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Numerical study on self-propulsion of a waterjet propelled trimaran
Ocean Engineering 195 (2020) 106655
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Numerical study on self-propulsion of a waterjet propelled trimaran Jun Guo a, c, Zuogang Chen a, b, c, *, Yuanxing Dai d, ** a
State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai Jiao Tong University, Shanghai, 200240, China c School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200040, China d Science and Technology on Water Jet Propulsion Laboratory, Marine Design & Research Institute of China, Shanghai, 200011, China b
A R T I C L E I N F O
A B S T R A C T
Keywords: Self-propulsion Numerical simulation Waterjet Trimaran
The hydrodynamics of the waterjet propelled ships represents a challenging problem due to the complexity of the waterjet system itself and the waterjet/hull interaction. In this paper, the self-propulsion computations of a trimaran were performed by solving the unsteady RANS equations. The waterjet was simulated directly with multi-reference frame model to improve the precision of the numerical simulations. Mesh independence studies of the hull and waterjet were carried out individually. Numerical simulations with/without the waterjet were performed in a speed range of 0.196 < Fr < 0.707. Comparisons between numerical predictions and experimental data showed the numerical method could accurately predict the self-propulsion performance. A numerical tool was developed to obtain the capture area based on tracking the streamlines upstream, which was practical and greatly simplified the post-processing. According to the ITTC procedures and guidelines, the overall efficiency and its components were analyzed in detail. The results showed that the resistance increment was always positive while the waterjet thrust deduction fraction was negative. The overall efficiency of the waterjet was mainly affected by the ideal jet efficiency and the pump efficiency. The analysis of the waterjet powering characteristics can better understand the energy conversion and the interaction between the ship hull and waterjet.
1. Introduction In recent years, the development of high-speed ships has attracted the attention of the shipbuilding industry and navies from all countries. Compared with propellers driven ships, waterjets driven ships exhibit high efficiency, good maneuverability, and good anti-cavitation per formance. Many high-speed ships choose waterjet propulsion as their driving force. Accurate prediction of propulsive performance of the waterjet sys tem has always been a concern of researchers. With the rapid develop ment of computational fluid dynamics (CFD) methods in the ship field, CFD technology has been widely used and has made considerable progress. Van Terwisga (1996) analyzed the interaction effects in the powering characteristics of waterjet propelled vessels. An empirical prediction model was recommended for preliminary power-speed computations. Bulten (2006) carried out a numerical study of the water jet system and analyzed the effects of the steady multi-reference frame (MRF) model and the transient moving mesh model on the per formance of the water system. The results showed that the head, torque,
and efficiency for the transient flow calculations were slightly higher. Numerical simulation of waterjet self-propulsion has also been car ried out by many researchers. Kandasamy et al. (2010) derived an in tegral force/moment waterjet model for ship local flow/powering predictions. An alternative control volume was used to balance the force and moment. The predicted resistance error was less than 5%, the average sinkage error was 9.0%, and the average trim error was 13.7%. Takai et al. (2011) analyzed the flow fields for a high-speed sea lift hull by applying a body force to model the pump effect. Moreover, the duct shape was optimized. The results showed that the pressure loss could be reduced by optimizing the upper curve and lip shape of the channel, and the inlet efficiency could be improved by optimizing the intake. Peri et al. (2012) optimized the high-speed waterjet catamaran, aiming at reducing the resistance and inlet loss of the waterjet. The total resistance was reduced by 6% after the optimization. During the optimization process, the low fidelity model was used to reduce the costs of the computation. Eslamdoost et al. (2014) proposed a pressure jump method to study the interaction between the waterjet and hull. The reason for the negative thrust reduction of the waterjet was analyzed. It was found that the resistance increment was not the main cause, but the
* Corresponding author. State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China. ** Corresponding author. Science and Technology on Water Jet Propulsion Laboratory, Marine Design & Research Institute of China, Shanghai, 200011, China. E-mail addresses: [email protected] (Z. Chen), [email protected] (Y. Dai). https://doi.org/10.1016/j.oceaneng.2019.106655 Received 12 April 2019; Received in revised form 19 September 2019; Accepted 27 October 2019 Available online 25 January 2020 0029-8018/© 2019 Elsevier Ltd. All rights reserved.
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Nomenclature Tgross Tnet IVR NVR A1 A6 t tr tj Rbh FD S U Cf Re PD PE PTE PJSE PPE H35 Qshaft QJ KQJ
n
Rotational speed Overall efficiency Free steam efficiency Interaction efficiency Ideal jet efficiency Momentum interaction Energy interaction Ducting efficiency Pump efficiency Duct Length Duct Diameter Pump Diameter Length between perpendiculars Ship width Ship height Displacement Froude number Non-dimensional wall distance Third root of the total mesh number Total resistance Resistance coefficient Sinkage Trim angle Thrust coefficient Torque coefficient Pressure coefficient
ηD η0 ηINT ηI ηmI ηeI ηduct ηP
Gross thrust Net thrust Intake velocity ratio Nozzle velocity ratio Area of capture area Area of nozzle section Total thrust deduction Resistance increment fraction Waterjet thrust deduction fraction Bare hull resistance External tow force Wetted surface Hull velocity Frictional resistance coefficient Reynolds number Delivered mechanical power Effective power Effective thrust power Effective jet system power Effective pump power Pump head Shaft torque Flow rate Flow rate coefficient
Lduct Dduct Dpump Lpp B D Δ Fr yþ hi Rt Ct
σ θ KT KQ Cp
Z pump 6
3
.
5
A’
C D 4
X A
1 B 1A
2
0
0 Free Stream 1A Capture Area 1 Inlet point of tangency 2 Intake throat 6 Nozzle 7 Vena Contracta Fig. 1. Control volume of waterjet.
non-atmospheric pressure on the nozzle exit caused the negative thrust deduction. Gong et al. (2017) carried out a numerical simulation of a waterjet self-propelled ship. The virtual disk and overset models were applied to compare the flow fields. The results revealed that the hull flow fields from the two models were basically the same, but the internal flow field calculated by the overset model was more applicable to the actual state of the impeller. YI et al. (2017) analyzed the hydrodynamic characteristics of submerged waterjet propulsion by combining experi mental and numerical simulation methods, and the experimental values were in good agreement with the CFD predictions. The predicted resis tance, thrust, and torque errors were 3.7%, 4.7%, and 4.6%, respectively. At present, most waterjet self-propulsion studies was based on the virtual disk model (Miller et al., 2006) or body force model (Rhee and Coleman, 2009) to simulate the pump effect. This method can reduce the calculation cost, but the thrust and torque coefficients are obtained in open water, and the influence of the hull boundary layer and the non-uniform flow distribution of the intake (Young et al., 2011) are not considered. Because the error of momentum flux is the square of the error of the flow rate, a 1.5%–2% error of the flow rate can cause a 2%– 4% error of the momentum flux, so the accuracy of the momentum flux depends on the accuracy of the flow rate. In this study, a waterjet was
simulated directly using the steady MRF model, which is more accurate than the virtual disk and body force models. The overset mesh method was used to cope with the large hull attitude at high speeds. The steady multi-reference frame model was employed for the rotation of the im pellers, and the thrust was determined by integrating the forces acting on the waterjet. The self-propulsion point was obtained by modifying the rotational speeds of the impellers until the horizontal force was balanced. Numerical simulation and analysis of the self-propulsion of a waterjet-propelled trimaran were carried out. First, the resistance of the bare hull with a free surface was calculated numerically, and the results were compared with the model test results to verify the accuracy. A self-propulsion simulation was subsequently performed. The powering characteristics of the waterjet were calculated and analyzed. The hy drodynamic characteristics of the waterjet and hull were obtained by this numerical study. 2. Basic theory In the waterjet experiments, there are two different methods for predicting the thrust of the waterjet: the momentum flux method and the direct thrust measurement method. At the 24th International Towing Tank Conference (ITTC, 2005), it was concluded that the direct thrust 2
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and merge lines of hull and duct. Surface 5 is a section in the intake throat. Surface 6 is the nozzle section at the station 6. Applying Newton’s second law to the control volume, the conser vation law of momentum follows the following equation in the i direction: ZZ ZZZ ZZZ ZZ ρui ðuk nk ÞdA ¼ σ ij nj dA þ ρFpi dV þ ρFi dV; (1)
D 0
PD
P
PPE
pump system
duct
ducting system
INT I
PJSE
eI
mI
jet system
PTE
1-t bare hull system
PE
Fig. 2. Energy conversion between subsystems.
A1 þA6
main body of trimaran
side body of trimaran
waterjet
5.235 0.41 0.4 0.116
2.0 0.112 0.262 0.006
Lduct (m) Dduct (m) Dpump (m)
V3
5
V1
6
where σ ij is the tensor, Fpi is the pump force and Fi is the external force (gravity force). The terms on the left- and right-hand-side represent the change in momentum flux and the forces acting on the control volume in the i direction, respectively. On the right-hand-side, the first term rep resents the pressure and tangential stress force, the second term repre sents the pump force acting on fluid, and the third term represents the gravity force acting on control volume. The gross thrust is the definition of the term on the left side of Equation (1). The horizontal component of the gross thrust in the x di rection is abbreviated as Tgross and defined as follows: ZZ (2) Tgross ¼ ρux ðuk nk ÞdA:
Table 1 Principal dimension of the hull and waterjet. Lpp (m) B (m) D (m) 3 ▽ (m )
A1 þA2 þA3 þA6
0.567 0.086 0.118
A1 þA6
The intake velocity ratio (IVR) is defined as the ratio of the average velocity on the capture area U1 to the hull velocity U, and the nozzle velocity ratio (NVR) is defined as the average velocity on the nozzle section U6 to the hull velocity U, defined as follows:
Fig. 3. Hull and waterjet geometry.
U1 U6 ; NVR ¼ : U U
(3)
measurement method was expensive and cumbersome by the Waterjet Specialist Committee. Since the momentum flux method can select any suitable pump that meets the flow requirement, and there is not complicated watertight sealing between the hull and waterjet system, the momentum flux method has become the main method used by re searchers in experiments and numerical calculations. Recommended procedures and guidelines for propulsive performance predictions (ITTC, 2005) and uncertainty analysis (ITTC, 2017) based on the mo mentum flow method were finally proposed based on the continuous improvements by the waterjet specialist committee.
IVR ¼
2.1. Momentum flux theory
The net thrust is defined as the force vector acting upon the duct boundary, the pump housing, and the shaft, which directly pass the force through to the hull. The horizontal component of the net thrust in x direction is abbreviated as Tnet and defined as follows: ZZ ZZZ Tnet ¼ σx dA ρFpx dV: (6)
The gross thrust can also be defined as follows: ZZ Tgross ¼ ρux ðuk nk ÞdA ¼ ρQJ UðNVR ⋅ cos θ IVRÞ;
where θ is the trim angle of the hull, QJ is the flow rate and the flow rate coefficient was defined as follows: KQJ ¼
Based on the recommended procedures and guidelines for propulsive performance predictions (ITTC, 2005), a control volume is shown in Fig. 1, which was applied to analyze the performance of the waterjet system using the momentum flux method. Numbers with circles denote the station numbers. Surface 1 is the imaginary capture area and is positioned one impeller diameter in front of the ramp tangency point A’. Surface 2 is the imaginary streamtube, which separates the control volume from the flow field. Surface 3 is the physical boundary of the waterjet system. Surface 4 is the surface between the stagnation lines
Lpp
2Lpp
4Lpp
QJ : nD3pump
A3 þA4
(5)
V3
5
It is difficult to measure the net thrust in experiments, and thus, the gross thrust is used to define the thrust deduction, which is different from the definition in the conventional hull/propeller theory. The total
10Lpp
Lpp Hull:No-slip Wall
4Lpp Wave Damping Length
Overset Region
Velocity Inlet
(4)
A1 þA6
Pressure Outlet
Symmetry Bachground Region
5
Fig. 4. Computational domain and boundary conditions. 3
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Fig. 5. Mesh of the computational domain and on the hull.
Table 2 Basic sizes of five sets of meshes for calculating the bare hull resistance. Mesh Number
Basic Size
Total Number of Mesh
Average yþ on the hull
1 2 3 4 5
0.05 m 0.06 m 0.08 m 0.12 m 0.16 m
4.93 million 3.23 million 1.69 million 0.74 million 0.44 million
35 43 57 86 114
7.0
EFD CFD
6.5 Ct × 103
6.0
5.0
5.5 5.0
Fitted curve
4.5
4.9
4.0
0.3
0.4
Ct
0.2
Fr
0.5
0.6
0.7
Fig. 8. Computed and measured resistance.
4.8 1 FD ¼ ρSU 2 Cfm 2
4.7 0.0
0.5
1.0
1.5 hi/h1
2.0
2.5
� Cfs ;
(8)
where t is the thrust deduction, Rbh is bare hull resistance, FD is the external tow force, S is the wet area of the hull at rest, U is the hull velocity at model scale, and Cfm and Cfs are the model and ship frictional resistance coefficients, respectively, which can be calculated from the 1957 ITTC formula
3.0
Fig. 6. Convergence of the total resistance coefficient.
Cf ¼
0:075 ðlgRe
2Þ2
(9)
;
where Re is the Reynolds number. The resistance increment fraction and the waterjet thrust deduction fraction are defined as follows: Fig. 7. yþ values on the hull at Fr ¼ 0.628.
thrust deduction is defined as the ratio of the difference between the bare hull resistance and the external tow force to the gross thrust, and the external tow force accounts for the difference of the frictional resistance coefficient between the model and full scale, 1
t¼
Rbh FD ; Tgross
Rbh FD ; 1 Tnet
Tnet : Tgross
1
tr ¼
1
Combining Equations (7) and (10) yields the following: � t ¼ ð1 tr Þ 1 tj :
tj ¼
(10)
(11)
2.2. Description of powering characteristics
(7)
Based on the ITTC regulations (ITTC, 2005), the overall efficiency of the waterjet-hull system ηD can be divided into the free steam efficiency 4
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0
The overall efficiency of the waterjet-hull system is given by
EFD CFD
ηD ¼
/ Lpp ×103
-1
PE PE PTE PTE0 PJSE0 PJSE PPE ¼ ; PD PTE PTE0 PJSE0 PJSE PPE PD
(14)
where PE is the effective power, PD is the delivered mechanical power, PTE is the effective thrust power, PJSE is the effective jet system power, PPE is the effective pump power, and the other terms with subscript 0 are corresponding powers in the free steam condition. The subsystem efficiencies are given as follows: Thrust deduction:
-2 -3
tÞ ¼
ð1
PE Rbh FD ¼ : PTE Tgross
(15)
Momentum interaction:
-4
0.2
0.3
0.4
Fr
0.5
0.6
1
0.7
ηmI
¼
ηI ¼
1.0
(deg)
PTE0 Tgross0 U0 Tgross0 U0 2 : ¼ ¼ ¼ NVR þ 1 PJSE0 QJ HJSE0 E6 E0
(17)
The total axial energy flux Es through a cross-sectional area As at station s is defined as follows: � Z � 1 P Es ¼ ρ u2i þ þ gzs ðui ni ÞdA: (18) 2 ρ
EFD CFD
1.2
(16)
Ideal jet efficiency:
Fig. 9. Computed and measured sinkage.
1.4
PTE Tgross 1 IVR : ¼ ¼1þ NVR 1 PTE0 Tgross0
As
Energy interaction:
0.8 0.6
ηeI ¼
PJSE0 E6 ¼ PJSE E6
E0 : E1
(19)
Ducting efficiency:
0.4 0.2 0.0
0.2
0.3
0.4
Fr
0.5
0.6
Table 3 Basic sizes of five meshes for calculating the pump performance.
0.7
Fig. 10. Computed and measured trim.
η0 in ideal conditions, where the intake velocity of the waterjet is uni
form U and the pressure at the nozzle center is atmospheric pressure P0, and the interaction efficiency ηINT, which accounts for the effect of the waterjet-hull interaction:
Mesh Number
Basic Size
Total Number of Mesh
Average yþ on the blades
1 2 3 4 5
0.004 m 0.006 m 0.008 m 0.010 m 0.0125 m
7.15 million 4.23 million 2.90 million 2.18 million 1.64 million
38 54 67 76 89
(12)
ηD ¼ η0 ηINT :
The waterjet-hull system is divided into subsystems, and the sche matic diagram of energy conversion between subsystems and the sub system efficiencies are shown in Fig. 2. The free steam efficiency and the interaction efficiency are defined as follows:
η0 ¼ ηI ηduct ηpump ; ηINT ¼ ð1
tÞ
ηeI : ηmI
(13)
Fig. 12. Mesh on the blades and housing.
5 4Dduct
No-slip Wall
Pressure Outlet
Velocity Inlet Rotating Region
No-slip Wall
Fig. 11. Computational domain and boundary conditions of a pump. 5
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1.28
ηduct ¼
Fitted curve
(20)
Pump efficiency:
1.26
ηP ¼
1.24
KT
PJSE E6 E0 ¼ : PPE ρgQJ H35
PPE ρgQJ H35 ¼ : PD 2π nQshaft
(21)
3. Hull and waterjet geometry The hull used in this study was a trimaran, and its main and side bodies were aligned at the stern. The hull and waterjet geometries were at the model scale. Two waterjet systems were installed on the main body. The numbers of impeller blades and guide vanes of the waterjet system were 6 and 11, respectively. Principal dimensions of the hull and waterjet are shown in Table 1. The hull and waterjet model are shown in Fig. 3.
1.22 1.20 1.18
4. Computations of bare hull resistance 4.1. Numerical methods
1.16 0.0
0.5
1.0 h1/hi
1.5
The numerical simulations were conducted using the finite volume method (FVM) commercial software STAR-CCMþ. The SST k-ω turbu lence model was applied to solve governing equations. The dimension less distance from the center of the first grid to the wall is defined as yþ. All yþ wall treatments (CD-adapco S. C., 2015) were selected, the viscous sub-layer was resolved if yþ<1, a wall function was used if yþ>30, and a blending function was used to resolve the buffer region 1 < yþ<30. The volume of fluid (VOF) method (Hirt and Nichols, 1981) was used to capture the free surface. The convective and temporal dis cretization schemes were second-order upwind schemes. The implicit unsteady solver based on the separated flow model was used. The physical time step was 0.02 s, and there were 10 iterations in each time step. A dynamic fluid body interaction (DFBI) rotation and translation motion (Ohmori, 1998) was applied to simulate the 6-DOF motion of hull, and the sinkage and trim were free. The numerical computational boundary conditions are shown in Fig. 4. Considering the symmetry of the geometry and flow, only half of the hull was modeled. The computational domain was split into two different regions: a background region and an overset region. The background region was stationary, and the overset region was moving with the hull. An overset mesh was built between the background region and the overset region. The length, width, and height of the computation domain were 13LPP, 5LPP, and 4LPP, respectively. The inlet was situated 2LPP in front of the stem, and the outlet was located 10LPP behind the
2.0
Fig. 13. Convergence of the thrust coefficient.
1.26
Fitted curve
10KQ
1.24
1.22
1.20 0.0
0.5
1.0 hi/h1
1.5
2.0
Fig. 14. Convergence of the torque coefficient.
Fig. 16. yþ values on the duct and blades of waterjet.
Fig. 15. Mesh distribution near the intake and inside the duct. 6
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Fig. 17. Streamlines tracked upstream and boundary layer at station 1A
Capture Area E:\waterjet
file :
dead rise angle(°)
20
reference Y (m)
0.12
reference Z (m)
-0.15
extension coefficient of Ymin
0.04
extension coefficient of Ymax 0.04 scaling factor
-0.05
-0.10 Z -0.15
1.01
Run
-0.20 0.2
0.15
0.1 Y
0.05
Fig. 18. Program for obtaining the capture area.
stern to completely develop the wake field. In front of the outlet, the VOF wave damping length was set 4LPP to avoid the reflection of waves. The boundary conditions were set as follows. The velocity inlet boundary condition was applied to the inlet, side, top, and bottom of the domain. A pressure outlet boundary condition was applied to the outlet. A symmetry boundary condition was set at the center plane of the hull. A no-slip wall boundary condition was used for the hull surface.
meshes with a growth ratio of 1.2 were generated in the boundary layer. Four levels of blocks were used to refine the mesh around the hull. Three levels of blocks were used to refine the mesh around the free surface. Three cones like Kelvin waves were used to capture the free surfaces better. The mesh of the computational domain is shown in Fig. 5. A mesh independence study was carried out at Fr ¼ 0.628, which is the design speed. By varying the basic size of the mesh parameters, five sets of meshes were generated. The basic sizes and the total numbers of the five sets of meshes are shown in Table 2. The total resistance coefficient, Ct, is defined as follows:
4.2. Mesh independence study of the bare hull Computations of the bare hull resistance in calm water were carried out to obtain a complete prediction of the self-propulsion. An unstruc tured trimmed mesh was generated in this study. Six layers of prism
Ct ¼
7
Rt ; 0:5ρSU 2
(22)
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uncertainty for these meshes was 2.65%. Fig. 7 shows the yþ values on the hull at Fr ¼ 0.628.
(yref,zref)
4.3. Results of bare hull resistance
convex set
dead rise angle
Rotation
The calm water resistance tests were carried out in Norwegian Ma rine Technology Research Institute (MARINTEK). The hull model was towed by the carriage and equipped with a trip-wire at the bow and stern. The bare hull resistance was calculated in a speed range of 0.196 < Fr < 0.707, and the hull was free to sink and trim. Fig. 8 shows the computed and measured bare hull resistance results. Figs. 9 and 10 show the sinkage and trim results, respectively. Both the resistance and sinkage were under-predicted compared to the experimental results, while the trim results were over-predicted. The minimum resistance, sinkage, and trim errors were 1.95%, 9.77%, and
boundary points Fitting
Rotation
extend
extend hull
Fig. 19. Steps for obtaining the capture area.
where Rt is the total resistance and S is the wet area of the hull at rest. According to the least squares root method proposed by Eça and Hoekstra (2014), a mesh independence study method for the non-uniform refinement ratio, the numerical uncertainty of the bare hull was determined. The non-uniform refinement ratio is defined as follows: p ffiffiffiffiffi 3 N1 hi ffiffiffiffi ; ¼p (23) 3 h1 Ni where Ni and hi are the total number of meshes and the typical mesh size for mesh number i, N1 and h1 correspond to the finest mesh. The convergence curve of Ct is shown in Fig. 6. Considering the computational accuracy and cost, mesh number 3 was selected for the computations. The numbers of mesh in background region and in the overset region were about 0.74 and 0.95 million. The numerical
Fig. 21. Free surface and the jet flow at Fr ¼ 0.628.
Fr=0.314
Fr=0.471
Fr=0.628
Fig. 20. Wave patterns of the self-propulsion. 8
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7.5 7.0
Ct × 103
reliable for further calculations of the self-propulsion.
EFD CFD
5. Computations of self-propulsion
6.5
5.1. Mesh independence study of the waterjet system
6.0
Because the pump is an important part of the waterjet system, to obtain an appropriate mesh size for the waterjet system, a mesh inde pendence study was carried out for the pump based on the least squares root method (Eça and Hoekstra, 2014). The numerical domain and boundary conditions of the waterjet pump are shown in Fig. 11. The domain was split into two different regions: a stationary region and a rotating region, in which the MRF model was set to simulate the rotation of the impellers. The inlet was situated 5Dduct in front of the pump, and the velocity was set to the design flow rate with a uniform velocity distribution. Atmospheric pressure was applied to the outlet boundary. No-slip wall boundary conditions were applied to the other boundaries. In the MRF model, the rotational speeds of the impellers were set to the design rotational speed. An unstructured trimmed mesh was generated for the pump. Feature curves of impellers and guide vanes were generated to refine the mesh around the curves. Five sets of meshes were generated, similar to the mesh independence study of the hull. Five sets of meshes are shown in Table 3. The mesh on the impellers, guide vanes, and housing of mesh number 3 are shown in Fig. 12. The thrust coefficient KT and the torque coefficient KQ were defined as follows:
5.5 5.0 4.5 4.0 0.2
0.3
0.4
0.5 Fr
0.6
0.7
0.8
Fig. 22. Computed and measured resistance.
0
EFD CFD
/ Lpp ×103
-1 -2
KT ¼
0.3
0.4
0.5 Fr
0.6
0.7
0.8
Fig. 23. Computed and measured sinkage.
4.59%, respectively. The average resistance, sinkage, and trim errors were 4.44%, 13.43%, and 7.34% at a high speed range of Fr > 0.4. In general, the calculated results of the bare hull were in good agreement with the experimental results. Thus, the accuracy of the numerical method was verified, and the numerical method is applicable and
1.4
EFD CFD
1.2 1.0
(deg)
; KQ ¼
Qshaft
ρn2 D5pump
;
(24)
where Tblade is the thrust of all the blades of the pump and Qshaft is the shaft torque. The convergence curves of KT and KQ are shown in Figs. 13 and 14. The results show that with the increase of mesh density level, KT converges to 1.182 gradually and KQ converges to 1.214 gradually. The torques of mesh number 1–4 are all close to its convergence value. Considering the accuracies of KT and KQ and the computational cost, mesh number 3 was selected for further calculations. The number of meshes in the rotating region was about 1.08 million, and the number of meshes in the remaining region was about 1.82 million. The numerical uncertainties of KT and KQ for this mesh were 1.06% and 2.18%, respectively. The mesh for calculating the self-propulsion was based on the mesh independence study of the bare hull and the pump. Since the flow fields around the waterjet intake, in the waterjet duct, and out of the nozzle were important, the meshes in these regions were refined. The total number of meshes for the simulation of the self-propulsion flow was 4.86 million, and the numbers of meshes in the background, overset, and rotating regions were about 0.68, 2.74, and 1.45 million, respectively. Fig. 15 shows the mesh around the waterjet duct. Fig. 16 shows the yþ values on the duct and blades of the waterjet.
-3 -4 0.2
Tblade
ρn2 D4pump
0.8
5.2. Numerical methods
0.6
The numerical method for simulating the self-propulsion was similar to the method for simulating the bare hull. The difference is that the rotating reference frame in the MRF model was the local hull-fixed co ordinate system, which was moving with the DFBI motion. The selfpropulsion point was obtained by modifying the rotational speeds of impellers until the total resistance was equal to the sum of the net thrust and the tow force. It is generally considered that the thrust is propor tional to the rotational speed in a small range of rotational speeds. After convergence the rotational speed was n1, and the corresponding hori zontal force was Fx1; then n1 was adjusted to n2 in a small range and after convergence the corresponding horizontal force was Fx2; n3 could be
0.4 0.2 0.0 0.2
0.3
0.4
0.5 Fr
0.6
0.7
0.8
Fig. 24. Computed and measured trim. 9
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Fr=0.471
self-propulsion
bare hull
self-propulsion
bare hull
Fr=0.628
self-propulsion
bare hull
Fig. 25. Comparison of wave pattern of the bare hull and self-propulsion.
Fr=0.314
Fr=0.393
Fr=0.471
Fr=0.55
Fr=0.628
Fr=0.707
Fig. 26. Velocity distribution on the capture area.
obtained according to n1, n2, Fx1 and Fx2 by a linear interpolation method. By changing the rotational speed three times, the horizontal force could be balanced. There are two methods to obtain the capture area. One method is
based on solving a scalar equation and was used by Bulten (2006), Ding and Wang (2010), and Eslamdoost et al. (2014). The other method is based on tracking streamlines upstream and was used by Delaney et al. (2009). In this study, the latter method was applied. Streamlines were 10
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0.5%–1% enlargement of the capture area is needed. Fig. 19 shows the steps for obtaining the capture area: the section data of the streamlines (blue dots) is rotated by the dead rise angle of the hull to reduce gradient and improve the fitting accuracy; the section data can be regarded as a convex set, and the boundary points of the convex set are calculated; the boundary points is fitted by a quadratic polynomial, and the fitting curve is extended at the ends; the fitting curve is rotated by the dead rise angle in reverse to restore its position. The accuracy of the program was mainly affected by the number of streamlines and was tested by changing the number of streamlines with 500, 1000, 2000, 4000 and 8000. The results showed that when the number of streamlines was greater than 1000, the shape of the capture area was no longer changed. The shape of the capture area could be easily and accurately obtained by the program with 1000 streamlines, and the time cost of post-processing
2.4 2.3
A1/A6
2.2 2.1 2.0 1.9 1.8 0.2
0.3
0.4
0.5 Fr
0.6
0.7
0.8
2.4
IVR EFD IVR CFD NVR EFD NVR CFD
2.0
Fig. 27. Variation of the capture area.
1.6 IVR NVR
tracked upstream from station 3, and the shapes of the capture area were fitted by a quadratic polynomial with the streamline data at Station 1A. Fig. 17 shows streamlines tracked upstream and the boundary layer at station 1A for Fr ¼ 0.628. A program was developed using the MATLAB language to simplify the post-processing. Fig. 18 shows the numerical tool for obtaining the capture area. The blue dots are the data to be processed and the red line is the fitting curve. The program is controlled by six parameters: the first parameter is the dead rise angle of the hull at Station 1A; the second and third parameters are center coordinates of the capture area; the fourth and fifth parameters are the extension coefficients used to ensure that the fitting curve exceeds the range of the streamlines; and the sixth parameter is the scaling factor, because the flow rate of the capture area calculated directly is slightly lower than the flow rate at station 3, a
1.2 0.8 0.4 0.0 0.2
0.3
0.4
0.5 Fr
0.6
0.7
Fig. 29. Calculated and measured IVR and NVR.
Fr=0.314
Fr=0.393
Fr=0.471
Fr=0.55
Fr=0.628
Fr=0.707
Fig. 28. Velocity distribution on the nozzle section. 11
0.8
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0.40
1.3
EFD CFD
KQJ
0.35 0
0.30
0
1.2
I
1.1
duct
1.0
pump
0.9 0.8 0.7 0.6
0.25
0.5
0.20 0.2
0.3
0.4
0.5 Fr
0.6
0.7
0.4 0.2
0.8
0.3
0.4
0.5 Fr
0.6
0.7
0.8
Fig. 33. Free stream efficiency and its component.
Fig. 30. Calculated and measured flow rate.
1.3
0.25
INT
1.1
tj
0
1.0 D
0.15
D
1.2
t tr
0.20
`
0.10
0.9
t
0.8 0.7
0.05
0.6
0.00
0.5
-0.05 0.2
0.3
0.4
0.5 Fr
0.6
0.7
0.4 0.2
0.8
0.3
0.4
0.5 Fr
0.6
0.7
0.8
Fig. 34. Overall efficiency and its components.
Fig. 31. Thrust deduction and its components.
was greatly reduced. In this paper, the capture area was obtained when the sinkage and trim were equal to the averages of that in several periods.
1.2
5.3. Results of the self-propulsion
INT
1-t
1.1
Self-propulsion tests were also carried out in MARINTEK based on the recommended procedures and guidelines for propulsive perfor mance predictions, and the trimaran equipped with a twin waterjet propulsion system. The flow rate was measured separately for each waterjet in the self-propulsion tests. Wave patterns of the self-propulsion at Fr ¼ 0.314, 0.471 and 0.628 are shown in Fig. 20.
mI eI
INT
1.0 0.9
5.3.1. Results of the resistance, sinkage, trim, and wave pattern The self-propulsion was calculated in a speed range of 0.275 < Fr < 0.707. The free surface and the jet flow at Fr ¼ 0.628 are shown in Fig. 21. Under the impact of the jet flow, a high and sharp wave peak formed behind the hull. Fig. 22 shows the computed and measured resistance results of the self-propelled hull. The experimental resistance was estimated by the gross thrust measured in the self-propulsion experiments plus the tow force. For without assuming a jet thrust deduction factor, the difference between computed and measured resistance of the self-propulsion was lower than that of the bare hull. Figs. 23 and 24 show the sinkage and
0.8 0.7 0.2
0.3
0.4
0.5 Fr
0.6
0.7
0.8
Fig. 32. Interaction efficiency and its components.
12
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Fr=0.314
Fr=0.471
Fr=0.628
Fig. 35. Pressure distribution on the duct and the blades.
trim results, respectively. The computed sinkage values were lower than the measured values. However, the computed trim values were higher than the measured values. In the high speed range of Fr > 0.4, the average sinkage and trim errors were 13.24%, and 12.04%, respectively. Like the results of the bare hull simulation, the match between the computed resistance, sinkage, and trim and the measured values was very good on the whole. Fig. 25 shows the comparison of the wave pattern around the bare hull and the hull with the waterjet. The wave patterns around the hull were basically the same, but the wave patterns behind the hull were significantly different due to the jet flow. The height of the stern wave peak was larger than that of the bare hull, the width of the stern wave was smaller than that of the bare hull, and a high and sharp wave peak formed, which is also shown in Figs. 20 and 21.
decreased with the increase in the Froude number. Fig. 30 shows the comparison of the calculated and measured flow rate coefficients. The flow rate coefficient increased slowly with the increase in the Froude number. The flow rate was over-estimated, and the average discrepancy was 2.63%. Finer mesh may be needed for the waterjet to predict the flow rate more accurately. As shown in Figs. 29 and 30, the measured IVR and the flow rate coefficient exhibited slight sudden changes at Fr ¼ 0.393, which was a critical speed when the trim angle increased rapidly and transom clearance occurred. 5.3.3. Analysis of powering characteristics To clearly understand the efficiency of energy conversion and the interaction between the ship hull and waterjet, the powering charac teristics were analyzed based on the theory in Section 2.2. The total thrust deduction, t, and its components, tr and tj, are shown in Fig. 31. Because the sinkage and trim of the self-propulsion was higher than that of the bare hull, the resistance increased at self-propulsion. The resistance increment, tr, was always positive, tr decreased with the in crease of speed for Fr < 0.393, and tr varied in a small range from 0.02 to 0.04 for Fr > 0.393. The waterjet thrust deduction fraction, tj, was negative for Fr < 0.668, meaning that Tgross was less than Tnet, and the absolute value of tj decreased with the increase of speed. Because the absolute values of tr were greater than those of tj, the trend of t was similar to that of tr. The interaction efficiency, ηINT, and its components, 1-t, ηmI, and ηeI, are shown in Fig. 32. Although the values of ηeI were about 0.05 greater than those of ηmI, their trends were basically the same, and gradually decreased with the increase of Fr. The trend of ηINT was determined by that of 1-t. The ηINT was greater than 1.0 at Fr > 0.314, indicating that the interaction of the hull and waterjet was beneficial for the rapidity performance. The free stream efficiency, η0, and its components, ηI, ηduct, and ηpump, are shown in Fig. 33. The ideal jet efficiency, ηI, increased monotonically due to the monotonic decrease in NVR with the increase of Fr. The
5.3.2. Analysis of the capture area and nozzle section Fig. 26 shows the shape of the capture area and the velocity distri bution on the capture area at different speeds. As the boundary layer became thinner from the longitudinal section to the side of the hull, the maximum velocity of the capture area was similar to the hull speed. With the increase in the hull speed, the width of the capture area basi cally remained unchanged, while the height gradually decreased, and the area of the capture area decreased monotonously consequently in Fig. 27. The area of the capture area was non-dimensionalized by the ratio of the capture area to the nozzle section area. Fig. 28 shows the velocity distribution on the nozzle section at the station 6. Through the rectification of the guide vanes, the velocity on the nozzle section was still not uniform. The velocity at center of the nozzle section was low. With the increase in the Froude number, the velocity distribution became increasingly more uniform. Fig. 29 shows the calculated and measured IVR and NVR. The match between the calculated and measured values was good. On average, the calculated IVR and NVR were over-estimated by 5.13% and 1.32%, respectively. Overall, the IVR did not change significantly, but the NVR 13
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ducting efficiency, ηduct, and the pump efficiency, ηpump, were nearly constant over the entire Froude number range. The average ηduct was 0.974, meaning that the energy loss caused by the duct was a small quantity at self-propulsion. The loss of the duct was very small when the design of the duct was reasonable. The free stream efficiency increased monotonically with the increase of Fr and was mainly affected by ηI and ηpump. The overall efficiency, ηD, and its components, ηINT and η0, are shown in Fig. 34. The overall efficiency increased with the increase of Fr, and the efficiency varied from 0.46 to 0.6, which were lower than that of the conventional propellers. The overall efficiency was mainly determined by η0, and influenced by ηINT. In the design of the waterjet, determining how to improve the ideal jet and pump efficiencies is important to the overall efficiency.
4. The energy loss caused by the duct was a small quantity over the entire Froude number range. 5. For a waterjet propelled ship, improving the ideal jet efficiency and the pump efficiency were the main methods to improve the overall efficiency. The analysis of the powering characteristics will pave the way for further improvements of the hydrodynamic performance. Acknowledgements This work was supported by the Foundation for Key Laboratory of National Science and Technology of China, Grant number 61422230203. The authors appreciate the second International Work shop on Waterjet Propulsion (IWWP 2017) and the Workshop on Waterjet Propulsion Technology (WORKSHOP 2018) for the academic exchange and discussion.
5.3.4. Pressure distribution of the waterjet Fig. 35 shows the pressure distribution on the duct and the blades of the waterjet. The pressure distribution coefficient is defined with reference to the atmospheric pressure P0 as follows: CP ¼
P P0 : 0:5ρU 2
References Bulten, N.W.H., 2006. Numerical Analysis of a Waterjet Propulsion System. Library Eindhoven University of Technology, Netherlands. Delaney, K., Donnely, M., Elbert, M., Fry, D., 2009. Use of RANS for Waterjet Analysis of a High-Speed Sealift Concept Vessel, 1st International Symposium on Marine Propulsors. Trondheim, Norway. Ding, J., Wang, Y., 2010. Research on flow loss of inlet duct of marine waterjets. Journal of Shanghai Jiaotong University (Science) 15 (2), 158–162. Eça, L., Hoekstra, M., 2014. A procedure for the estimation of the numerical uncertainty of CFD calculations based on grid refinement studies. J. Comput. Phys. 262, 104–130. Eslamdoost, A., 2014. The Hydrodynamics of Waterjet/hull Interaction. Chalmers University of Technology. Eslamdoost, A., Larsson, L., Bensow, R., 2014. A pressure jump method for modeling waterjet/hull interaction. Ocean. Eng. 88, 120–130. Gong, J., Guo, C., Zhang, H., 2017. Numerical analysis of impeller flow field of waterjet self-propelled ship model. J. Shanghai Jiaot. Univ. 51 (3), 326–331. Hirt, C.W., Nichols, B.D., 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39 (1), 201–225. ITTC, 2005. The Specialist Committee on Validation of Waterjet Test Procedures: Final Report and Recommendations to the 24th ITTC, pp. 476–483. Edinburgh, England. ITTC, 2017. Recommended Procedures and Guidelines: Uncertainty Analysis – Example for Waterjet Propulsion Test. Kandasamy, M., Ooi, S.K., Carrica, P., Stern, F., 2010. Integral force/moment waterjet model for CFD simulations. J. Fluids Eng. 132 (10), 101103. Miller, R., Gorski, J., Xing, T., Carrica, P., Stern, F., 2006. Resistance predictions of high speed mono and multihull ships with and without water jet propulsors using URANS. In: 26th Symposium on Naval Hydrodynamics, pp. 1–16. Ohmori, T., 1998. Finite-volume simulation of flows about a ship in maneuvering motion. J. Mar. Sci. Technol. 3 (2), 82–93. Peri, D., Kandasamy, M., Tahara, Y., Wilson, W., Miozzi, M., Campana, E., Stern, F., 2012. Simulation based design with variable physics modeling and experimental verification of a waterjet propelled catamaran. In: Proc. 29th Symposium on Naval Hydrodynamics, Gothenburg, Sweden. Rhee, B., Coleman, R., 2009. Computation of Viscous Flow for the Joint High Speed Sealift Ship with Axial-Flow Waterjets, First International Symposium on Marine Propulsors. Trondhein, Nor-Way. MARINTEK. Citeseer, pp. 395–407. Takai, T., Kandasamy, M., Stern, F., 2011. Verification and validation study of URANS simulations for an axial waterjet propelled large high-speed ship. J. Mar. Sci. Technol. 16 (4), 434–447. Van Terwisga, T.J.C., 1996. Waterjet-hull Interaction. Delft University of Technology, Netherlands. YI, W., Wang, Y., Liu, C., et al., 2017. Submerged waterjet self-propulsion test and numerical simulation. J. Ship Mech. 21 (4), 407–412. Young, Y.L., Savander, B.R., Kramer, M.R., 2011. Numerical investigation of the impact of SES-Waterjet interactions and flow non-uniformity on pump performance. In: Proceedings of the 11th International Conference on Fast Sea Transportation (FAST’11).
(25)
The pressure on the duct slowly decreased from the intake to the pump. Due to the rotation of the impellers, the pressure gradient around the pump region varied significantly. The guide vanes were in a high pressure environment, and the regions near the tip were high pressure regions. The regions around the leading edge and the tip clearance of the suction surface of the impellers were low pressure regions, and cavita tion phenomenon may have occurred. 6. Conclusion In this paper, numerical simulations and analysis on the selfpropulsion performance of a waterjet propelled trimaran were con ducted based on a RANS solver. The pump effect of the waterjet system was simulated directly by using the MRF model to improve the accuracy of prediction. Mesh independence studies have been performed for both the bare hull and for the isolated waterjet system to address the nu merical uncertainty and define the computational mesh. The validity of the numerical method was proven by comparing the numerical results of the bare hull and the self-propulsion with the experimental results. The good match between the computed and measured results showed that the present numerical method could accurately predict the selfpropulsion performance. A numerical tool was developed to obtain the capture area by tracking streamlines upstream, which greatly reduced the time cost of post-processing. Based on the ITTC regulations, the powering characteristics were investigated to allow the energy conver sion processes and the interaction between the hull and the waterjet to be easily understood. The main conclusions are presented below. 1. With the increase in the hull speed, the area of the capture area decreased monotonically, and the velocity distribution of the nozzle section became uniform. 2. The resistance increment was always positive while the waterjet thrust deduction fraction was negative. 3. The interaction of the hull and waterjet was beneficial for the rapidity performance at high speed.
14
Contents lists available at ScienceDirect
Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng
Numerical study on self-propulsion of a waterjet propelled trimaran Jun Guo a, c, Zuogang Chen a, b, c, *, Yuanxing Dai d, ** a
State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai Jiao Tong University, Shanghai, 200240, China c School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200040, China d Science and Technology on Water Jet Propulsion Laboratory, Marine Design & Research Institute of China, Shanghai, 200011, China b
A R T I C L E I N F O
A B S T R A C T
Keywords: Self-propulsion Numerical simulation Waterjet Trimaran
The hydrodynamics of the waterjet propelled ships represents a challenging problem due to the complexity of the waterjet system itself and the waterjet/hull interaction. In this paper, the self-propulsion computations of a trimaran were performed by solving the unsteady RANS equations. The waterjet was simulated directly with multi-reference frame model to improve the precision of the numerical simulations. Mesh independence studies of the hull and waterjet were carried out individually. Numerical simulations with/without the waterjet were performed in a speed range of 0.196 < Fr < 0.707. Comparisons between numerical predictions and experimental data showed the numerical method could accurately predict the self-propulsion performance. A numerical tool was developed to obtain the capture area based on tracking the streamlines upstream, which was practical and greatly simplified the post-processing. According to the ITTC procedures and guidelines, the overall efficiency and its components were analyzed in detail. The results showed that the resistance increment was always positive while the waterjet thrust deduction fraction was negative. The overall efficiency of the waterjet was mainly affected by the ideal jet efficiency and the pump efficiency. The analysis of the waterjet powering characteristics can better understand the energy conversion and the interaction between the ship hull and waterjet.
1. Introduction In recent years, the development of high-speed ships has attracted the attention of the shipbuilding industry and navies from all countries. Compared with propellers driven ships, waterjets driven ships exhibit high efficiency, good maneuverability, and good anti-cavitation per formance. Many high-speed ships choose waterjet propulsion as their driving force. Accurate prediction of propulsive performance of the waterjet sys tem has always been a concern of researchers. With the rapid develop ment of computational fluid dynamics (CFD) methods in the ship field, CFD technology has been widely used and has made considerable progress. Van Terwisga (1996) analyzed the interaction effects in the powering characteristics of waterjet propelled vessels. An empirical prediction model was recommended for preliminary power-speed computations. Bulten (2006) carried out a numerical study of the water jet system and analyzed the effects of the steady multi-reference frame (MRF) model and the transient moving mesh model on the per formance of the water system. The results showed that the head, torque,
and efficiency for the transient flow calculations were slightly higher. Numerical simulation of waterjet self-propulsion has also been car ried out by many researchers. Kandasamy et al. (2010) derived an in tegral force/moment waterjet model for ship local flow/powering predictions. An alternative control volume was used to balance the force and moment. The predicted resistance error was less than 5%, the average sinkage error was 9.0%, and the average trim error was 13.7%. Takai et al. (2011) analyzed the flow fields for a high-speed sea lift hull by applying a body force to model the pump effect. Moreover, the duct shape was optimized. The results showed that the pressure loss could be reduced by optimizing the upper curve and lip shape of the channel, and the inlet efficiency could be improved by optimizing the intake. Peri et al. (2012) optimized the high-speed waterjet catamaran, aiming at reducing the resistance and inlet loss of the waterjet. The total resistance was reduced by 6% after the optimization. During the optimization process, the low fidelity model was used to reduce the costs of the computation. Eslamdoost et al. (2014) proposed a pressure jump method to study the interaction between the waterjet and hull. The reason for the negative thrust reduction of the waterjet was analyzed. It was found that the resistance increment was not the main cause, but the
* Corresponding author. State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China. ** Corresponding author. Science and Technology on Water Jet Propulsion Laboratory, Marine Design & Research Institute of China, Shanghai, 200011, China. E-mail addresses: [email protected] (Z. Chen), [email protected] (Y. Dai). https://doi.org/10.1016/j.oceaneng.2019.106655 Received 12 April 2019; Received in revised form 19 September 2019; Accepted 27 October 2019 Available online 25 January 2020 0029-8018/© 2019 Elsevier Ltd. All rights reserved.
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Nomenclature Tgross Tnet IVR NVR A1 A6 t tr tj Rbh FD S U Cf Re PD PE PTE PJSE PPE H35 Qshaft QJ KQJ
n
Rotational speed Overall efficiency Free steam efficiency Interaction efficiency Ideal jet efficiency Momentum interaction Energy interaction Ducting efficiency Pump efficiency Duct Length Duct Diameter Pump Diameter Length between perpendiculars Ship width Ship height Displacement Froude number Non-dimensional wall distance Third root of the total mesh number Total resistance Resistance coefficient Sinkage Trim angle Thrust coefficient Torque coefficient Pressure coefficient
ηD η0 ηINT ηI ηmI ηeI ηduct ηP
Gross thrust Net thrust Intake velocity ratio Nozzle velocity ratio Area of capture area Area of nozzle section Total thrust deduction Resistance increment fraction Waterjet thrust deduction fraction Bare hull resistance External tow force Wetted surface Hull velocity Frictional resistance coefficient Reynolds number Delivered mechanical power Effective power Effective thrust power Effective jet system power Effective pump power Pump head Shaft torque Flow rate Flow rate coefficient
Lduct Dduct Dpump Lpp B D Δ Fr yþ hi Rt Ct
σ θ KT KQ Cp
Z pump 6
3
.
5
A’
C D 4
X A
1 B 1A
2
0
0 Free Stream 1A Capture Area 1 Inlet point of tangency 2 Intake throat 6 Nozzle 7 Vena Contracta Fig. 1. Control volume of waterjet.
non-atmospheric pressure on the nozzle exit caused the negative thrust deduction. Gong et al. (2017) carried out a numerical simulation of a waterjet self-propelled ship. The virtual disk and overset models were applied to compare the flow fields. The results revealed that the hull flow fields from the two models were basically the same, but the internal flow field calculated by the overset model was more applicable to the actual state of the impeller. YI et al. (2017) analyzed the hydrodynamic characteristics of submerged waterjet propulsion by combining experi mental and numerical simulation methods, and the experimental values were in good agreement with the CFD predictions. The predicted resis tance, thrust, and torque errors were 3.7%, 4.7%, and 4.6%, respectively. At present, most waterjet self-propulsion studies was based on the virtual disk model (Miller et al., 2006) or body force model (Rhee and Coleman, 2009) to simulate the pump effect. This method can reduce the calculation cost, but the thrust and torque coefficients are obtained in open water, and the influence of the hull boundary layer and the non-uniform flow distribution of the intake (Young et al., 2011) are not considered. Because the error of momentum flux is the square of the error of the flow rate, a 1.5%–2% error of the flow rate can cause a 2%– 4% error of the momentum flux, so the accuracy of the momentum flux depends on the accuracy of the flow rate. In this study, a waterjet was
simulated directly using the steady MRF model, which is more accurate than the virtual disk and body force models. The overset mesh method was used to cope with the large hull attitude at high speeds. The steady multi-reference frame model was employed for the rotation of the im pellers, and the thrust was determined by integrating the forces acting on the waterjet. The self-propulsion point was obtained by modifying the rotational speeds of the impellers until the horizontal force was balanced. Numerical simulation and analysis of the self-propulsion of a waterjet-propelled trimaran were carried out. First, the resistance of the bare hull with a free surface was calculated numerically, and the results were compared with the model test results to verify the accuracy. A self-propulsion simulation was subsequently performed. The powering characteristics of the waterjet were calculated and analyzed. The hy drodynamic characteristics of the waterjet and hull were obtained by this numerical study. 2. Basic theory In the waterjet experiments, there are two different methods for predicting the thrust of the waterjet: the momentum flux method and the direct thrust measurement method. At the 24th International Towing Tank Conference (ITTC, 2005), it was concluded that the direct thrust 2
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and merge lines of hull and duct. Surface 5 is a section in the intake throat. Surface 6 is the nozzle section at the station 6. Applying Newton’s second law to the control volume, the conser vation law of momentum follows the following equation in the i direction: ZZ ZZZ ZZZ ZZ ρui ðuk nk ÞdA ¼ σ ij nj dA þ ρFpi dV þ ρFi dV; (1)
D 0
PD
P
PPE
pump system
duct
ducting system
INT I
PJSE
eI
mI
jet system
PTE
1-t bare hull system
PE
Fig. 2. Energy conversion between subsystems.
A1 þA6
main body of trimaran
side body of trimaran
waterjet
5.235 0.41 0.4 0.116
2.0 0.112 0.262 0.006
Lduct (m) Dduct (m) Dpump (m)
V3
5
V1
6
where σ ij is the tensor, Fpi is the pump force and Fi is the external force (gravity force). The terms on the left- and right-hand-side represent the change in momentum flux and the forces acting on the control volume in the i direction, respectively. On the right-hand-side, the first term rep resents the pressure and tangential stress force, the second term repre sents the pump force acting on fluid, and the third term represents the gravity force acting on control volume. The gross thrust is the definition of the term on the left side of Equation (1). The horizontal component of the gross thrust in the x di rection is abbreviated as Tgross and defined as follows: ZZ (2) Tgross ¼ ρux ðuk nk ÞdA:
Table 1 Principal dimension of the hull and waterjet. Lpp (m) B (m) D (m) 3 ▽ (m )
A1 þA2 þA3 þA6
0.567 0.086 0.118
A1 þA6
The intake velocity ratio (IVR) is defined as the ratio of the average velocity on the capture area U1 to the hull velocity U, and the nozzle velocity ratio (NVR) is defined as the average velocity on the nozzle section U6 to the hull velocity U, defined as follows:
Fig. 3. Hull and waterjet geometry.
U1 U6 ; NVR ¼ : U U
(3)
measurement method was expensive and cumbersome by the Waterjet Specialist Committee. Since the momentum flux method can select any suitable pump that meets the flow requirement, and there is not complicated watertight sealing between the hull and waterjet system, the momentum flux method has become the main method used by re searchers in experiments and numerical calculations. Recommended procedures and guidelines for propulsive performance predictions (ITTC, 2005) and uncertainty analysis (ITTC, 2017) based on the mo mentum flow method were finally proposed based on the continuous improvements by the waterjet specialist committee.
IVR ¼
2.1. Momentum flux theory
The net thrust is defined as the force vector acting upon the duct boundary, the pump housing, and the shaft, which directly pass the force through to the hull. The horizontal component of the net thrust in x direction is abbreviated as Tnet and defined as follows: ZZ ZZZ Tnet ¼ σx dA ρFpx dV: (6)
The gross thrust can also be defined as follows: ZZ Tgross ¼ ρux ðuk nk ÞdA ¼ ρQJ UðNVR ⋅ cos θ IVRÞ;
where θ is the trim angle of the hull, QJ is the flow rate and the flow rate coefficient was defined as follows: KQJ ¼
Based on the recommended procedures and guidelines for propulsive performance predictions (ITTC, 2005), a control volume is shown in Fig. 1, which was applied to analyze the performance of the waterjet system using the momentum flux method. Numbers with circles denote the station numbers. Surface 1 is the imaginary capture area and is positioned one impeller diameter in front of the ramp tangency point A’. Surface 2 is the imaginary streamtube, which separates the control volume from the flow field. Surface 3 is the physical boundary of the waterjet system. Surface 4 is the surface between the stagnation lines
Lpp
2Lpp
4Lpp
QJ : nD3pump
A3 þA4
(5)
V3
5
It is difficult to measure the net thrust in experiments, and thus, the gross thrust is used to define the thrust deduction, which is different from the definition in the conventional hull/propeller theory. The total
10Lpp
Lpp Hull:No-slip Wall
4Lpp Wave Damping Length
Overset Region
Velocity Inlet
(4)
A1 þA6
Pressure Outlet
Symmetry Bachground Region
5
Fig. 4. Computational domain and boundary conditions. 3
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Fig. 5. Mesh of the computational domain and on the hull.
Table 2 Basic sizes of five sets of meshes for calculating the bare hull resistance. Mesh Number
Basic Size
Total Number of Mesh
Average yþ on the hull
1 2 3 4 5
0.05 m 0.06 m 0.08 m 0.12 m 0.16 m
4.93 million 3.23 million 1.69 million 0.74 million 0.44 million
35 43 57 86 114
7.0
EFD CFD
6.5 Ct × 103
6.0
5.0
5.5 5.0
Fitted curve
4.5
4.9
4.0
0.3
0.4
Ct
0.2
Fr
0.5
0.6
0.7
Fig. 8. Computed and measured resistance.
4.8 1 FD ¼ ρSU 2 Cfm 2
4.7 0.0
0.5
1.0
1.5 hi/h1
2.0
2.5
� Cfs ;
(8)
where t is the thrust deduction, Rbh is bare hull resistance, FD is the external tow force, S is the wet area of the hull at rest, U is the hull velocity at model scale, and Cfm and Cfs are the model and ship frictional resistance coefficients, respectively, which can be calculated from the 1957 ITTC formula
3.0
Fig. 6. Convergence of the total resistance coefficient.
Cf ¼
0:075 ðlgRe
2Þ2
(9)
;
where Re is the Reynolds number. The resistance increment fraction and the waterjet thrust deduction fraction are defined as follows: Fig. 7. yþ values on the hull at Fr ¼ 0.628.
thrust deduction is defined as the ratio of the difference between the bare hull resistance and the external tow force to the gross thrust, and the external tow force accounts for the difference of the frictional resistance coefficient between the model and full scale, 1
t¼
Rbh FD ; Tgross
Rbh FD ; 1 Tnet
Tnet : Tgross
1
tr ¼
1
Combining Equations (7) and (10) yields the following: � t ¼ ð1 tr Þ 1 tj :
tj ¼
(10)
(11)
2.2. Description of powering characteristics
(7)
Based on the ITTC regulations (ITTC, 2005), the overall efficiency of the waterjet-hull system ηD can be divided into the free steam efficiency 4
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0
The overall efficiency of the waterjet-hull system is given by
EFD CFD
ηD ¼
/ Lpp ×103
-1
PE PE PTE PTE0 PJSE0 PJSE PPE ¼ ; PD PTE PTE0 PJSE0 PJSE PPE PD
(14)
where PE is the effective power, PD is the delivered mechanical power, PTE is the effective thrust power, PJSE is the effective jet system power, PPE is the effective pump power, and the other terms with subscript 0 are corresponding powers in the free steam condition. The subsystem efficiencies are given as follows: Thrust deduction:
-2 -3
tÞ ¼
ð1
PE Rbh FD ¼ : PTE Tgross
(15)
Momentum interaction:
-4
0.2
0.3
0.4
Fr
0.5
0.6
1
0.7
ηmI
¼
ηI ¼
1.0
(deg)
PTE0 Tgross0 U0 Tgross0 U0 2 : ¼ ¼ ¼ NVR þ 1 PJSE0 QJ HJSE0 E6 E0
(17)
The total axial energy flux Es through a cross-sectional area As at station s is defined as follows: � Z � 1 P Es ¼ ρ u2i þ þ gzs ðui ni ÞdA: (18) 2 ρ
EFD CFD
1.2
(16)
Ideal jet efficiency:
Fig. 9. Computed and measured sinkage.
1.4
PTE Tgross 1 IVR : ¼ ¼1þ NVR 1 PTE0 Tgross0
As
Energy interaction:
0.8 0.6
ηeI ¼
PJSE0 E6 ¼ PJSE E6
E0 : E1
(19)
Ducting efficiency:
0.4 0.2 0.0
0.2
0.3
0.4
Fr
0.5
0.6
Table 3 Basic sizes of five meshes for calculating the pump performance.
0.7
Fig. 10. Computed and measured trim.
η0 in ideal conditions, where the intake velocity of the waterjet is uni
form U and the pressure at the nozzle center is atmospheric pressure P0, and the interaction efficiency ηINT, which accounts for the effect of the waterjet-hull interaction:
Mesh Number
Basic Size
Total Number of Mesh
Average yþ on the blades
1 2 3 4 5
0.004 m 0.006 m 0.008 m 0.010 m 0.0125 m
7.15 million 4.23 million 2.90 million 2.18 million 1.64 million
38 54 67 76 89
(12)
ηD ¼ η0 ηINT :
The waterjet-hull system is divided into subsystems, and the sche matic diagram of energy conversion between subsystems and the sub system efficiencies are shown in Fig. 2. The free steam efficiency and the interaction efficiency are defined as follows:
η0 ¼ ηI ηduct ηpump ; ηINT ¼ ð1
tÞ
ηeI : ηmI
(13)
Fig. 12. Mesh on the blades and housing.
5 4Dduct
No-slip Wall
Pressure Outlet
Velocity Inlet Rotating Region
No-slip Wall
Fig. 11. Computational domain and boundary conditions of a pump. 5
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1.28
ηduct ¼
Fitted curve
(20)
Pump efficiency:
1.26
ηP ¼
1.24
KT
PJSE E6 E0 ¼ : PPE ρgQJ H35
PPE ρgQJ H35 ¼ : PD 2π nQshaft
(21)
3. Hull and waterjet geometry The hull used in this study was a trimaran, and its main and side bodies were aligned at the stern. The hull and waterjet geometries were at the model scale. Two waterjet systems were installed on the main body. The numbers of impeller blades and guide vanes of the waterjet system were 6 and 11, respectively. Principal dimensions of the hull and waterjet are shown in Table 1. The hull and waterjet model are shown in Fig. 3.
1.22 1.20 1.18
4. Computations of bare hull resistance 4.1. Numerical methods
1.16 0.0
0.5
1.0 h1/hi
1.5
The numerical simulations were conducted using the finite volume method (FVM) commercial software STAR-CCMþ. The SST k-ω turbu lence model was applied to solve governing equations. The dimension less distance from the center of the first grid to the wall is defined as yþ. All yþ wall treatments (CD-adapco S. C., 2015) were selected, the viscous sub-layer was resolved if yþ<1, a wall function was used if yþ>30, and a blending function was used to resolve the buffer region 1 < yþ<30. The volume of fluid (VOF) method (Hirt and Nichols, 1981) was used to capture the free surface. The convective and temporal dis cretization schemes were second-order upwind schemes. The implicit unsteady solver based on the separated flow model was used. The physical time step was 0.02 s, and there were 10 iterations in each time step. A dynamic fluid body interaction (DFBI) rotation and translation motion (Ohmori, 1998) was applied to simulate the 6-DOF motion of hull, and the sinkage and trim were free. The numerical computational boundary conditions are shown in Fig. 4. Considering the symmetry of the geometry and flow, only half of the hull was modeled. The computational domain was split into two different regions: a background region and an overset region. The background region was stationary, and the overset region was moving with the hull. An overset mesh was built between the background region and the overset region. The length, width, and height of the computation domain were 13LPP, 5LPP, and 4LPP, respectively. The inlet was situated 2LPP in front of the stem, and the outlet was located 10LPP behind the
2.0
Fig. 13. Convergence of the thrust coefficient.
1.26
Fitted curve
10KQ
1.24
1.22
1.20 0.0
0.5
1.0 hi/h1
1.5
2.0
Fig. 14. Convergence of the torque coefficient.
Fig. 16. yþ values on the duct and blades of waterjet.
Fig. 15. Mesh distribution near the intake and inside the duct. 6
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Fig. 17. Streamlines tracked upstream and boundary layer at station 1A
Capture Area E:\waterjet
file :
dead rise angle(°)
20
reference Y (m)
0.12
reference Z (m)
-0.15
extension coefficient of Ymin
0.04
extension coefficient of Ymax 0.04 scaling factor
-0.05
-0.10 Z -0.15
1.01
Run
-0.20 0.2
0.15
0.1 Y
0.05
Fig. 18. Program for obtaining the capture area.
stern to completely develop the wake field. In front of the outlet, the VOF wave damping length was set 4LPP to avoid the reflection of waves. The boundary conditions were set as follows. The velocity inlet boundary condition was applied to the inlet, side, top, and bottom of the domain. A pressure outlet boundary condition was applied to the outlet. A symmetry boundary condition was set at the center plane of the hull. A no-slip wall boundary condition was used for the hull surface.
meshes with a growth ratio of 1.2 were generated in the boundary layer. Four levels of blocks were used to refine the mesh around the hull. Three levels of blocks were used to refine the mesh around the free surface. Three cones like Kelvin waves were used to capture the free surfaces better. The mesh of the computational domain is shown in Fig. 5. A mesh independence study was carried out at Fr ¼ 0.628, which is the design speed. By varying the basic size of the mesh parameters, five sets of meshes were generated. The basic sizes and the total numbers of the five sets of meshes are shown in Table 2. The total resistance coefficient, Ct, is defined as follows:
4.2. Mesh independence study of the bare hull Computations of the bare hull resistance in calm water were carried out to obtain a complete prediction of the self-propulsion. An unstruc tured trimmed mesh was generated in this study. Six layers of prism
Ct ¼
7
Rt ; 0:5ρSU 2
(22)
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uncertainty for these meshes was 2.65%. Fig. 7 shows the yþ values on the hull at Fr ¼ 0.628.
(yref,zref)
4.3. Results of bare hull resistance
convex set
dead rise angle
Rotation
The calm water resistance tests were carried out in Norwegian Ma rine Technology Research Institute (MARINTEK). The hull model was towed by the carriage and equipped with a trip-wire at the bow and stern. The bare hull resistance was calculated in a speed range of 0.196 < Fr < 0.707, and the hull was free to sink and trim. Fig. 8 shows the computed and measured bare hull resistance results. Figs. 9 and 10 show the sinkage and trim results, respectively. Both the resistance and sinkage were under-predicted compared to the experimental results, while the trim results were over-predicted. The minimum resistance, sinkage, and trim errors were 1.95%, 9.77%, and
boundary points Fitting
Rotation
extend
extend hull
Fig. 19. Steps for obtaining the capture area.
where Rt is the total resistance and S is the wet area of the hull at rest. According to the least squares root method proposed by Eça and Hoekstra (2014), a mesh independence study method for the non-uniform refinement ratio, the numerical uncertainty of the bare hull was determined. The non-uniform refinement ratio is defined as follows: p ffiffiffiffiffi 3 N1 hi ffiffiffiffi ; ¼p (23) 3 h1 Ni where Ni and hi are the total number of meshes and the typical mesh size for mesh number i, N1 and h1 correspond to the finest mesh. The convergence curve of Ct is shown in Fig. 6. Considering the computational accuracy and cost, mesh number 3 was selected for the computations. The numbers of mesh in background region and in the overset region were about 0.74 and 0.95 million. The numerical
Fig. 21. Free surface and the jet flow at Fr ¼ 0.628.
Fr=0.314
Fr=0.471
Fr=0.628
Fig. 20. Wave patterns of the self-propulsion. 8
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7.5 7.0
Ct × 103
reliable for further calculations of the self-propulsion.
EFD CFD
5. Computations of self-propulsion
6.5
5.1. Mesh independence study of the waterjet system
6.0
Because the pump is an important part of the waterjet system, to obtain an appropriate mesh size for the waterjet system, a mesh inde pendence study was carried out for the pump based on the least squares root method (Eça and Hoekstra, 2014). The numerical domain and boundary conditions of the waterjet pump are shown in Fig. 11. The domain was split into two different regions: a stationary region and a rotating region, in which the MRF model was set to simulate the rotation of the impellers. The inlet was situated 5Dduct in front of the pump, and the velocity was set to the design flow rate with a uniform velocity distribution. Atmospheric pressure was applied to the outlet boundary. No-slip wall boundary conditions were applied to the other boundaries. In the MRF model, the rotational speeds of the impellers were set to the design rotational speed. An unstructured trimmed mesh was generated for the pump. Feature curves of impellers and guide vanes were generated to refine the mesh around the curves. Five sets of meshes were generated, similar to the mesh independence study of the hull. Five sets of meshes are shown in Table 3. The mesh on the impellers, guide vanes, and housing of mesh number 3 are shown in Fig. 12. The thrust coefficient KT and the torque coefficient KQ were defined as follows:
5.5 5.0 4.5 4.0 0.2
0.3
0.4
0.5 Fr
0.6
0.7
0.8
Fig. 22. Computed and measured resistance.
0
EFD CFD
/ Lpp ×103
-1 -2
KT ¼
0.3
0.4
0.5 Fr
0.6
0.7
0.8
Fig. 23. Computed and measured sinkage.
4.59%, respectively. The average resistance, sinkage, and trim errors were 4.44%, 13.43%, and 7.34% at a high speed range of Fr > 0.4. In general, the calculated results of the bare hull were in good agreement with the experimental results. Thus, the accuracy of the numerical method was verified, and the numerical method is applicable and
1.4
EFD CFD
1.2 1.0
(deg)
; KQ ¼
Qshaft
ρn2 D5pump
;
(24)
where Tblade is the thrust of all the blades of the pump and Qshaft is the shaft torque. The convergence curves of KT and KQ are shown in Figs. 13 and 14. The results show that with the increase of mesh density level, KT converges to 1.182 gradually and KQ converges to 1.214 gradually. The torques of mesh number 1–4 are all close to its convergence value. Considering the accuracies of KT and KQ and the computational cost, mesh number 3 was selected for further calculations. The number of meshes in the rotating region was about 1.08 million, and the number of meshes in the remaining region was about 1.82 million. The numerical uncertainties of KT and KQ for this mesh were 1.06% and 2.18%, respectively. The mesh for calculating the self-propulsion was based on the mesh independence study of the bare hull and the pump. Since the flow fields around the waterjet intake, in the waterjet duct, and out of the nozzle were important, the meshes in these regions were refined. The total number of meshes for the simulation of the self-propulsion flow was 4.86 million, and the numbers of meshes in the background, overset, and rotating regions were about 0.68, 2.74, and 1.45 million, respectively. Fig. 15 shows the mesh around the waterjet duct. Fig. 16 shows the yþ values on the duct and blades of the waterjet.
-3 -4 0.2
Tblade
ρn2 D4pump
0.8
5.2. Numerical methods
0.6
The numerical method for simulating the self-propulsion was similar to the method for simulating the bare hull. The difference is that the rotating reference frame in the MRF model was the local hull-fixed co ordinate system, which was moving with the DFBI motion. The selfpropulsion point was obtained by modifying the rotational speeds of impellers until the total resistance was equal to the sum of the net thrust and the tow force. It is generally considered that the thrust is propor tional to the rotational speed in a small range of rotational speeds. After convergence the rotational speed was n1, and the corresponding hori zontal force was Fx1; then n1 was adjusted to n2 in a small range and after convergence the corresponding horizontal force was Fx2; n3 could be
0.4 0.2 0.0 0.2
0.3
0.4
0.5 Fr
0.6
0.7
0.8
Fig. 24. Computed and measured trim. 9
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Ocean Engineering 195 (2020) 106655
Fr=0.471
self-propulsion
bare hull
self-propulsion
bare hull
Fr=0.628
self-propulsion
bare hull
Fig. 25. Comparison of wave pattern of the bare hull and self-propulsion.
Fr=0.314
Fr=0.393
Fr=0.471
Fr=0.55
Fr=0.628
Fr=0.707
Fig. 26. Velocity distribution on the capture area.
obtained according to n1, n2, Fx1 and Fx2 by a linear interpolation method. By changing the rotational speed three times, the horizontal force could be balanced. There are two methods to obtain the capture area. One method is
based on solving a scalar equation and was used by Bulten (2006), Ding and Wang (2010), and Eslamdoost et al. (2014). The other method is based on tracking streamlines upstream and was used by Delaney et al. (2009). In this study, the latter method was applied. Streamlines were 10
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0.5%–1% enlargement of the capture area is needed. Fig. 19 shows the steps for obtaining the capture area: the section data of the streamlines (blue dots) is rotated by the dead rise angle of the hull to reduce gradient and improve the fitting accuracy; the section data can be regarded as a convex set, and the boundary points of the convex set are calculated; the boundary points is fitted by a quadratic polynomial, and the fitting curve is extended at the ends; the fitting curve is rotated by the dead rise angle in reverse to restore its position. The accuracy of the program was mainly affected by the number of streamlines and was tested by changing the number of streamlines with 500, 1000, 2000, 4000 and 8000. The results showed that when the number of streamlines was greater than 1000, the shape of the capture area was no longer changed. The shape of the capture area could be easily and accurately obtained by the program with 1000 streamlines, and the time cost of post-processing
2.4 2.3
A1/A6
2.2 2.1 2.0 1.9 1.8 0.2
0.3
0.4
0.5 Fr
0.6
0.7
0.8
2.4
IVR EFD IVR CFD NVR EFD NVR CFD
2.0
Fig. 27. Variation of the capture area.
1.6 IVR NVR
tracked upstream from station 3, and the shapes of the capture area were fitted by a quadratic polynomial with the streamline data at Station 1A. Fig. 17 shows streamlines tracked upstream and the boundary layer at station 1A for Fr ¼ 0.628. A program was developed using the MATLAB language to simplify the post-processing. Fig. 18 shows the numerical tool for obtaining the capture area. The blue dots are the data to be processed and the red line is the fitting curve. The program is controlled by six parameters: the first parameter is the dead rise angle of the hull at Station 1A; the second and third parameters are center coordinates of the capture area; the fourth and fifth parameters are the extension coefficients used to ensure that the fitting curve exceeds the range of the streamlines; and the sixth parameter is the scaling factor, because the flow rate of the capture area calculated directly is slightly lower than the flow rate at station 3, a
1.2 0.8 0.4 0.0 0.2
0.3
0.4
0.5 Fr
0.6
0.7
Fig. 29. Calculated and measured IVR and NVR.
Fr=0.314
Fr=0.393
Fr=0.471
Fr=0.55
Fr=0.628
Fr=0.707
Fig. 28. Velocity distribution on the nozzle section. 11
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0.40
1.3
EFD CFD
KQJ
0.35 0
0.30
0
1.2
I
1.1
duct
1.0
pump
0.9 0.8 0.7 0.6
0.25
0.5
0.20 0.2
0.3
0.4
0.5 Fr
0.6
0.7
0.4 0.2
0.8
0.3
0.4
0.5 Fr
0.6
0.7
0.8
Fig. 33. Free stream efficiency and its component.
Fig. 30. Calculated and measured flow rate.
1.3
0.25
INT
1.1
tj
0
1.0 D
0.15
D
1.2
t tr
0.20
`
0.10
0.9
t
0.8 0.7
0.05
0.6
0.00
0.5
-0.05 0.2
0.3
0.4
0.5 Fr
0.6
0.7
0.4 0.2
0.8
0.3
0.4
0.5 Fr
0.6
0.7
0.8
Fig. 34. Overall efficiency and its components.
Fig. 31. Thrust deduction and its components.
was greatly reduced. In this paper, the capture area was obtained when the sinkage and trim were equal to the averages of that in several periods.
1.2
5.3. Results of the self-propulsion
INT
1-t
1.1
Self-propulsion tests were also carried out in MARINTEK based on the recommended procedures and guidelines for propulsive perfor mance predictions, and the trimaran equipped with a twin waterjet propulsion system. The flow rate was measured separately for each waterjet in the self-propulsion tests. Wave patterns of the self-propulsion at Fr ¼ 0.314, 0.471 and 0.628 are shown in Fig. 20.
mI eI
INT
1.0 0.9
5.3.1. Results of the resistance, sinkage, trim, and wave pattern The self-propulsion was calculated in a speed range of 0.275 < Fr < 0.707. The free surface and the jet flow at Fr ¼ 0.628 are shown in Fig. 21. Under the impact of the jet flow, a high and sharp wave peak formed behind the hull. Fig. 22 shows the computed and measured resistance results of the self-propelled hull. The experimental resistance was estimated by the gross thrust measured in the self-propulsion experiments plus the tow force. For without assuming a jet thrust deduction factor, the difference between computed and measured resistance of the self-propulsion was lower than that of the bare hull. Figs. 23 and 24 show the sinkage and
0.8 0.7 0.2
0.3
0.4
0.5 Fr
0.6
0.7
0.8
Fig. 32. Interaction efficiency and its components.
12
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Fr=0.314
Fr=0.471
Fr=0.628
Fig. 35. Pressure distribution on the duct and the blades.
trim results, respectively. The computed sinkage values were lower than the measured values. However, the computed trim values were higher than the measured values. In the high speed range of Fr > 0.4, the average sinkage and trim errors were 13.24%, and 12.04%, respectively. Like the results of the bare hull simulation, the match between the computed resistance, sinkage, and trim and the measured values was very good on the whole. Fig. 25 shows the comparison of the wave pattern around the bare hull and the hull with the waterjet. The wave patterns around the hull were basically the same, but the wave patterns behind the hull were significantly different due to the jet flow. The height of the stern wave peak was larger than that of the bare hull, the width of the stern wave was smaller than that of the bare hull, and a high and sharp wave peak formed, which is also shown in Figs. 20 and 21.
decreased with the increase in the Froude number. Fig. 30 shows the comparison of the calculated and measured flow rate coefficients. The flow rate coefficient increased slowly with the increase in the Froude number. The flow rate was over-estimated, and the average discrepancy was 2.63%. Finer mesh may be needed for the waterjet to predict the flow rate more accurately. As shown in Figs. 29 and 30, the measured IVR and the flow rate coefficient exhibited slight sudden changes at Fr ¼ 0.393, which was a critical speed when the trim angle increased rapidly and transom clearance occurred. 5.3.3. Analysis of powering characteristics To clearly understand the efficiency of energy conversion and the interaction between the ship hull and waterjet, the powering charac teristics were analyzed based on the theory in Section 2.2. The total thrust deduction, t, and its components, tr and tj, are shown in Fig. 31. Because the sinkage and trim of the self-propulsion was higher than that of the bare hull, the resistance increased at self-propulsion. The resistance increment, tr, was always positive, tr decreased with the in crease of speed for Fr < 0.393, and tr varied in a small range from 0.02 to 0.04 for Fr > 0.393. The waterjet thrust deduction fraction, tj, was negative for Fr < 0.668, meaning that Tgross was less than Tnet, and the absolute value of tj decreased with the increase of speed. Because the absolute values of tr were greater than those of tj, the trend of t was similar to that of tr. The interaction efficiency, ηINT, and its components, 1-t, ηmI, and ηeI, are shown in Fig. 32. Although the values of ηeI were about 0.05 greater than those of ηmI, their trends were basically the same, and gradually decreased with the increase of Fr. The trend of ηINT was determined by that of 1-t. The ηINT was greater than 1.0 at Fr > 0.314, indicating that the interaction of the hull and waterjet was beneficial for the rapidity performance. The free stream efficiency, η0, and its components, ηI, ηduct, and ηpump, are shown in Fig. 33. The ideal jet efficiency, ηI, increased monotonically due to the monotonic decrease in NVR with the increase of Fr. The
5.3.2. Analysis of the capture area and nozzle section Fig. 26 shows the shape of the capture area and the velocity distri bution on the capture area at different speeds. As the boundary layer became thinner from the longitudinal section to the side of the hull, the maximum velocity of the capture area was similar to the hull speed. With the increase in the hull speed, the width of the capture area basi cally remained unchanged, while the height gradually decreased, and the area of the capture area decreased monotonously consequently in Fig. 27. The area of the capture area was non-dimensionalized by the ratio of the capture area to the nozzle section area. Fig. 28 shows the velocity distribution on the nozzle section at the station 6. Through the rectification of the guide vanes, the velocity on the nozzle section was still not uniform. The velocity at center of the nozzle section was low. With the increase in the Froude number, the velocity distribution became increasingly more uniform. Fig. 29 shows the calculated and measured IVR and NVR. The match between the calculated and measured values was good. On average, the calculated IVR and NVR were over-estimated by 5.13% and 1.32%, respectively. Overall, the IVR did not change significantly, but the NVR 13
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Ocean Engineering 195 (2020) 106655
ducting efficiency, ηduct, and the pump efficiency, ηpump, were nearly constant over the entire Froude number range. The average ηduct was 0.974, meaning that the energy loss caused by the duct was a small quantity at self-propulsion. The loss of the duct was very small when the design of the duct was reasonable. The free stream efficiency increased monotonically with the increase of Fr and was mainly affected by ηI and ηpump. The overall efficiency, ηD, and its components, ηINT and η0, are shown in Fig. 34. The overall efficiency increased with the increase of Fr, and the efficiency varied from 0.46 to 0.6, which were lower than that of the conventional propellers. The overall efficiency was mainly determined by η0, and influenced by ηINT. In the design of the waterjet, determining how to improve the ideal jet and pump efficiencies is important to the overall efficiency.
4. The energy loss caused by the duct was a small quantity over the entire Froude number range. 5. For a waterjet propelled ship, improving the ideal jet efficiency and the pump efficiency were the main methods to improve the overall efficiency. The analysis of the powering characteristics will pave the way for further improvements of the hydrodynamic performance. Acknowledgements This work was supported by the Foundation for Key Laboratory of National Science and Technology of China, Grant number 61422230203. The authors appreciate the second International Work shop on Waterjet Propulsion (IWWP 2017) and the Workshop on Waterjet Propulsion Technology (WORKSHOP 2018) for the academic exchange and discussion.
5.3.4. Pressure distribution of the waterjet Fig. 35 shows the pressure distribution on the duct and the blades of the waterjet. The pressure distribution coefficient is defined with reference to the atmospheric pressure P0 as follows: CP ¼
P P0 : 0:5ρU 2
References Bulten, N.W.H., 2006. Numerical Analysis of a Waterjet Propulsion System. Library Eindhoven University of Technology, Netherlands. Delaney, K., Donnely, M., Elbert, M., Fry, D., 2009. Use of RANS for Waterjet Analysis of a High-Speed Sealift Concept Vessel, 1st International Symposium on Marine Propulsors. Trondheim, Norway. Ding, J., Wang, Y., 2010. Research on flow loss of inlet duct of marine waterjets. Journal of Shanghai Jiaotong University (Science) 15 (2), 158–162. Eça, L., Hoekstra, M., 2014. A procedure for the estimation of the numerical uncertainty of CFD calculations based on grid refinement studies. J. Comput. Phys. 262, 104–130. Eslamdoost, A., 2014. The Hydrodynamics of Waterjet/hull Interaction. Chalmers University of Technology. Eslamdoost, A., Larsson, L., Bensow, R., 2014. A pressure jump method for modeling waterjet/hull interaction. Ocean. Eng. 88, 120–130. Gong, J., Guo, C., Zhang, H., 2017. Numerical analysis of impeller flow field of waterjet self-propelled ship model. J. Shanghai Jiaot. Univ. 51 (3), 326–331. Hirt, C.W., Nichols, B.D., 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39 (1), 201–225. ITTC, 2005. The Specialist Committee on Validation of Waterjet Test Procedures: Final Report and Recommendations to the 24th ITTC, pp. 476–483. Edinburgh, England. ITTC, 2017. Recommended Procedures and Guidelines: Uncertainty Analysis – Example for Waterjet Propulsion Test. Kandasamy, M., Ooi, S.K., Carrica, P., Stern, F., 2010. Integral force/moment waterjet model for CFD simulations. J. Fluids Eng. 132 (10), 101103. Miller, R., Gorski, J., Xing, T., Carrica, P., Stern, F., 2006. Resistance predictions of high speed mono and multihull ships with and without water jet propulsors using URANS. In: 26th Symposium on Naval Hydrodynamics, pp. 1–16. Ohmori, T., 1998. Finite-volume simulation of flows about a ship in maneuvering motion. J. Mar. Sci. Technol. 3 (2), 82–93. Peri, D., Kandasamy, M., Tahara, Y., Wilson, W., Miozzi, M., Campana, E., Stern, F., 2012. Simulation based design with variable physics modeling and experimental verification of a waterjet propelled catamaran. In: Proc. 29th Symposium on Naval Hydrodynamics, Gothenburg, Sweden. Rhee, B., Coleman, R., 2009. Computation of Viscous Flow for the Joint High Speed Sealift Ship with Axial-Flow Waterjets, First International Symposium on Marine Propulsors. Trondhein, Nor-Way. MARINTEK. Citeseer, pp. 395–407. Takai, T., Kandasamy, M., Stern, F., 2011. Verification and validation study of URANS simulations for an axial waterjet propelled large high-speed ship. J. Mar. Sci. Technol. 16 (4), 434–447. Van Terwisga, T.J.C., 1996. Waterjet-hull Interaction. Delft University of Technology, Netherlands. YI, W., Wang, Y., Liu, C., et al., 2017. Submerged waterjet self-propulsion test and numerical simulation. J. Ship Mech. 21 (4), 407–412. Young, Y.L., Savander, B.R., Kramer, M.R., 2011. Numerical investigation of the impact of SES-Waterjet interactions and flow non-uniformity on pump performance. In: Proceedings of the 11th International Conference on Fast Sea Transportation (FAST’11).
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The pressure on the duct slowly decreased from the intake to the pump. Due to the rotation of the impellers, the pressure gradient around the pump region varied significantly. The guide vanes were in a high pressure environment, and the regions near the tip were high pressure regions. The regions around the leading edge and the tip clearance of the suction surface of the impellers were low pressure regions, and cavita tion phenomenon may have occurred. 6. Conclusion In this paper, numerical simulations and analysis on the selfpropulsion performance of a waterjet propelled trimaran were con ducted based on a RANS solver. The pump effect of the waterjet system was simulated directly by using the MRF model to improve the accuracy of prediction. Mesh independence studies have been performed for both the bare hull and for the isolated waterjet system to address the nu merical uncertainty and define the computational mesh. The validity of the numerical method was proven by comparing the numerical results of the bare hull and the self-propulsion with the experimental results. The good match between the computed and measured results showed that the present numerical method could accurately predict the selfpropulsion performance. A numerical tool was developed to obtain the capture area by tracking streamlines upstream, which greatly reduced the time cost of post-processing. Based on the ITTC regulations, the powering characteristics were investigated to allow the energy conver sion processes and the interaction between the hull and the waterjet to be easily understood. The main conclusions are presented below. 1. With the increase in the hull speed, the area of the capture area decreased monotonically, and the velocity distribution of the nozzle section became uniform. 2. The resistance increment was always positive while the waterjet thrust deduction fraction was negative. 3. The interaction of the hull and waterjet was beneficial for the rapidity performance at high speed.
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