4.4 Coarser Mesh setup parameters . . . . . . . . . . . . . . . . . . . . . 27
4.5 Coarser Volumetric Control Refinement . . . . . . . . . . . . . . . . . 27
4.6 Finer Mesh setup parameters . . . . . . . . . . . . . . . . . . . . . . 27
4.7 Finer Volumetric Control Refinement . . . . . . . . . . . . . . . . . . 27
4.8 Computational domain Number of cells . . . . . . . . . . . . . . . . . 28

5.1 Inlet velocities according to the flow rate coefficients . . . . . . . . . . 32
5.2 Mesh sensitivity study range for the AxWJ-2 validation simulation . . 32
5.3 Discretization uncertainty values for all number of cells (validation

study) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

6.1 Original intake design parameters . . . . . . . . . . . . . . . . . . . . 37
6.2 Mesh sensitivity study range for the whole computational domain

simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
6.3 Discretization uncertainty values for all number of cells (computa-

tional domain study) . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
6.4 mass flow rate variation for finding the system performance curve . . 40
6.5 pump-intake connection length variation . . . . . . . . . . . . . . . . 45
6.6 Without intake setup results . . . . . . . . . . . . . . . . . . . . . . . 48
6.7 Results comparison between original and optimized intake design . . 65
6.8 Optimized intake and original intake parameters comparison . . . . . 65
6.9 Results for the optimized intake comparison between shaft-existing

and shaft removal conditions . . . . . . . . . . . . . . . . . . . . . . . 68

xix



List of Tables

xx



1
Introduction

This section describes an overview of the project, including background on the wa-
terjet propulsion system, objectives, a project structure, and limitations.

1.1 Background

The waterjet propulsion system uses a reaction force created by high-speed water
jetting to propel vessels. The waterjet propulsion system draws water from the ves-
sel’s bottom and uses a propulsion pump to accelerate the flow and generate thrust
using momentum change. Waterjets are commonly used in high-speed crafts because
they have a better propulsive efficiency compared to conventional marine propellers
at high speed. In comparison to propellers, waterjets are quieter and produce less
vibration and noise, which improves not only passenger comfort but also undersea
noise and vibration. The system comprises the intake duct, the waterjet pump, the
nozzle, and the steering device (Bulten, 2006b).

The waterjet intake is used to connect the propulsion pump and the hull bottom.
The cavitation, vibration, and noise performance of the waterjet propulsion pump
are significantly affected by the hydraulic performance of the intake. The flow sep-
aration loss of the inlet, the constriction loss of the flow channel, the blockage loss,
and the friction loss are the key components of the hydrodynamic loss of the intake
(Weixuan Jiao et al., 2019). Therefore, it is necessary to find the best intake design
for a specific pump at the operating condition.

After passing through the intake, the flow gains a transversal velocity component
when it enters the impeller zone due to the impeller’s rotation. The impeller-induced
transversal velocity becomes the major non-axial component. The non-axial veloc-
ity components are considered the energy loss in the discharged jet. In theory, the
guiding vanes or stator should remove the flow swirl caused by impeller rotation so
that the nozzle released flow contains no velocity components other than the axial
component. As a result, the torque applied to guide vanes should be equal to the
impeller torque but in the opposite direction (Eslamdoost and Vikström, 2019). The
steering device is mounted downstream of the nozzle, which can deflect the jet in
order to create steering and reversing forces.

1



1. Introduction

1.2 Objectives
Nowadays, combustion engines often power modern waterjet units. The installa-
tion of waterjet propulsion units and their intake design are constrained by the size
of the engine and the gearbox. The application of electric drives can reduce the
dictated constraints of the conventional waterjet units and thus open new oppor-
tunities for modifying the placement of the waterjet unit, the intake design, and
the waterjet pump’s design. The main objectives of this project are to optimize the
waterjet intake that can maximize the overall system performance and to investi-
gate the hydrodynamic performance of the entire system when some constraints can
be modified due to the introduction of electric waterjet propulsion. From the two
main objectives, this project’s goals can be specified in further detail as shown below.

• Develop a parametric waterjet intake model, which can be parameterized for
both profile curves and cross sections along the longitudinal position.

• Find the best efficiency of the waterjet propulsion system.

• Study the effect of extending pump-intake connection.

• Study the effect of shaft removal.

• Study the effect using a rim-driven impeller.

• Optimize the intake geometry for maximizing the entire system efficiency.

1.3 Project Structure
At the beginning of the project, a literature review is conducted, so general ideas and
knowledge from previous research regarding waterjet propulsion are obtained, and
the studies that have been carried out in such investigations will not be repeated.
Many papers can be useful for furthering the study, such as the methodology of
capture area extraction and waterjet profile curve definition. After that, the pa-
rameterized intake duct is developed using CAESES software. The geometries of
the entire system have been prepared, including the rotor, stator, intake, tank, and
extension pipe. After having the whole domain, CFD simulation can be set up on
STAR CCM+. Before starting optimization, the verification and validation of the
AxWJ-2, which is the pump used in the simulations are conducted. During op-
timization, it is good to study and understand the system behavior with certain
geometry changes and investigate how the electrification of the waterjet gives room
for system geometry changes.

Firstly, in the study, the optimum operating condition of the waterjet system has to
be determined. The inlet velocity ratio of the system, which is defined by the pump
inlet velocity over the ship velocity, is the indicator for the optimum system operating

2



1. Introduction

condition. This ratio can be controlled by the mass flow rate specified at the nozzle
exit. After that, the studies of the extending pump-intake connection, shaft removal,
and rim-driven impeller are carried out. Finally, the intake optimization study is
performed.

1.4 Limitations
The time frame is the first limitation, as the project runs from January 2022 until
August 2022. The second is the pump model. The AxWJ-2 waterjet pump from
John Hopkins University is used for studying. During this project, this pump model
is used in all simulations and studies. Third, the focus of this thesis is to study
the water propulsion system itself, so hull interaction effects are neglected. The last
limitation is that all the results are from the simulations. Due to a lack of time and
equipment, no actual testing is performed.

3



1. Introduction

4



2
Literature review

In this section, a thorough literature study is conducted. The most interesting
sources for our propose are summarised in chronological order.

Bulten (2006b) studies the detailed analysis of a waterjet propulsion system from
theory until full scale application. The research shows that the major problem that
decreases the system efficiency is the large velocity variation due to non-uniformity.
It can cause lower impeller efficiency, cavitation, noise, and vibration due to blade
loading variation. There are four reasons that cause non-uniformity. First is the
boundary layer ingestion. Second is the deceleration of the flow at the inlet. Third
is the shaft inside the intake, and finally the bend of the duct. Different CFD solvers
are studied to analyse the flow. The solver that has an ability to capture vorticity
is beneficial due to large velocity variation. (Bulten, 2006b) comes up with RANS
and wall function methods. The paper does not study more in turbulence models
because it is not a goal of the research, so k-epsilon is good enough to close the
Navier Stoke equation. The validation of the CFD simulation with the experiment
with and without the pump is conducted. Finally, the study performs a full-scale
analysis for validation.

Jiang-ming and Yong-sheng (2010) conduct the flow loss of the waterjet intake study.
The flow loss of the intake is normally estimated by empirical rules, but the value is
over-predicted and might lead to the wrong power prediction. Therefore, this paper
introduced the new method to estimate the flow loss to be more precise. The flow
loss can be determined by the difference between the total energy at the outlet and
the captured area. The mass flow rate at the capture area must be equal to the
flow rate at the intake outlet. The capture area can be known if the streamtube
is obtained. The streamtube varies with the geometry and operating conditions.
The study introduces the method for finding the exact shape of the streamtube.
Firstly, the simulation must be done, and the flow field is obtained. After that, a
user-defined scalar equation is defined based on the transport equation, considering
only the convection term. The internal flow from the outlet of the intake is made by
the scalar value equal to one, while the external flow that does not pass through the
duct is marked by the scalar value equal to zero. Tracing the streamline backward
will give the streamtube shape.

Takai (2010) develops a CFD-based optimization system for waterjets with con-
sidering the interaction of a hull. An optimization tool can be done manually or
automatically by using an algorithm. There are three main steps. Firstly, a nonlin-

5



2. Literature review

ear problem is solved by forming an objective function and a constraint. Secondly,
geometry is generated by the design parameters. Finally, a CFD solver is used to
return the values. The paper Introduces many algorithms that help finding a multi-
objective design. During optimization, sensitivity analysis is performed manually
using a small number of design parameters to obtain the trend toward the objective
function. After that, several geometries are selected and applied with a morphing
scheme in the optimization loop. This research studies the optimization of the in-
take duct by varying the lip and ramp structure. The objective is to minimise the
friction loss. At the end, merging intake is investigated. The idea is to reduce the
wetted surface area that leads to minimising friction loss.

Eslamdoost (2014) studies the physics of waterjet and hull interaction, particularly
in the negative thrust deduction phenomenon, and develops a more accurate method
for predicting the gross thrust. Two methods are used to model the waterjet/hull
interaction. The pressure jump method is the first method, while another one is
RANS simulations. Regarding the pressure jump method, the waterjet induces a
lower pressure due to the suction process, so the sinkage is increased and leads to
the higher resistance. Regarding the self-propulsion RANS method and application,
it is found that the difference between gross thrust and net thrust comes from a
non-atmospheric pressure at the nozzle exit. Because of a transom wave, the nozzle
can be operated in ventilated or submerged condition. Non-atmospheric pressure at
the nozzle exit causes the thrust deduction factor to be less than zero. Furthermore,
It is shown that the capture area derived from the streamtube is quite different from
the shape that the ITTC Specialist Committee on Waterjets proposes. However, the
average velocities on the capture area section are still similar. Finally, the capture
area is not constant and depends on the operating conditions.

Budziszewski and Friedrichs (2018) research the optimization of an aircraft by the
boundary layer ingestion method. This method can reduce power consumption and
lead to lower fuel consumption and fewer emissions. The study is done by moving all
the propulsors to the rear part of the aircraft and embedding the engines to ingest
more boundary layers. When more boundary layer is ingested into the duct, propul-
sive power can be reduced while the thrust remains constant. There is a drawback
to this method due to the fact that more non-uniform flow into the fan will reduce
the fan’s efficiency. However, it demonstrates that using this method, propulsive
power can be reduced by one to four percent.

Huang et al. (2019) proposes a parametric waterjet intake CAD model and finds the
optimized intake duct without considering hull interaction by varying four param-
eters. These varying parameters include slope angle, ramp radius, lip radius, and
lip height. The fixed parameters are pump diameter, duct height, and duct length.
There are three optimization objectives. The first goal is to achieve as uniform flow
as possible at the outlet. The second goal is to have as much perpendicular flow at
the outlet as possible. The final goal is to achieve maximum hydraulic efficiency. A
sensitivity analysis for each parameter is also carried out. The study shows that the
slope angle has a significant effect on the hydrodynamic performance, while the lip

6



2. Literature review

height does not affect much. The research also studies the operating conditions with
an inlet velocity ratio. It is found that the inlet velocity ratio of 0.6 to 0.8 is the
suitable operating condition, otherwise the hydraulic efficiency will drop drastically.
Finally, after determining the best design, the model is tested with a mixed-flow
waterjet. The more uniform inflow mainly affects the pressure distribution on the
impeller suction surface and causes different shaft power.

Weixuan Jiao et al. (2019) proposes a parametric waterjet intake CAD model and
finds the optimized intake duct without considering hull interaction by varying three
parameters, including duct length, slope angle, and lip structure. No parameters
are fixed. The optimization goals are uniform flow, perpendicularity, and maximum
hydraulic efficiency. Moreover, the study of cavitation is included. In the beginning,
grid convergence is studied, then a validation of the CFD solver with the experi-
mental data is performed and it shows a good agreement with each other. The inlet
velocity ratio is studied. The optimized inlet velocity ratio is 0.78 to 0.96. If the
intake is operated outside this range, cavitation will occur. A low inlet velocity ratio
will have less cavitation risk but will have poor uniformity and separation risk. A
high inlet velocity ratio will have better uniformity but also a higher risk of cavi-
tation. After that, ship speed is investigated. The study finds that there is a ship
speed limitation and It is limited by cavitation.

Eslamdoost and Vikström (2019) develop a body-force model for waterjet pump
simulation. The sliding mesh technique can capture the pump flow physics and is
the most accurate approach to represent the pump operation in reality. This paper
demonstrates the validation between the sliding mesh technique and the experiment.
The result shows a small difference between each other, so the sliding mesh technique
is used as the benchmark when studying other pump model techniques. Because
pump geometries exist in the sliding mesh technique and the impeller blades have to
rotate during the simulation, this method has an extremely high computational cost,
and it is not worthwhile to use it for other studies such as waterjet hull interaction.
Thus, the moving reference frame technique (MRF) and the body force technique
are introduced. The body force technique, in which the stator is present in the
simulation and only the impeller blades are neglected, shows quite similar results to
MRF, but gradually faster in computational time. Moreover, it can predict the jet
stream better. It can be said that the overall performance of the body force technique
is better than MRF. In addition, the body force method shows an acceptable result
compared to the sliding mesh technique. Furthermore, it is much faster because
the impeller is gone. This leads to simpler geometries. Therefore, the body force
approach is fast and practical, while the result is still acceptable.

7



2. Literature review

8



3
Theory

3.1 Characteristic Velocities in a Waterjet
This project proposes the study of waterjet intake optimization. In order to carry out
such an investigation, the efficiency of the system should be determined. Therefore,
the velocity definitions at specific parts of the entire system are required. Four
main velocities can be extracted from fig. 3.1, including ship velocity (Vs), ingested
averaged velocity at the inlet (Vin), averaged velocity at the pump entrance (Vpump),
and outlet averaged velocity (Vout) (Bulten, 2006b). A good understanding of the
figures and velocities mentioned above is crucial for a waterjet performance study.
Aspects such as head rise, pressure, efficiency, and thrust are directly correlated to
the different flow velocities across the unit.

Figure 3.1: Characteristic velocities of a waterjet (Bulten, 2006b)

3.2 Control Volume of the Waterjet Unit
The control volume for the waterjet unit comprises different seven crucial parts
numbered in fig. 3.2. From left to right, surface number 1 is commonly named
vena-contracta, where the jet reaches its minimum diameter. Right before that,
surface number 2 represents the nozzle exit, where the flow exits the waterjet unit.
Surface number 3 represents the pump unit. The fourth surface shows the intake
duct along with region 5 named "lip" which works as the connection point between
the duct and the bottom plate. Surfaces 6 and 7 represent, respectively, the stream
tube area and the capture area (Eslamdoost, 2014).

9



3. Theory

Figure 3.2: Control volume of the waterjet Unit

3.3 Capture Area

The capture area is the region where the flow enters the waterjet system. The cap-
ture area provides information on the flow entering the waterjet. The capture area
shape varies according to the operational condition. However, the experts (ITTC
2002) developed the methods to estimate the capture area geometry. Regarding this
method, it was observed that the width of the capture area is almost constant even if
the Froude number is large. Empirical widths of the rectangular and half-elliptical
capture areas are shown in fig. 3.3. The height of the capture area varies based
on the flow rate through the system, and it is a bit higher in half-elliptical intake
geometry compared to the rectangular one (Eslamdoost, 2014).

Figure 3.3: Capture area geometry - ITTC Method

Another way to predict the most accurate shape of the capture area is by using
CFD. This method requires backward tracing of the streamlines from the pump
inlet down to the duct inlet. Fig. 3.4 shows the exact capture area shape from the
simulation.

10



3. Theory

Figure 3.4: Capture area geometry - CFD Method

3.4 Head Rise

The pump head (H) defines the added pressure in a pump due to Bernoulli’s prin-
ciple. Because of the waterjet condition of the pump elevation concerning the inlet,
there is an added energy difference, measured in meters as a derivative from the
Bernoulli equation (Carlton, 2012).

P1

ρg
+ (V1)2

2g +H = P2

ρg
+ (V2)2

2g + δh+ hloss (3.1)

H = (V2)2 − (V1)2

2g + (P2 − P1)
ρg

+ δh+ hloss (3.2)

Where in eq. (3.1) and (3.2), P stands for pressure, ρ stands for the fluid density, V
stands for fluid velocity at the different measured points, and h defines the height
at those sections as shown in fig. 3.5.

Figure 3.5: Waterjet head rise sketch

11



3. Theory

3.5 Momentum Flux
From Eslamdoost (2014), the thrust generated by the waterjet unit is always related
to the momentum flux variation through the waterjet unit. Why cannot the power
of a waterjet be expressed as net thrust? The reason is due to the limitations of
measurement methods. The momentum flux change concept can be defined as the
change of momentum through the waterjet. The reason is due to the limitations
of measurement methods, which measure from the low speed at the intake until
the high speed jet at the nozzle exit of the waterjet system. The momentum flux
balance on the control volume gives the resultant forces from the waterjet and can
be expressed as the following in eq. (3.3).

M̂i =
∫ ∫

A
ρui · (uknk)dA (3.3)

ρ is the fluid density, u is the velocity, and n is the normal vector to the volume
surface.

3.6 Waterjet System Performance
The efficiency of a waterjet unit can be described as the correlation between the
pump torque (τ) and the impeller angular velocity (ω), the head of the pump (H)
in meters, and the flow rate (Q) in m3/s.

η = ρgHQ

τω
(3.4)

It can be also expressed as a dimensionless equation, by adding non-dimensional
terms for flow rate (ϕ) as shown in eq. (3.5) and head rise (ψ) as shown in eq. (3.6).

ϕ = Q

nD3 (3.5)

ψ =
P2 − P1 + ρ

2((V2)2 − (V1)2)
ρn2D2 (3.6)

Where P states for pressure and V is the velocity at different measurement points.
Extracting the capture area information is an added complex procedure. Therefore,
another simplistic and less accurate way to calculate the system efficiency without
the need of extracting information from the capture area can be described as the
relationship of thrust (T ) and torque (τ). However, this method only gives the trend
of how efficiency will change. It does not tell the exact number.

η = TVs

τω
(3.7)

Where Vs is the ship speed and ω for the rotational speed of the pump impeller.

12



3. Theory

3.7 Impeller Theory
The impeller theory comprises velocity and force components. Figure 3.6 sketches
both components schematically. Starting from the velocity components, the triangle
is formed by Va as the flow velocity and the side rotational speed of the impeller,
ending with Vr as the resultant velocity of the two previous named components. The
triangle of velocities will determine the angle of attack (α), which is an essential
parameter for the blade design. On the left-hand side, the force components D
represents the drag force, L represents the lift force, and R represents the resultant
force combined from the drag and lift force. Finally, torque is the force rotating the
impeller and thus generating the thrust (T ) needed to power the ship.

Figure 3.6: Impeller velocity and force components

3.8 Flow Separation
Flow Separation is a phenomenon that occurs due to the three main forces acting on
a fluid. This force equilibrium occurs between pressure, inertia, and friction forces.
Krause (2005) proposes an example to explain such a phenomenon, assuming a flat
plate boundary layer as shown in fig. 3.7. According to fig. 3.7, the flow velocity
profile has a point of inflection at the flat plate due to friction forces. The flow static
pressure and friction forces slow down the flow near the flat plate. Separation will
occur when the velocity of the particle due to the wall shear stress reduces to zero,
which can develop a negative direction of the fluid flow.

13



3. Theory

Figure 3.7: Boundary layer flow

Because of the low fluid velocity and the high-pressure gradient at the ramp region,
there is a high risk of separation around the ramp region of the duct, as shown
in figure 3.8. This risk increases when the inlet velocity ratio is low. The flow
separation dramatically affects the inflow to the pump and the pump performance.

Figure 3.8: Risk of separation

3.9 Tip Clearance
The tip clearance is defined as the gap between the blade of the impeller and the
casing. It is the main parameter to take into account for blade design. In shaft-
driven impellers, tip clearance is required for correct operation, and it has a direct
impact on the system efficiency as it can cause tip leakage and tip vortex, in that
way causing potential flow separation to affect the inflow to the impeller (Moon-
Chan and Chun Ho-Hwan, 2005). These two effects are the result of the pressure
difference between the two sides of the impeller blade. Some flow from the pressure
side can be re-directed upstream towards the suction side of the blade. The physic
phenomena are further represented in fig. 3.9.

14



3. Theory

Figure 3.9: Tip Clearance

3.10 Meshing Techniques
Using the right meshing techniques is essential for a successful simulation and ob-
taining the correct flow characteristics. In this project, three different meshing
techniques have been used: prism layer, trimmed mesh, and advanced layer mesher.

3.10.1 Prism Layer Mesher
Prism layer meshing is used mainly to simulate the flow behaviour at the boundary
layer, where the flow gets influenced by the wall friction. The boundary layer thick-
ness can be estimated by assuming the logarithmic relationship in eq. (3.8). The
following equations are from White (2011).

Log-Law
u

u∗ = 1
κ
ln
yu∗

ν
+B (3.8)

where
u∗ =

√
τw

ρ
(3.9)

Reynolds Number
Re = Ux

ν
(3.10)

15



3. Theory

where ν is the kinematic viscosity

δ = 0.16x

Re

1
7

(3.11)

Cf = 0.027

Re

1
7

(3.12)

y+ = yu∗

ν
(3.13)

3.10.2 Trimmed Mesher
The trimmed mesher cuts and generates hexahedral volume cells from a template
mesh. It is commonly applied when the base custom mesh needs to be used or for
further improvement of mesh quality for polyhedral grids (Siemens, 2018).

3.10.3 Advancing Layer Mesher
The Advancing Layer Mesher generates a high-quality prismatic cell layer. It is used
to generate volume mesh out of prismatic cells next to the wall boundaries, as well
as polyhedral mesh elsewhere. The advanced layer mesher improves information
from the boundary layer (Siemens, 2018).

16



4
Methods

4.1 Parametric Geometry Generation

This chapter will introduce how the geometry is generated in CAESES (2019) and
the design parameters on which it depends. The main features of the model are
to be reliable for geometry parameter changes. A high degree of modification and
avoiding abrupt transitions are needed to ensure a good inflow to the pump. All
components are dependent on each other to ensure robustness to change.

4.1.1 Profile

As shown in Figure 4.1, the waterjet intake geometry is divided into four different
parts, including the horizontal straight pipe, the intake elbow, the ramp, and the
lip. Each of these sections is controlled by dependent and independent parameters.

Figure 4.1: Geometry Parts
The horizontal straight pipe length is defined by L1 and it has an outlet diameter
of D. The elbow radius is determined by R1 and R1 −D. L2 and R2 are defined to
control the ramp shape. L3, R3, R4, and hlip are used to control the lip shape. Table
4.1 shows the dependency conditions of the different parameters that generate the
waterjet intake model.

17



4. Methods

Figure 4.2: Design Parameters of an Intake duct. Huang et al. (2019)

Table 4.1: Profile Design Parameters

Fixed Independent Dependent
L α (Slope Angle) L0

D R2 L1

R3,original fb (Beam Factor) L2

hlip,original H L3

H0 R1

R4

hlip (Lip Height)
R3

The intake duct length (L) and pump diameter (D) are fixed. The independent
variables have to be determined for the purpose of generating the model. These
independent variables can be used for optimization later on. After defining the values
of the fixed parameters and independent parameters, the dependent parameters are
calculated by the following equations as shown below. Eq. (4.1), (4.2), (4.3), (4.4),
(4.7), and (4.8) are from Huang et al. (2019).

L0 =
√

(R4 −R3)2 − (R4 − hlip)2−L3 ·cos(α)−(R1−D−R3)·sin(α)+L−L1 (4.1)

L1 = R2 · sin(α) − L2 · cos(α) −R1 · sin(α) (4.2)

L2 = H + D

2 − (R1 · (1 − cos(α) −R2 · (1 − cos(α)
sin(α)) (4.3)

L3 = H − D

2 − hlip − (R3 · cos(α) − (R1 −D) · (1 − cos(α)
sin(α)) (4.4)

18



4. Methods

R3 = R3,Original − (H0 −H) · 0.1 · 3 (4.5)

hlip = hlip,Original − (H0 −H) · 0.1 · 3 (4.6)

R1 = 1.89 ·D (4.7)

R4 = D (4.8)

In order to permit the geometry to handle height modification, which is one of the
strong reference parameters for most of the dependent variables, equation (4.5) and
(4.6) has been introduced. To avoid cad generation error when optimizing height,
this scaling equation modifies parameters hlip and R3 at the same time, and it uses
original values as initial reference parameters.

4.1.2 Cross Section
Another feature required for better geometry optimization is a variable cross-section
along with the waterjet intake. Therefore, a cross-section of NURBS curves has been
created. NURBS curves are initially defined from three different reference points,
A, B, and C, as shown on the left side of figure 4.3. Modifying the position of
points A and B will vary the cross-section size, allowing a transition from a circular
cross-section to ellipse-shaped sections. The weight factor parameter is introduced
to constrain the distance between the curve and the reference point C. In that way,
the varying weight factor accomplishes obtaining unsymmetrical and variable corner
shapes between the top and the bottom part of the section. An example of the weight
factor influence can be found in fig. 4.3. As observed, the higher the weight factor,
the closer the curve to point C.

Figure 4.3: NURBS Curves

19



4. Methods

Table 4.2: Cross-Section Design Parameters

Fixed Independent Dependent
weight bottom area adjust factor weight top area adjust factor (farea) end tangential angle
weight bottom (wb) weight top (wt)
Beam factor (fb) start tangential angle (θt)
width adjust area

In order to control the section shape along the duct, engine F-Spline curves are used
to determine the value of the design parameters across the length of the intake. The
following Figure 4.4 shows two cross-sections, at the outlet and inlet, defined as
section A and section B respectively. From Table 4.2 the parameters governing how
the reference curves for the cross-section transition from points A to B are presented.

Figure 4.4: Cross-Section Variation
Section A must be a circular cross-section to match with the pump geometry casing,
so the values for the weight factor and the width are fixed in the following values:

wt = wb = 1√
2

(4.9)

width = D (4.10)

Figure 4.5 represents the reference curves for the cross-section variation. After
the initial desired value for the parameter is defined, weight top and bottom take
different shape until the inlet position. The ending value of the F-Spline curve will
determine the shape of section B as shown before in fig. 4.4. The evolution of the
cross-section shape is then defined by the F-Spline curves as shown in fig. 4.5. In
that way, a flexible and manageable way of controlling the section is accomplished.
As stated in Table 4.2, the top, bottom, and width curves can be further adjusted
by modifying the area below the curve. Notice that the weight reference curves for

20



4. Methods

the bottom and top are distinct to obtain asymmetric upper and lower corners if
needed.

Figure 4.5: Engine Curves for cross-section variation
For a better transition between the inlet and outlet of the intake duct, the weight top
area adjust factor can be modified as shown in fig. 4.6. Where the dashed curve 1
represents the original reference curve, and the rest 0.8, 1.2, 2, and 1.5 are possible
options for curve area modifications. This adjustment parameter allows a high
degree of change in the cross-section transition. Moreover, two more parameters
have been introduced to control the starting and ending tangential angles of the
reference curves. In that way, more abrupt transitions can also be obtained by
setting the start angle to 90 deg, or smoother either way.

Figure 4.6: Reference curves for cross section transition

4.1.3 Surface
After defining the cross section and profile curves as stated above, a feature defini-
tion is created to obtain cross sections at any position along the length of the intake.

21



4. Methods

Feature definitions are a sequence of commands which help customize curves with
specific routines. From these feature definitions, a curve engine is created to further
describe the curve cross-sections along the domain and to obtain curves per length
of intake.

A meta surface is used to generate the intake surface. The meta surface is the
most flexible surface type on CAESES. It lets users design their own parametric
surface based on arbitrarily complex curve descriptions. The use of meta surfaces
allows a great degree of modification of the surface morphology, which is suitable
for optimization studies (CAESES, 2019).

4.2 Pump Geometry and Characteristics

The AxWJ-2 waterjet pump from John Hopkins University is used for studying the
intake shape behavior. The AxWJ-2 waterjet pump is an axial flow pump, which
has 6 rotor blades. The stator downstream of the rotor has 8 blades. During the
simulation, the AxWJ-2 is run at 2000 rpm, which is a design point for an impeller
model scale in accordance with Thad J et al. (2008). The main particulars of the
pump are depicted in table 4.3.

Casing diameter 305.2 mm
Pump inner diameter 304.8 mm
Outlet diameter 213.4 mm

Rotor
Number of blades 6
Rotor diameter 303.8 mm
Tip clearance 0.46 mm
Tip profile chord length 274.3 mm
Tip profile axial chord length 127.4 mm

Stator
Number of blades 8

Table 4.3: The main particulars of the AxWJ-2 waterjet pump

22



4. Methods

Figure 4.7: AxWJ-2 pump from John Hopkins University

4.3 Set up the CFD simulation

In the following section, computational domain generation, physics model, boundary
conditions, pump modeling, mesh generation, and post-processing are described.

4.3.1 Computational Domain Generation

Five regions are generated, including water tank, intake, rotor part, stator part, and
extended pipe to appropriately define the boundary condition, mesh, and physics
condition. The water tank is the region that mimics the water volume below the
hull. It has the reasonable dimension of 30D (length) * 10D (width) * 8D (height),
which is recommended by Liu et al. (2010). The intake is located on top of the
water tank with the specific location as shown in figure 4.9 recommended by Liu
et al. (2010). The pump model from John Hopkins University is modified and
divided into two parts. The first part is the rotor region, which has the impeller
inside. Generally, this part shall be moving in the sliding mesh approach, but since
the moving reference method is used, this part is treated specifically as will mention
in section 4.3.4. The second part is the stator region. This region is stationary, and
a nozzle outlet is included in the casing. The last part, the extended pipe, which
is extruded from the nozzle outlet with a length of 10D and has the same diameter
as the nozzle outlet. This extended pipe is generated for computational stability as
the outlet section boundary shall have a fully developed flow characteristic.

23



4. Methods

(a) Rotor and Stator (b) Rotor (c) Stator

Figure 4.8: Rotor and Stator regions

Figure 4.9: Computational Domain

Figure 4.10: Computational Domain (side view)

Figure 4.11: Computational Domain (Zoom in)

24



4. Methods

4.3.2 Physics model
Reynolds-Averaged Navier-Stokes method is used to close the Navier-Stokes equa-
tions. The SST k-ω turbulence model is used to simulate the internal flows since it
is good enough to predict the flow near a wall and can capture the adverse pressure
gradient (Huang et al., 2019). Fluid is water at 15◦C. The water density is 999.1
kg/m3. The water dynamic viscosity is 0.001139 Pa·s. Even though the coupled
solver is more robust and faster than the segregated solver, it consumes a lot more
memory than the segregated solver. The segregated solver converges quite slow,
but requires low memory consumption, which is a good trade off (Siemens, 2018).
Thus, the segregated flow solver is selected. Finally, implicit unsteady is chosen,
and performed with a time step of 0.01 s.

4.3.3 Boundary conditions
The ship speed of 16.62 m/s will be input as the velocity inlet uniformity into the
water tank. To simplify the simulation, the boundary layer of the hull is neglected
before the water enters the tank. The outlet of the water tank is set as a pressure
outlet equal to the atmospheric pressure, while another outlet through the extended
straight pipe is applied as the mass flow rate. The lateral and the bottom wall of
the water tank are set as slip walls, so the mesh does not need to be fine there and
can reduce the computational time. The top wall of the water tank, which can be
considered as the hull bottom flat plate and the intake surface are set as non-slip
walls. There are two parts that are needed to input the wall’s relative motion.
They are the pump housing in the rotor region and the shaft inside the intake. The
shaft wall relative motion is equal to the rpm of the impeller, which is 2000 rpm.
The pump housing’s relative motion is equal to the impeller’s rpm as well but in
the opposite direction. This part has to cancel the rotation movement from the
moving reference frame because the coordinate system is moving around its region,
but the pump housing is not moving in practice. The stator region is stationary and
regarded as a non-slip wall. The extended pipe wall is considered a slip wall because
it is unnecessary to concern the boundary layer around this region. Its responsibility
is only to apply the proper outlet boundary condition.

4.3.4 Pump modeling
For the impeller shaft, assigning a wall relative motion can be done easily. How-
ever, the impeller region is more complicated. There are three main techniques to
simulate the rotation movement of the impeller. There are sliding mesh approach,
moving reference frame approach (MRF), and body force approach. All of them
have their own advantages and disadvantages that have to be chosen carefully.

Sliding Mesh approach
The sliding mesh technique can capture the pump flow physics and is the most
accurate approach to represent the pump operation in reality (Eslamdoost, 2014).
Because pump geometries exist in the sliding mesh technique and the impeller region

25



4. Methods

has to rotate during the simulation, this method has an extremely high computa-
tional cost. Thus, it is not worthwhile to use it for other studies such as waterjet
hull interaction and optimization tasks. Siemens (2018) recommends a time step
for the simulation that gives a rotation of 1 degree between each time step. For a
rotational speed of 2000 rpm, this will give a time step of 7.88*10−6s.

Moving Reference Frame approach
The coordinate system for the impeller region is rotated instead of the geometries
around the rotational axis with the specific rpm. The impeller is stationary in this
method. There is no physical rotation of the geometry within this approach. Thus,
this method is less accurate than the sliding mesh approach. It cannot capture the
relative position between impeller blades and stator. However, this technique is not
dependent on the time step. A larger time step can be used compared to the sliding
mesh approach. In this project, a time step of 0.01s is used and it is good enough
to have a converged solution. Therefore, the moving reference frame approach is
extremely cheaper than the sliding mesh approach.

Body Force approach
For this method, the stator is presented in the simulation and only the impeller
blades are neglected, so the computational time is decreased because there is no
mesh for the impeller (Eslamdoost, 2014). The virtual disk model then is applied
for the impeller region. The axial body force and the tangential body force per unit
volume have to be added in the model, so this virtual disk can perform its function
as a pump. However, it is tricky to define a proper body force distribution, which
will give good flow results that matches with the actual flow.

To sum up, this project is studied about the optimization and there will be various
simulations because of the geometry variations. Thus, it is not suitable to use the
sliding mesh approach, because this approach is too expensive. Although it is the
most accurate method, the time limitation is an important factor to be concerned.
In addition, it is difficult and complicated to set up the force distribution for the
body force approach to matching with the actual pump flow. Hence, the moving
reference frame approach is chosen for this project. It is good enough to predict the
flow without taking a too long time.

4.3.5 Mesh generation

There are two mesh types that are used in the computational domain. The first one
is polyhedral mesh. It is generated for complex geometries such as rotor and stator.
The second type is hexahedral mesh. It is used for simple geometries and is good
to satisfy the continuity equation. On top of the base meshing, extra refinements
in the computational domain have been created. One upstream refinement, pipe
extension refinement, intake refinement, and pump region refinement are presented
in fig 4.12.

26



4. Methods

Figure 4.12: Mesh refinement regions

The hexahedral meshing region includes parts of the domain such as intake and
shaft, tank, and pipe extension. Prism layer meshing, trimmer mesh, and surface
re-meshing are used as meshing criteria. Table 4.4 and Table 4.5 present the main
setup features of the mesh used in these parts.

Base Size 20 mm
Number of Prism Layers 16
Thickness of Near Wall Prism Layer 2.4 x 10−4 mm

Table 4.4: Coarser Mesh setup parameters

Upstream Refinement 500 %
Pipe extension Refinement 50 %
Intake Refinement 50 %
General Refinement 100 %

Table 4.5: Coarser Volumetric Control Refinement

The polyhedral mesh has been used in more complex geometries such as the pump
unit, using the Advanced Layer Mesh method, which is more suitable for complex
regions. These pump regions include the impeller, the stator, hub, and casing of
such regions. Table 4.6 and Table 4.7 present the main setup features of the mesh
used in the pump region.

Base Size 20 mm
Number of Prism Layers 25
Thickness of Near Wall Prism Layer 2.4 x 10−6 mm

Table 4.6: Finer Mesh setup parameters

Pump and Nozzle Exit refinement 50 %

Table 4.7: Finer Volumetric Control Refinement

27



4. Methods

(a) Intake (b) Stator (c) Rotor

Figure 4.13: Volume meshes of Intake, Stator and Rotor.

Stator 2,404,182
Rotor 1,509,347
Intake + Tank 1,655,922
Pipe Extension 82,714
TOTAL 5,652,165

Table 4.8: Computational domain Number of cells

Figure 4.14 shows in further detail a section plane of three different meshing tech-
niques in the domain. From left to right: pipe extension, pump, and intake.

Figure 4.14: Mesh Section representation

4.3.6 Post processing
To visualize the results after the simulation is done, post-processing scenes and re-
ports have to be created.

There are several reports that are needed. The first report is the pressure and
velocity report at the inlet and outlet of the pump and at the capture area. Pressure
and velocity at the inlet, which can be called the pump upstream section, can be
measured in front of the intake end section about 0.1D, while pressure and velocity
at the outlet can be measured at the nozzle exit as shown in the figure 4.15. These

28



4. Methods

values are obtained by finding the average pressure and velocity on those surfaces.
The second report is the thrust report, which is generated by the impeller, stator,
casing, and intake. Finally, the moment report is created to monitor the impeller
torque. With all these data, delivered shaft power, head rise, and pump efficiency
can be calculated.

Figure 4.15: Sections representation

The scalar scenes for visualizing pressure and velocity are created. The flow behavior
that can be observed in these scenes depends on which sections or parts are selected.
For velocity, there are two main components including tangential velocity and axial
velocity that can be extracted to understand the flow behavior better. In addition,
the wall y+ scenes are visualized for both pump and domain regions as these values
need to be controlled. For the pump region, the wall y+ value should be less or
around 1 for a wall-resolved boundary layer. For the domain region, the wall y+

value should be above 30, but under 150, so the wall function is applied correctly
(Huang et al., 2019). Finally, the vector scene can be plotted as well to visualize
the flow direction.

4.4 Capture area extraction
The capture area is unknown until the simulation is done. It can be varied due to
intake shape, pump model, and operating conditions. Thus, the special procedure
needs to be carried out to extract the capture area for each simulation. The capture
area cross section is located one intake diameter ahead of the intake tangency point
to the hull as recommended by the ITTC Specialist Committee on Waterjets. To
define the capture area shape, an extra passive scalar equation is solved for obtaining
the actual geometry of the capture area.

4.5 CAESES coupled with STAR CCM+
The intake geometry is controlled by many parameters. Some parameters, which
significantly affect the hydrodynamics performance are picked to study on the intake
optimization. In order to run the optimization study, STAR CCM+ has to be
coupled with CAESES, so the several simulations due to the geometry variation can

29



4. Methods

be automated. Fortunately, CAESES has the feature named software connection.
This connection allows users to connect the CAD modeling with other software
including STAR CCM+. Firstly, in the coupling process, the general simulation set
up in STAR CCM+ needs to be ready. After that, the users have to record the
java macro in STAR CCM+ for telling CAESES what to do and how to run the
simulation file in batch mode. During recording the java macro, the intake geometry
is replaced, so later on STAR CCM+ in batch mode will understand that they have
to run the simulation based on the latest geometry from CAESES. In addition,
the simulation results such as figures and physical values can be exported during
recording, so the users can visual and analyze the results in CAESES after running
various simulations.

30



5
Verification and Validation

5.1 Set up of AxWJ-2 validation simulation
In order to make sure that the studies have been done correctly related to the quan-
tification of modeling errors, i.e. the difference between the outcome of a mathe-
matical/computational model and the physical reality, the validation is carried out.
The aim is to demonstrate that the right equations are chosen. As the AxWJ-2
pump is selected and there is the experimental data available from the John Hop-
kins University, the CFD simulation results are compared to the experimental data.

The AxWJ-2 pump is tested at the John Hopkins University with a liquid solution
of sodium iodide (NaI) in water (62-63 percent of weight). This liquid has a density
of 1800 kg/m3 and it has a dynamic viscosity of 0.00198 Pas. Thus, the density and
dynamic viscosity of the water in STAR CCM+ is set up to match the experimental
fluid properties. The experimental setup is shown below in figure 5.1.

Figure 5.1: Experimental setup of the AxWJ-2 pump

To validate the simulation properly, the experimental setup at the John Hopkins
University is imitated in STAR CCM+ as shown in figure 5.2. In order to obtain
the head rise from eq. (6.1), The inlet velocity and inlet pressure can be defined
from the average values on the cross section before the pump inlet, while the outlet

31



5. Verification and Validation

velocity and outlet pressure can be defined from the average values on the cross sec-
tion surface at the nozzle exit. The positions of the cross section are matched with
the experimental measuring positions. Rotational rate of the impeller (ω) is fixed
at 900 rpm. The impeller thrust and torque (τ) can be extracted from the simulation.

Figure 5.2: Setup of the AxWJ-2 pump in STAR CCM+

The range of the inlet velocity to the domain is calculated backward from the eq.
(5.1) as the flow rate coefficient range is known from the experimental measurement.
Thus, the results from the simulation will be in the same range as the experimental
data. To compare the results with the experiment, the head coefficient is needed
and can be calculated following the eq. (5.2). Table 5.1 shows ten inlet velocity
values, which are set up in the simulations.

V1(m/s) 3.655 3.883 4.112 4.340 4.569 4.797 5.026 5.254 5.482 5.711
ϕ 0.608 0.646 0.684 0.722 0.760 0.798 0.836 0.874 0.912 0.950

Table 5.1: Inlet velocities according to the flow rate coefficients

ϕ = Q

nD3 (5.1)

ψ = H

ρn2D2 (5.2)

To obtain a suitable mesh for the AxWJ-2 validation simulation, the investigation
of mesh influence is performed by monitoring the impeller torque. While changing
the mesh density, the y+ values are guaranteed to comply with the computational
requirements. For the AxWJ-2 validation simulation, the total number of cells is
varied from 3.7 x 106 up to 5.8 x 106 as shown in table 5.2.

values (x 106)
the total number of cells 3.77 3.94 4.22 4.67 5.56 5.84

Table 5.2: Mesh sensitivity study range for the AxWJ-2 validation simulation

32



5. Verification and Validation

5.2 Validation Results of AxWJ-2 pump
First of all, the mesh quality needs to be checked. Figure 5.3 demonstrates the y+

values in the rotor and stator regions as the y+ values must be controlled to have
the value less than or around 1 for a wall resolved boundary layer.

Figure 5.3: y+ values for the AxWJ-2 pump at V1 = 5.711 m/s

The values between the simulations in STAR CCM+ and the experimental data are
compared. The pump performance curve can be shown in fig. 5.4. It presents the
relation between head rise (H) and volumetric flow rate (Q). Figure 5.5 compares
the values of flow coefficient (ϕ) and head coefficient (ψ). The flow coefficients (ϕ)
are scaled with the best flow coefficient (ϕBEP ) of 0.76, while the head coefficients
(ψ) are scaled with the best head coefficient (ψBEP ) of 2.46. The values of ϕBEP and
ψBEP are obtained from the John Hopkins University. According to the plots, it can
be seen that the validation is satisfied since the simulation results match remarkably
good with the experimental data.

Figure 5.4: Head rise vs volumetric flow rate

33



5. Verification and Validation

Figure 5.5: Comparison between measured and simulated head coefficient

The pump efficiency can be shown below in fig. 5.6. However, there is no data on
torque measurement available from the experiment, so the comparison for the pump
efficiency is not performed. Although no torque measurements are available, Thad J
et al. (2008) mentions that AxWJ-2 pump is designed to have a maximum efficiency
of about 90%. Figure 5.6 shows that the maximum efficiency reaches 89.5%, which
matches what the pump designer was aiming for.

Figure 5.6: efficiency vs volumetric flow rate

According to the mesh sensitivity analysis, figure 5.7 shows the numerical uncer-
tainty study for the AxWJ-2 pump. It contains a refinement ratio ranging from
1 to 1.2. A decent study must cover a refinement ratio range of at least between
1 to 2, while 1 is the finest mesh. Thus, the future project should have increased
the refinement steps for a more accurate study. A formal verification based on the
Least Squares Root method by Eca L. and Hoekstra (2014) was carried out. The
mesh number of 4.6E6 cells shows a good compromise between numerical accuracy

34



5. Verification and Validation

and computational effort and was used for the validation study. The numerical
uncertainty for this grid was 3.25%.

Figure 5.7: numerical uncertainty study for the AxWJ-2 pump

Number of cells (x 106) refinement ratio Discretization uncertainty (%)
5.84 1.000 3.06
5.56 1.016 3.08
4.67 1.077 3.25
4.22 1.114 3.44
3.94 1.140 3.51
3.77 1.156 4.09

Table 5.3: Discretization uncertainty values for all number of cells (validation
study)

35



5. Verification and Validation

36



6
Optimization Study

6.1 Original intake geometry

After introducing the methodology used to generate the parametric intake model,
Table 6.1 represents the initial design parameters to start the investigation. Such
parameters are the ones used to generate the metasurface.

parameters values units
L 1.441 m
D 0.3048 m
H 0.265 m
α 26 deg
R2 1.3 m
hlip 0.0375 m
R3 0.0245 m
beam factor (fb) 1.5 -
weight top (wt) 3 -
weight bottom (wb) 1.2 -
weight top area adjust (farea) 1 -
start tangential angle top (θt) 45 deg
end tangential angle top 45 deg

Table 6.1: Original intake design parameters

37



6. Optimization Study

Figure 6.1: Original intake design

6.2 Verification and Mesh sensitivity analysis

Theoretically, the higher number of mesh and grids density, the computation ac-
curacy will generally be improved. However, as the number of grids increases, the
computational cost is more expensive. Therefore, the final grid number of the en-
tire computational domain is needed to be determined. To obtain a suitable mesh,
the investigation of mesh influence is performed by monitoring the impeller torque.
While changing the mesh density, the y+ values are guaranteed to comply with the
computational requirements. For the whole computational domain simulation, the
total number of cells is varied from 4.4 x 106 up to 7.2 x 106 as shown in table 6.2.

values (x 106)
the total number of cells 4.47 4.68 5.02 5.63 6.02 7.18

Table 6.2: Mesh sensitivity study range for the whole computational domain sim-
ulation

Figure 6.2 shows the numerical uncertainty study for the computational domain.
It contains a refinement ratio ranging from 1 to 1.2. A decent study must cover a
refinement ratio range of at least between 1 to 2, while 1 is the finest mesh. Thus,
the future project should have increased the refinement steps for a more accurate
study. A formal verification based on the Least Squares Root method by Eca L.
and Hoekstra (2014) was carried out. The mesh number of 5.6E6 cells shows a good
compromise between numerical accuracy and computational effort and was used for
further studies. The numerical uncertainty for this grid was 3.85%.

38



6. Optimization Study

Figure 6.2: numerical uncertainty study for the computational domain

Number of cells (x 106) refinement ratio Discretization uncertainty (%)
7.18 1.000 3.56
6.02 1.061 3.78
5.63 1.084 3.85
5.02 1.127 4.01
4.68 1.153 4.29
4.47 1.171 5.01

Table 6.3: Discretization uncertainty values for all number of cells (computational
domain study)

6.3 System Performance Curve Set up

At the first stage of this study, the system performance curve shall be determined
before starting a geometry variation study. Thus, when the geometry variation
is performed, the best system operational point is selected. The mass flow rate
variation is set at the extended pipe outlet boundary from 561.1 kg/s to 961.9 kg/s.
To obtain the smooth system performance curve, eight mass flow rate values are
defined. It means that there are eight simulations, which are carried out to obtain
the system performance curve. The mass flow rate ranges can be seen in table 6.4
below.

39



6. Optimization Study

value (kg/s)
mass flow rate 561.1 641.3 721.4 761.9 801.6 842.1 881.7 961.9

Table 6.4: mass flow rate variation for finding the system performance curve

The system efficiency is obtained from the ratio between the hydraulic power gen-
erated by the pump and the shaft delivered power as shown in eq. (6.4). In order
to compute the hydraulic power, eq. (6.2) is applied. The inlet velocity and inlet
pressure can be defined from the average values on the capture area surface, while
the outlet velocity and outlet pressure can be defined from the average values on the
cross section surface at the nozzle exit. Rotational rate of the impeller (ω) is fixed
to 2000 rpm and the impeller torque (τ) can be extracted from the simulation, so
the shaft delivered power can be computed following eq. (6.3).

H =
(pout − pcapture) + ρ

2(V 2
out − V 2

capture)
ρg

(6.1)

Pout = ρgQH (6.2)

Pin = τω (6.3)

η = Pout

Pin

(6.4)

6.4 System Performance Curve Results

Firstly, the mesh quality needs to be checked. Figure 6.3 shows the y+ values in the
rotor and stator regions, the y+ values must be controlled to have a value less than
or around 1. In addition, the y+ values in the intake and hull bottom regions must
be controlled above 30 but less than 150 following the wall function criterion, are
shown as well in fig. 6.4.

40



6. Optimization Study

Figure 6.3: y+ values for the rotor and stator regions at mass flow rate of 961.9
kg/s

Figure 6.4: y+ values for the intake and hull bottom regions at mass flow rate of
961.9 kg/s

Figure 6.5 presents the system efficiency curve obtained from eq. (6.4) and head
rise curve obtained from eq. (6.1). The curve shows that the system will have the
highest efficiency when operating at the mass flow rate of 761.9 kg/s. The maximum
efficiency is found to be 72.44%.

41



6. Optimization Study

(a) system efficiency vs mass flow rate (b) head rise vs mass flow rate

Figure 6.5: System performance curves

To verify the stator performance, the impeller and stator torques are plotted together
in fig. 6.6. It shows that the stator performs an excellent function in reducing the
flow’s swirl motion as the torque produced by the stator has a value close to the
impeller torque but in the opposite direction. The impeller and stator torque ratio
is close to 1 when the mass flow rate is 761.9 kg/s. This supports the result of the
highest efficiency as the loss from swirl motion is reduced significantly by the stator
at this mass flow rate.

(a) impeller and stator torque vs mass flow
rate (sign negligible)

(b) the ratio between impeller and stator
torque

Figure 6.6: Comparison between impeller and stator torque

In this section, the capture areas from eight different mass flow rates are shown in
fig 6.7. The capture area is larger when the mass flow rate is higher because more
flow is pulled into the intake. Figure 6.8 depicts the streamtube for the mass flow
rate of 761.9 kg/s which is obtained from the capture area extraction procedure as
mentioned in section 4.4.

42



6. Optimization Study

Figure 6.7: Capture area from eight different mass flow rates

Figure 6.8: streamtube at mass flow rate of 761.9 kg/s

One phenomenon that can be observed when studying the system performance curve
is flow separation. From the mass conservation rule, the higher the mass flow rate,
the faster fluid flow will be. Separation occurs when the fluid velocity in the duct is
lower than a certain value and affects the whole system performance. This obviously
happens with low mass flow rates such as 561.1 ks/s and 641.3 kg/s. As shown in
fig. 6.9, the separation occurs at the top of the intake ramp region because the
velocity there is low enough and cannot overcome the adverse pressure gradient.

43



6. Optimization Study

(a) 561.1 kg/s (b) 961.9 kg/s

Figure 6.9: Streamline for the mass flow rate of 561.1 kg/s and 961.9 kg/s

6.5 Extending Pump-Intake Connection Set up
Before starting optimization, it is good to understand the general physics of the
system. There are two parameters that might help to increase the system efficiency.
First is the surface uniformity of the axial velocity at the pump upstream cross
section, which can be called as a pump inflow uniformity. This pump upstream
cross section is located at 0.1D before the pump inlet surface (Siemens, 2018). The
pump should operate more effectively if the inlet axial velocity of the fluid is more
uniform. This helps to reduce the non-uniform blade loading problem and is good
for noise and vibration reduction. The pump inflow uniformity can be defined by the
following eq. (6.5). The second parameter is the flow perpendicularity at the pump
upstream cross section. It can be said that the pump can operate more efficiently
when the axial component of the flow velocity is as high as possible compared
to its magnitude. This can be explained as follows: if the flow is not perfectly
perpendicular to the cross section plane, this can affect the blade’s angle of attack.
The perpendicularity parameter can be defined by the following eq. (6.6).

ξva = 1 − [
∑

f |Va,f − Va|Af

2|Va| ∑
f Af

] (6.5)

ϕp = 1
Q

∫
dA
Va[90◦ − arctan(Vt

Va

)]dA (6.6)

From eq. (6.5), it can be seen that the surface uniformity of the axial velocity is
good if this value is close to 1. If the quantity is distributed equally, the resulting
number is 1 (Siemens, 2018). From eq. (6.6), if the perpendicularity is equal to 90,
it means that the flow is perfectly perpendicular to the cross section plane. Thus,
it is good to have this resulting number as close to 90 as possible (Huang et al., 2019).

In order to verify this hypothesis, the extending pump-intake connection study has
been carried out. During this study, the mass flow rate is fixed at 761.9 kg/s,
which is the best system operating point obtained from the system performance
study. The pump-intake connection is basically the circular pipe that connects
the intake to the pump. In the original geometry, the pump is connected directly
to the intake. The pump-intake connection length variation is set from 0 to 4D.
Furthermore, one additional simulation is performed to have a better understanding

44



6. Optimization Study

of these parameters. For this extra one, the intake is removed and there is a long
straight pipe with a length of 10D before the pump inlet as shown in fig. 6.12. It
is assumed to be the best working operational condition for the pump because the
intake is actually the main reason for non-perpendicularity and non-uniform flow.
The intake connection length ranges can be seen in table 6.5 below.

value (m)
with intake without intake

intake connection length 0 0.3 0.6 0.9 1.2 3

Table 6.5: pump-intake connection length variation

(a) intake connection length = 0.3 m (b) intake connection length = 0.6 m

Figure 6.10: Pump-Intake connection length variation

(a) intake connection length = 0.9 m (b) intake connection length = 1.2 m

Figure 6.11: Pump-Intake connection length variation

Figure 6.12: Without intake setup

45



6. Optimization Study

6.6 Extending Pump-Intake Connection Results

Figure 6.13 shows the intake connection study results in terms of efficiency. The
efficiency increases gradually when the intake connection is extended. Moreover, it
can be seen that the thrust-over-torque parameter, which is mentioned in section
6.11.1 can be used to represent the trend of the system efficiency when the intake
geometry is changed. As expected, the longer the intake connection, the inflow to
the pump is better for both pump inflow uniformity and perpendicularity, as shown
in fig 6.14. This also results in lower torque and higher thrust summation when the
intake connection length is longer, as shown in fig. 6.15. However, there is a limit
to this efficiency increase when extending the intake connection because the inflow
is better, but the friction loss in the intake connection part is larger as well. Thus,
at a certain point, the friction loss overcomes the benefit of a more uniform inflow.

Figure 6.13: Efficiency vs intake connection length

46



6. Optimization Study

(a) Pump Inflow Uniformity vs intake con-
nection length

(b) Perpendicularity vs intake connection
length

Figure 6.14: Pump Inflow Uniformity and Perpendicularity vs intake connection
length

(a) Torque vs intake connection length (b) Thrust Summation vs intake connec-
tion length

Figure 6.15: Thrust and Torque vs intake connection length

Table 6.6 depicts the results from the simulation without intake setup. The efficiency
can reach 90.5%. This is extremely high. It also matches the pump designer’s aim
because this pump is designed to have a maximum efficiency of about 90% in the
horizontal domain. The physical quantities also support the study, including the
higher pump inflow uniformity, higher perpendicularity, and lower torque.

47



6. Optimization Study

parameters values units
efficiency 90.5 %
surface uniformity 0.968 -
perpendicularity 86.88 deg
torque 971.3 Nm

Table 6.6: Without intake setup results

The axial velocity profile at the pump upstream cross section can be extracted
as shown in fig. 6.16. The inflow to the pump is more uniform when the intake
connection is longer. Because of the intake shape, it results in a higher velocity
at the bottom and a lower velocity at the top. However, this is not the case for
the without intake setup as there is no upward movement of the flow, so the inflow
to the pump is remarkably uniform compared to with intake simulations. As the
shaft is rotating in the counter clockwise direction and the flow is moving upward
when passing through the intake, the axial velocity is lower near the shaft line on
the left side because the shaft rotation motion and the flow motion are in different
directions.

(a) length = 0 m (b) length = 0.3 m (c) length = 0.6 m

(d) length = 0.9 m (e) length = 1.2 m (f) length = 3 m (without in-
take)

Figure 6.16: axial velocity vs intake connection length

To observe the inflow quality to the pump, the ratio of the tangential velocity and
axial velocity (Vt/Va) can be used. The lower this ratio, the better inflow quality

48



6. Optimization Study

to the pump is obtained as the tangential velocity will normally degrade the pump
performance. Vt/Va profile at the pump upstream cross section can be extracted as
shown in fig. 6.17. The tangential velocity component is generated due to the shaft
rotation and the intake shape. Thus, it can be seen that Vt/Va is remarkably low in
the without intake setup case.

(a) length = 0 m (b) length = 0.3 m (c) length = 0.6 m

(d) length = 0.9 m (e) length = 1.2 m (f) length = 3 m (without in-
take)

Figure 6.17: Vt/Va vs intake connection length

6.7 Shaft Removal Set up

Nowadays, electric propulsion has been developed worldwide. This allows the possi-
bility to do more research on how it can affect the hydrodynamic performance of the
waterjet propulsion system. With electric propulsion, one can think of employing
a rim-driven pump instead of driving it with a shaft line. This may also reduce
the nonuniform flow into the pump, which is good for the pump’s performance.
This section will study the effects of the shaft removal condition compared to the
shaft-existing condition. The eight simulations, which varied eight mass flow rates
as before, are repeated. The computational domain is modified by removing the
shaft and adding the impeller hub tip as shown in fig. 6.19. This section is just
for educational purposes, so it might not work in practice, as it is assumed that the
motor can be fitted inside the impeller hub. The pump housing in the rotor region
is not moving, similar to the previous simulation.

49



6. Optimization Study

Figure 6.18: absence of shaft simulation domain

Figure 6.19: absence of shaft simulation domain (perspective view)

6.8 Shaft Removal Results

The performance of all mass flow rate conditions for both shaft-existing and shaft
removal conditions are shown in this section. As shown in fig. 6.20, the system
efficiency for the shaft removal condition is a little bit higher than the shaft-existing
condition for most cases except the mass flow rate of 641.3 kg/s. Looking at ef-
ficiency, there is no large difference. However, the trust summation for the shaft
removal condition is significantly higher than the shaft-existing condition for most
cases. Although the thrust is higher, the torque is also higher, as shown in fig 6.21.
This is the reason why the efficiency does not change much in the end.

50



6. Optimization Study

Figure 6.20: Efficiency vs mass flow rate between shaft-existing and shaft removal

(a) Thrust summation vs mass flow rate (b) Torque vs mass flow rate

Figure 6.21: Torque and Thrust vs mass flow rate between shaft-existing and shaft
removal

To support the results, the head plot between the shaft-existing and shaft removal
conditions for the mass flow rate of 801.6 kg/s along the longitudinal position is
shown in fig. 6.22. The intake end cross section, which is attached to the rotor
region, is located at x = 0 m. The intake has the length about 1.4 m, so the capture
area cross section is located at x = 1.7 m. According to the plot, the head generated
by the impeller for the shaft removal condition is higher than the shaft-existing
condition. It results in a higher thrust summation as mentioned before.

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6. Optimization Study

Figure 6.22: Head plot vs longitudinal position between shaft existing and without
shaft conditions at 801.6 kg/s

The axial velocity at the pump upstream cross section comparison between the
shaft-existing and shaft removal conditions for the mass flow rate of 761.9 kg/s is
presented in fig. 6.23. The wake fields for both conditions are different because of
the shaft rotation effect. The different wake field can induce different angle of attack
on the blades and results in different thrust.

(a) Shaft existing (b) Without shaft

Figure 6.23: Axial velocity at the pump upstream cross section comparison be-
tween shaft-existing and shaft removal

Vt/Va at the pump upstream cross section comparison between the shaft-existing
and shaft removal conditions for the mass flow rate of 761.9 kg/s is depicted in
fig. 6.24. the inflow to the pump between both conditions is different and results
in different pump performance. Even though the efficiencies are quite similar, the
thrust generated by the shaft removal condition is higher. At this stage, it can
be said that the angle of attack for the shaft removal condition is higher than the
shaft-existing condition.

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6. Optimization Study

(a) Shaft existing (b) Without shaft

Figure 6.24: Vt/Va at the pump upstream cross section comparison between shaft-
existing and shaft removal

The tip leakage phenomenon can be detected easily with a mass flow rate of 641.3
kg/s. Figure 6.25 shows the axial velocity contour. At the top of the section, the
backward flow can be seen with a blue color because of the tip leakage phenomenon.
This phenomenon can degrade the efficiency of the entire system and can be observed
obviously when the pressure difference between the pressure side and the suction side
of the pump is large. It can be seen that the position where the tip leakage occurs
appears at the same position where the pressure on the suction side is extremely
low, while the pressure on the pressure side is quite high, as shown in fig. 6.26.

Figure 6.25: Axial velocity field at the pump upstream cross section for the mass
flow rate of 641.3 kg/s

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6. Optimization Study

(a) Suction side (b) Pressure side

Figure 6.26: Pressure contour plot of the mass flow rate of 641.3 kg/s

Figure 6.27 presents the head plot along the longitudinal position of three different
mass flow rates. It can be seen that the pressure difference for the mass flow rate of
561.1 kg/s is much larger than others. Thus, the tip leakage phenomenon tends to
occur more easily when the waterjet operates in the low mass flow rate range.

Figure 6.27: Head plot vs longitudinal position with different mass flow rate
conditions

6.9 Rim-driven Impeller Set up
As the effect of shaft removal is investigated in the section 6.7, the rim-driven
impeller is introduced in this section. The impeller hub is still in the same position.
However, the rotor is modified a little bit by closing the tip gap between the blade
tip and the pump housing as shown in fig. 6.28. Now, the pump housing has to be
rotated as the pump is rotated by a rim-driven mechanism. Therefore, the pump
housing’s relative motion is removed.

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6. Optimization Study

Figure 6.28: Rim driven pump (no tip gap)

6.10 Rim-driven Impeller Results

Fig. 6.29 presents the efficiency for each mass flow rate comparison between having
a tip gap and no tip gap conditions. The system efficiency of the studies pump
without a tip gap is significantly lower than having a tip gap. Although the thrust
summation values are quite similar for both conditions, torque values are remarkably
different, as shown in fig. 6.30. It is observed that the pump housing in the rotor
region is the main reason. Because it is rotating in the rim-driven case, higher torque
is needed to rotate this housing apart from the impeller, which results in the larger
delivered shaft power demanded.

Figure 6.29: Efficiency vs mass flow rate between having tip gap and no tip gap

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6. Optimization Study

(a) Thrust summation vs mass flow rate (b) Torque vs mass flow rate

Figure 6.30: Torque and Thrust vs mass flow rate between having tip gap and no
tip gap

The difference between both conditions is the tip clearance, so everything apart
from that is still the same. Thus, the inflow to the pump remains similar as shown
in fig. 6.31 and 6.32. However, the behavior is different when the fluid enters the
pump region. Figure 6.33 shows the Vt/Va field at the stator start cross section
comparison between having a tip gap and no tip gap. This cross section is found
where the flow enters the stator region after passing the impeller. It is evident that
the contour plots are different near the pump housing. Due to the housing rotation,
the tangential velocity component is high there, making the red color zone on the
wall easily visible.

(a) having tip gap (b) no tip gap

Figure 6.31: Axial velocity field at the pump upstream cross section comparison
between having tip gap and no tip gap

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6. Optimization Study

(a) having tip gap (b) no tip gap

Figure 6.32: Vt/Va at the pump upstream cross section comparison between having
tip gap and no tip gap

(a) having tip gap (b) no tip gap

Figure 6.33: Vt/Va at the stator start cross section comparison between having tip
gap and no tip gap

6.11 Intake Optimization Set up
An optimization procedure can be done in CAESES as it has a DAKOTA tool plug-
in, which can perform the optimization investigation based on the response surface
method. Due to the optimization computation requirements, simulations must be
run on a cluster. CAESES is already coupled with STAR CCM+ as mentioned in
section 4.5, so the only thing left here is to find a way to execute CAESES in batch
mode, so the geometry variation is taken into account and the optimization can be
performed on Linux. Fortunately, it is simple to execute CAESES on Linux because
the only things that need to be written in the script are the geometry variation setup
and the command to run the engine. The script can be found in the appendix.

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6. Optimization Study

6.11.1 Objective definition
Before running the optimization, an objective has to be defined. Normally, the
objective should be the entire system efficiency, which is described in section 6.3.
However, the capture extraction is an obstacle here because there is no automated
way to perform it yet. It has to be done manually as mentioned in section 4.4.
Thus, the entire system efficiency cannot be used. The new objective is introduced,
which is the thrust-over-torque parameter. the idea is that thrust, which is created
by all components in the system including impeller, stator, casing, and intake can
represent the power output when times with the ship speed. The thrust summation
can be computed following eq. (6.7), while the thrust -over-torque parameter can
be determined following eq. (6.8). To prove this hypothesis, the trends between
the entire system efficiency and the thrust-over-torque parameter are plotted in the
intake connection study as mentioned in section 6.6, when the intake connection
length is varied and the mass flow is constant. The trends are pretty similar, so
this parameter can be used as an indicator. later on, after obtaining the best intake
shape, the entire system efficiency will be taken into account for a real comparison
with the original one.

Tsum = Timpeller + Tstator + Tintake + Tcasing (6.7)

T/τ = TsumVs

τω
(6.8)

6.11.2 Intake height
After obtaining the basic idea and knowledge of the waterjets’ entire system from
many investigations, intake optimization can now be carried out. The most signif-
icant parameter, which affects the entire performance, is the intake height. The
lower intake height is expected to give better efficiency than the higher one because
of two main reasons. Firstly, the inflow to the pump should be better, including
more uniform and perpendicular, as there is less vertical momentum needed. Sec-
ondly, the duct loss should be lower because less energy is demanded to lift the flow
upward. Normally, the installation of waterjet propulsion units and their intake
design is constrained by the size of the engine and the gearbox. However, the intake
height can be varied and not be constrained as the possibility of an electric waterjet
is introduced in this project. During the investigation, the intake height varies from
0.21 m to 0.29 m. A smaller intake height than 0.21 m cannot be produced due to
CAD design restrictions.

(a) Height = 0.21 m (b) Height = 0.25 m (c) Height = 0.29 m

Figure 6.34: Intake height variation

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6. Optimization Study

6.11.3 Cross section

Many parameters can be changed as inputs in this intake model such as the slope
angle (α), ramp radius (R2), beam factor (fb), weight bottom (wb) and weight top
(wt). The intake cross section variation is performed for this project because many
studies had already optimized profile intake features such as Weixuan Jiao et al.
(2019) and Huang et al. (2019). However, how the cross section variation influences
the system efficiency has not been studied in detail yet. After obtaining the best
intake height, the cross section optimization can be investigated. Three parameters
are selected to run the cross section optimization study, including start tangential
angle (θt), weight top (wt), and area adjust factor (farea). Section 4.1.2 defines the
meaning of all these parameters. As shown below, fig. 6.35, fig. 6.36, and fig. 6.37
depict how each parameter will affect the shape of the intake.

(a) θt = 0◦ (b) θt = 45◦ (c) θt = 90◦

Figure 6.35: Effect of start tangential angle (θt), while wt = 3 and farea = 1

(a) wt = 1 (b) wt = 3 (c) wt = 5

Figure 6.36: Effect of weight top (wt), while θt = 45◦ and farea = 1

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6. Optimization Study

(a) farea = 0.8 (b) farea = 1 (c) farea = 1.2

Figure 6.37: Effect of area adjust factor (farea), while θt = 45◦ and wt = 3

6.12 Intake Optimization Results
In this section, the optimization results are shown starting from the intake height
optimization. After the best intake height is chosen, the cross section optimization
is performed. Finally, the effect of shaft removal on the pump efficiency is studied
in the best design.

6.12.1 Intake height
As expected, the lowest intake height gives the best efficiency in terms of thrust-
over-torque. The trend is obvious as shown in fig. 6.38. The efficiency for the height
of 0.21 m is higher than the height of 0.29 m by approximately 5%, which is quite
significant. Thus, the intake height of 0.21 m is selected for study in cross section
optimization.

Figure 6.38: Thrust-over-Torque vs intake height

Surface uniformity and perpendicularity are proper indicators to assess the pump
efficiency as they give a trend that is similar to the efficiency trend as shown in fig.
6.39. the lowest intake height has the best surface uniformity and perpendicularity

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6. Optimization Study

values. The lower the intake height, the vertical movement of the flow is reduced
and resulting in a better inflow to the pump. Moreover, the shaft wake disturbs
the flow to the pump less when the intake flow has a smaller non-axial component
(more aligned with the shaft).

(a) Surface Uniformity vs intake height (b) Perpendicularity vs intake height

Figure 6.39: Surface Uniformity and Perpendicularity vs intake height

Figure 6.40 represents the thrust and torque comparison for each intake height. The
lowest intake height has the lowest torque value and also has the highest thrust
summation value. This is the reason why the efficiency of the lowest intake height
of 0.21 m differs a lot from the largest intake height of 0.29 m.

(a) Torque vs intake height (b) Thrust Summation vs intake height

Figure 6.40: Thrust and Torque vs intake height

The inflow to the pump is more uniform when the intake height is lower. This is
frankly shown in fig. 6.41. The axial velocity field at the bottom of the section is
very high for the height of 0.29 m compared to the height of 0.21 m. In addition,
the axial velocity field at the top of the section is drastically low for the height of
0.29 m compared to the height of 0.21 m. It can be said that the inflow to the pump

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6. Optimization Study

at a height of 0.21 m is more uniform compared to the heights of 0.25 m and 0.29
m.

(a) height = 0.21 m (b) height = 0.25 m (c) height = 0.29 m

Figure 6.41: axial velocity vs intake height

Figure 6.42 presents the ratio of the tangential velocity to the axial velocity (Vt/Va).
The higher intake height the tangential velocity component and Vt/Va are higher
and will affect the inflow to the pump. The tangential velocity can happen due to
the shaft rotation and the vertical momentum that the flow needs to move upward
following the intake shape. In addition, when the axial velocity component is lower,
it is easier to get disturbed by the shaft rotation effect.

(a) height = 0.21 m (b) height = 0.25 m (c) height = 0.29 m

Figure 6.42: Vt/Va vs intake height

6.12.