Int. J. Nav. Archil Ocean Eng. (2013) 5:502-512 http://dx.doi.org/10.2478/IJNAOE-2013-0149
plSSN: 2092-6782, elSSN: 2092-6790
RANS simulation of cayitation and liull pressure fluctuation for
marine propeller operating behind-hull condition
Kwang-Jun Paik, Hyung-Gil Park and Jongsoo Seo
Samsung Ship Model Basin (SSMB), Samsung Heavy Industries Co., Ltd., Daejeon, Korea
A B S T R A C T : Simulations of cavitation flow and hull pressure fluctuation for a nmrine propeller operating behind a
hull using the unsteady Reynolds-Averaged Navier-Stokes equations (RANS) are presented. A full hull body submerged under the free surface is modeled in the computational domain to simulate directly the wake field of the ship at the propeller plane. Simulations are performed in design and ballast draught conditions to study the effect of cavitation
number And two propellers with slightly different geometry are simulated to validate the detectability of the numerical simulation. All simulations are performed using a commercial CFD software FLUENT. Cavitation patterns of the si-mulations show good agreement with the experimental results carried out in Samsung CAvitation Tunnel (SCAT). The simulation residts for the hull pressure fluctuation induced by a propeller are also compared with the experimental re-sidts showing good agi-eement in the tendency and amplitude, especially, for the first blade frequency.
KEYWORDS: Propeller; Cavitation; Hull pressure fluctuation; RANS; Propeller-hull interaction.
I N T R O D U C T I O N
The practical importance of accurate numerical simulations to predict the cavitation pattern and hull pressure amplitude has increased in the field of ship building industries. The researches to simulate the cavitation flow using RANS solver were per-formed actively in the last several yeai-s because cavitation models for RANS solver and computation power have been rapidly developed in the last decade.
Watanabe et al. (2003) performed a pioneering study on the cavitation flow for a maiine propeller using RANS. Salvatore et al. (2009) compared seven computational models using RANS, LES, and BEM for the INSEAN E779A propeller in tiie uni-fonn flow and the wake field. The cavitation simulation for conventional and highly-skewed propellers in the behind-hull condition using an in-house RANS solver was peifomed by Shin et al. (2011). Hasuike et al. (2010) simulated the cavitation flow and showed a possibihty to predict the cavitation erosion risk with the indexes using time differential of cavity void frac-tion or pressme.
On tiie other hand, the usage of commercial CFD sofhvare gi-adually increased to simulate the cavitation flow for marine propellers. Boorsma and Whitworth (2011) used STAR-CCIVH- to study on the prediction of cavitation and erosion for a pro-peller and radder. Bertetta et al. (2011) compai-ed the results of RANS solver using STAR-CCM+ witii tiiose of potential solver for the cavitation flow of a conü-ollable pitch propeller. Morgut and Nobile (2011) studied on the peifoimance of three cavi-tation models for a marine propeller using ANSYS-CFX. L i and Terwisga (2011) used FLUENT to investigate unsteady
Corresponding author: Kwang-Jun Paik, e-mail: k.j.paik@samsung.com This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses^y-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Int. J. Nav. ArchU. Ocean Eng. (2013) 5:502-512 503
cavitation phenomena for 2D and 3D foils. Kawamura (2010) assessed cavitation erosion risk based on pressure impacts and simulated the cavitation flow and the amplitude of pressure fluctuation for a marine propeller using FLUENT.
Most of simulations except for Kawamura (2010) prescribed a velocity dishibution at the inlet boundaiy of the computa-tional domain to achieve the wake field at the propeller plane, hi that case, the adjushnent of mlet boundaiy condition to get a desired velocity contoui- at propeller plane is of primary importance and very laborious work. Therefore, Kawamui-a (2010) used a fliU hull body to generate the wake field at propeller plane. Nevertheless, the cavity extent was under-predicted and the pressure amphtudes were about 70% of the experimental results.
til this paper the results of numerical sunulations using RANS for the cavitation pattem and hull pressure fiuctuation of marine propeUers are presented. A commercial CFD software FLUENT version 14.0 is used for the numerical simulations. The cavitation model of Schneer and Sauer (2001) is apphed to simulate the cavitation flow. A computational domain including a fiill huU body submerged under the fi'ee srvrface is used to simulate dhectly the wake field at the propeller plane. Two kinds of shidies vaiying cavitation nimiber and propeller geomehy are executed in order to validate the numerical simulation method. And the numerical simulations are performed at the same as the test conditions in the cavitation tunnel and compared with the experimental results.
N U M E R I C A L M E T H O D S A N D M O D E L S
A commercial CFD software FLUENT version 14.0 was used for the numerical simulations, in which the cavitation flow was solved by a mixture model based on a single-fluid multiphase mixture flow approach.
Governing equations
In the mixture model, the contmuity equation and tiie momenhrm equation become as
f
(/'J + V-U,v„,) = 0 (1)
^ ( P „ , v „ j + V • (p,„v,„v„,) = -Vj7 + V • (vv„, + Vv,^)]+ p„,g + F (2)
The rmxture density and viscosity coeificient are defmed as
A „ = « A . + ( 1 - « ) P /
M,n =«/^„+(!-«)//,
where a is the vapor volume fraction. Subscripts m , v, and / represent nuxture, vapor, and hquid phase, respectively.
Cavitation model
The cavitation model of Schneer and Sauer (2001) applied in this research solves the vapor volume fraction witii fohowing transport equation:
^^{ap,)+V-{ap^v^)=R,-R, (4)
where the terms in the right hand side, R^ and R^, account for the mass transfer between the liquid and vapor phase in cavi-tation denoting the evaporation and condensation of the vapor bubbles. The forms of R^ and R^ are written as foUows:
504 Int. J. Nav. Archil Ocean Eng. (2013) 5:502-512 when Pv^P , Pm Pl (5) when p^,<p. •Pm ^i? V 3 Pl (6)
Here, the bubble radius, R^, is expressed as
_a 3_J_ I-a An 7!j
(7)
where is the bubble number density. The source terms, R^ and R^, in the ti'ansport equation approach zero when
a = 0 and a = l.
M O D E L TEST
Model tests to observe cavitation flow on a propeller blade and to measure pressui'e fluctuation on a huh suiface induced by the propeller cavitation were carried out in Samsung CAvitation Tunnel (SCAT). The principal particulars of the test section of SCAT are summarized in Table 1 and the set-up of a model ship and propeller is shown in Fig. 1. The definition of propeller blade angle is depicted in Fig. 2. The propeller blade angle begins from the top position toward propeller rotation direction. Pressure hansducers to measure the pressure fluctuation on a huU surface were mstalled on the top of propeller with the inter-vals of 30 mm as iUustrated in Fig. 3.
Table 1 Pruicipal particulars of the test section of SCAT.
Item Value
Dimension of test section (L x B x D) 12.0 X 3.0 X 1.4 m
Maximum speed 12.0 m/s
Contraction ratio 2.75
180'
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The length of the model ship, a cmde oil tanker, was about 7.6 m and the diameter of the model propeller was 226.1 mm in this research. The vertical distance between propeller tip and the pressure hansducer P3 is about 30% of propeller diameter. The blockage of the test section due to the model ship was about 13.2%. The surface of the model propeller was coated with a rough paint to stabilize the behavior of cavitation flow. The inflow velocity of model test was frxed as 5.5 m/s. The propeUer rotation speed was set with the thrast identity method based on the results of self-propulsion test carried out in a towmg tank.
P R O P E L L E R P L A N E D W L D I S T A N C E EE7V/EEN T W O P R E S S U R E R l i . K - L I P S 3 0 MM IHQDEL S E A L E I P l P 7 • INDEX DF P R E S S U R E P l f . K - U P \ P O R T S I D E S T A R B O A R D / — 1 I 1 1 I ViJ \ a P R O P E L L E R S H A F T l E N T E R L I N E ^ -C D.W.L. PROPEL
Fig. 3 Position of pressure transducers installed on a model ship.
NUMERICAL SIMULATION
Grid systemTo shnulate the propeller cavitation flow under similar sihiation to the model test, a full hull body submerged rmder the free surface was modeled in the computational domain. The free surface was substihited with a symmetry boundary condition because the mixture model for the cavitation flow and the Volume of Fluid (VOF) model for the free surface could not be im-plemented simultaneously in FLUENT.
A sliding block surroundmg the propeher, composed of unshoichired girds, was apphed to unplement the effect of propeller rotation. Pyramid ceUs were used for the suiface of propeller and boundaries, and tehahedral ceUs were filled ia the block. On the other hand, stmchored ghds were applied to the other domaias expect for the slidmg block. Fig. 4 shows the outline of giid system mcludmg boundary conditions and the interface between shduig and other blocks. While the test section of the cavi-tation hinnel was rectangular, a half chcular sectional profile was used for the compucavi-tational domam to achieve a good grid quahty of shuctared giid. The grid sizes were 1.4 M and 2.6 M ceUs for the shduig block and the other blocks, respectively.
506 Int. J. Nav. Archit Ocean Eng. (2013) 5:502-512
Fig. 4 Outline of grid system for computational domain (top left) and propeller block (top right) and x-z plane section showing the interface between sliding and outer blocks (bottom).
Simulation method
As the numerical model for cavitation flow, Schneer and Sauer (2001) was apphed in this research. Bubble number density was set as le+15, which corresponds to the bubble radius of 3 pm and 13jUm at a= 0.1 and a= 0.9, respectively. To improve the convergency of cavitation flow and reduce the computational tune. Multiple Reference Frame (MFR) was used at first and Shdmg Mesh Model (SMM) was tiien apphed to shnulate tiie rotation of propeUer. Propeller rotated with a constant time step corresponding to the rotating angle of 1.5° to obtain 60 data per propeUer blade phase. Time histories of fluctuating pressure on the hull surface were recorded to compare with the experimental results at the same positions as the pressure fransducers instaUed on the model test. The simulation methods applied in this research are summaiized hi Table 2. The utiet boundaiy condition was set as constant velocity witii 3% and 20Ö for turbulent intensity and turbulent viscosity ratio, respectively. The waU y+ on huU and propeller were about 130 and 200.
A propeUer coated with the rough pamt tended to increase the cavity extent and pressm-e fluchiation as compared witii a smooth surface propeller m the expeiiment. However, smce it was hnpossible that the effect of the pamt was knplemented m numerical shnulation, a smaUer cavitation number was used for the simulation uistead of the rough paint. The adjustment was approached with ignomg a wave height at stem which was considered in the model test.
Table 2 Summary of simulation methods.
Item Method
Governing equation RANS
Turbulence model RSM w/ standard wall function
Cavitation model Mixture
P-V coupling SIMPLEC
Pressure solver Standard
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RESULTS A N D DISCUSSION
In this research two kmds of sunulations were executed and compared with the experimental results. The first shnulation was perfbiTtied at two draught conditions to investigate the effect of cavitation number. The other shidy was to validate the detectability of the numerical shnulation about the differences of cavitation pattem and pressui'e amplihide fi-om the smaU mo-dification of propeUer geomehy.
Prior to the cavitation shnulation, the bare huh without the propeller was shnulated to compare the wake field at the pro-peller plane. Fig. 5 shows the comparison of velocity contours and vectors between the experimental data and simulation resuh at the propeUer plane. Model ship speed was 1.35 m/s in the towhig tank test. Inlet velocity of the numerical shnulation was 5.5
m/s, which was tiie same velocity as the cavitation hinnel. The velocity contour and vector are nomalized by the ship speed or
utiet velocity. The wake velocities and contours at the towmg tank and shnulation are very sunilar, while the axial velocity at tiie cavitation hmnel is about 0.1 faster at outer radh of propeller disk. It means that the velocity at propeUer plane hi the cavita-tion tunnel is probably conhacted and accelerated due to the blockage effect. The variacavita-tion of axial velocity at the cavitacavita-tion tunnel is not smooth aroimd 20° and 340°.
- • . m i
:'\ir:V -A^^it^.^
1.00 0 . 9 5 0,90 0 . 8 5 0.80 0,75 0,70 0,55 0 . 6 0 0,55 0,50 0,^15 0,40 0 . 3 5 0,30Fig. 5 Velocity contours and vectors of experiments (left: towing tank, middle: cavftation hmnel) and simulation (right) at propeller plane (dashed circle: outhne of propeller disk).
Draught condition
The sunulations were performed at design and baUast di-aught condhions, and tiie shnulation results were compared with the experimental results of SCAT. The propeller tested m the model test is a 4-blade propeUer (Prop-A) designed for a crade oil tanker. Mean pitch ratio and expanded area ratio of the propeUer are 0.655 and 0.480, respectively. The shnulation conditions are summarized in Table 3. The cavitation number is defined as
P-Pv
O.Spn^D^ (8)
where /> is a static pressure at the 70% of propeller radius above tiie propeUer shaft center and p^, is a vapor pressure. A propeller rotation speed and a propeller diameter are denoted as n and D, respectively.
Table 3 Sununaiy of simulation conditions to shidy the effect o f draught condition.
Design Ballast
Inflow speed 5.5 m/s
Propeller diameter 226.1 mm
Propeller speed 38.0 rps 39.3 rps
508 Int. J. Nav. ArchU. Ocean Eng. (2013) 5:502-512
The thrusts of the sunulations at the design and ballast conditions were about 4% higher than those of the expeiiments. The larger thrusts of the sunulations resuh fi-om the slower axial velocity at the propeUer plane as compared in Fig. 5.
Cavitation patterns at the propeller blade angle of 0°, 20°, and 40° at the design and baUast di-aught conditions are compared with tiie expeiimental resuhs hi Figs. 6 and 7. The cavity extent in the simulation ai-e expressed with tiie isosmface of « = 0 . 1 . The shnulation results have some limitetions to caphu'e the tip vortex cavitation, but the cavity patterns generally well agi'ee with the expeiiments. At the design di'aught condition, the leadmg edge cavitation near 0.8 R of the propeller blade is not appeared hi the numerical shnulation, while it is observed witii veiy unstable behavior hi the expemnent. A t the ballast draught condition, the cavity extents at aU blade angles weU coirespond with the experiments. The sheet cavitetion was not appeared m the range between 90° and 330° m tiie expemnents, but it was observed until about 240° m the sunulations due to the slower axial velocity than the experunent as shown hi Fig. 5.
Fig. 6 Comparison of cavhation patterns at design draught condition for Prop-A (top: EFD, bottom: CFD; left: 0°, middle: 20°, right: 40°).
!
Fig. 7 Comparison of cavitation patterns at ballast draught condition for Prop-A (top: EFD, bottom: CFD; left: 0°, middle: 20°, right: 40°).
Int. J. Nav. ArchU. Ocean Eng. (2013) 5:502-512 509
Fig. 8 shows an instantaneous pressm-e dishibution on the huU suiface mduced by the propeUer cavitation as well as field velocity around propeller in x-z plane section. Very high pressure concenhates above the propeUer position, especially on star-board side rather than port side. Thne histories of pressui'e fluchiation on P2 hansducer at the design and ballast draught con-ditions are plotted in Fig. 9. Hull pressure is expressed with the pressure coefficient defined as
where Ap is the pressure fluchiation amplihide from the mean pressiu-e. The pressure fluchiation at the design draught condi-tion has eight peaks timing one revolucondi-tion, whUe that at the baUast di'aught condicondi-tion has four peaks.
20£K1Q - ] 150Ö0 lODoa 5CG0 -5DÜ0 -10000 -isooa •2 5 000 • :-0v.> --iCDÜO -iQOGO H 6500 62(ra [ - j EGCO 5300 5Q0O 4700 4400 4100 aecD 3S00 320D 3&00 2600 -I 230Q 2000
Fig. 8 Instantaneous pressure distributions in x-z plane section including hull and propeller surfaces (left) and hull suiface pressure above propeller position (right) during propeller operation.
0.04
-0.04
Design Draught Condition Ballast Draught Condition
90 180 270
Propeller Blade Angle (deg.)
360
Fig. 9 Comparison of pressure fluchiations of P2 transducer at ballast and ballast draught conditions for Prop-A.
The hull pressme amplihides for Prop-A at the design draught condition are compared with the experimental resitits m Fig. 10. Since the position of P7 was concealed beneath the radder hnnlc, P7 could not be measmed in this research. For the fust blade fi-equency (IBF), the shnulation results show good agi-eement with the expeiimental results m tiie tendency and magni-hide of pressure fluchiation, but the pressure amplitudes of Pl and P2 at starboard side ai-e about 20% and 10% higher than the expeiiments, respectively. At the other pressure hansducers, the pressure amplitudes are very simUar to the expeiiments. The second blade fi equencies (2BF) of the shnulation are ahnost half of the experimental results, even though the tendency is si-milar to the experhnents. As explahied hi Fig. 5, tiie gradient of axial velocity ai-ound 20° and 340° probably affects the hicrease of 2BF amplihide m the expeiiment. In conhast, the velocity gi-adient in the simulation is very smootii, resulting in relatively small amplihide of 2BF. And the numerical difhision and giid fmeness around the propeller tip nught be another reason for
510 Int. J. Nav. Archit. Ocean Eng. (2013) 5:502-512
smaller 2BF amplitude in the shnulation. OveraU, the hull pressure amplihides of sterboard side are higher than port side, and the pressui-e amplihide of P6 located upsheam fi-om the propeUer plane is higher tiian P3 located at tiie propeller plane.
Fig. 11 shows tiie comparison of the huU pressm-e amplihides at the baUast di-aught condition witii the experimental results. The amplitudes of IBF are about 10% higher than the experiments except for Pl and P6. The pressure amplihide of P l is about 28% higher than the experhnent, while that of P6 is about 5% lower. Neveitheless, the tendency of pressure amplitude is very close to the expei-iment. However, the amplihides of 2BF are significantly lower than the expei-hnents because the effect of axial velocity gi-adient hi the shnulation may be duninished due to the relatively large cavity extent m flie baUast di-aught con-dition. This phenomenon can be explamed tlii-ough Fig. 9. The two peaks with the hiteival of about 40° at the crest of the signal obseived hi tlie design load condition are not obseived in the ballast condition.
0.020 0.015 o (U 0.010 O O Ü) 0.005 00 <v Pl P2 • EFD (IBF) • EFD{2BF) • CFD (IBF) • CFD(2BF) P5 P6
Fig. 10 Comparison of pressure amphtudes at design draught condition for Prop-A.
0.030 •a 0.025 £ 0.020 'o % 0.015 O O ï 0.010 =1 </) in ï 0.005 Ü . 0.000 • EFD(IBF) • EFD(2BF) • CFD(IBF) UCFD(2BF) P3 P5
Fig. 11 Comparison of pressure amplitudes at ballast draught condition for Prop-A.
Propeller geometry
Anotiier propeUer (Prop-B) was designed to shidy on the effect of propeUer rake dishibution. Prop-B has tiie baclcward rake of 0.014D at tip, while Prop-A has the forward ralce of 0.007D at tip. The other pai-ameters for propeller geomehy such as pitch, camber, and chord mcludmg propeller diameter are exactly same. Due to the rake dishibution, the rotation speed of Prop-B is slightly higher tiian that of Prop-A; as a result, the cavitation number of Prop-B is relatively lower than that of Prop-A. The si-mulation conditions for Prop-A and Prop-B are smnmaiized m Table 4.
The cavitation patterns at tiie ballast draught condition for Prop-B are compared with the expeiimental results m Fig. 12. The cavity extents of Prop-B are not different fi-om Prop-A hi both expeiiment and shnulation. However, the effect of propeller rake is disthiguislied hi the hull pressme amplihide as shovm m Fig. 13. Prop-B with tiie baclcward rake reduces the pressm-e amplitade of about 5% at P l to P3 and about 13% at P4 and P5 hi tiie expeiiment. Shnilarly, the amounts of reduction are about 10% at Pl to P3, about 5% atP4 and about 10% at P5 m the shnulation. From the shnulation results, h can be concluded that the numerical simulation usmg RANS is useful to detect the difference of pressiue amplimde due to the smaU modification of propeller geomehy.
Table 4 Summai-y of simulation conditions to study the effect of propeller geomeh-y.
Prop-A Prop-B
Inflow speed 5.5 m/s
Propeller diameter 226.1 mm
Propeller speed 39.3 rps 40.6 rps
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CONCLUSIONS
Numerical simulation studies using RANS for cavitation flow and hull pressure fluchjation of maihie propeUers were pre-sented in this paper. A computahonal domain including a firU huU body submerged under the free suiface was used to simulate dhectly the wake field at the propeller plane. And the sunulahon results were compared wifli the experimental results peifoimed hi the cavitation tunnel.
Fig. 12 Comparison of cavitation patterns at ballast draught condition for Prop-B (top: EFD, bottom: CFD; left:0°, middle:20°, right: 40°).
Two Idnds of smdies were executed hi this research. A t fii'st, the numerical simulations were peifonned hi design and ballast draught conditions to smdy the effect of cavitation number. The cavitation patterns at both conditions agreed weU with the experimental results. The first blade frequencies of the pressme flucmations in the simulations were shghtly larger than the expeiiments, whereas the tendency of the pressm'e amphtudes according to the location of the hansducers was very sunilar to the experiments. However, for the second blade frequencies the sunulations showed some hmitations to predict the magnihide of pressm'e fluctaation due to the difference of walce field at the propeUer plane. The other stody was to validate the detectabihty of the numerical shnulation for the cavitation pattem and huU pressm'e amplitade. Two propellers with shghtly different geo-mehy were shnulated and compared with the experimental results. The cavity extents of the simulation and experiment were not different between two propellers. However, the pressm'e amplitades of two propellers had small difference, and that was vahdated hi the numerical shnulation.
0.030 q: 0.025 e 0) ' ü i t O) o O Ï 0.010 =! c/1 u~> 0.020 0.015 0.005 0.000 • EFD (Prop-A) • EFD (Prop-B) • CFD (Prop-A) • CFD (Prop-B) Pl P2 P3 P4 PS P5
512 Int. J. Nav. Archit Ocean Eng. (2013) 5:502-512
In conclusion, the cavitahon shnulation usmg RANS showed reliable peifoimance to predict the cavitation pattem and hull pressure amplitude Üirough this research. To improve the accm-acy of 2BF haimoiucs m the simulation, however, numerical methods to achieve more accui'ate wake field at the propeller plane need to be stodied m detail. For the fiiither work, various ship types wiU be simulated and compared with expeiimental data to evaluate tins numerical shnulation method.
A C K N O W L E D G E M E N T S
This work was partiaUy cairied out m the research gi'ant. Development of New Propulsion System for Fuel Saving of Ships (No. 2011-10040081), fimdedby the Korean Mmishy of Knowledge Economy.
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