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ТЕОРИЯ КОРАБЛЯ И СТРОИТЕЛЬНАЯ МЕХАНИКА
DOI: 10.24937/2542-2324-2021-4-398-15-23 UDC 629.5.018.12+629.5.035:532.51
Zhang Qingshan*' **, Chen Weimin*' **, Du Yunlong*' **, Dong Guoxiang*' **
State Key Laboratory of Navigation and Safety Technology, Shanghai Ship and Shipping Research Institute, Shanghai, China Key Laboratory of Marine Technology, Shanghai Ship and Shipping Research Institute, Shanghai, China
FULL-SCALE SELF-PROPULSION SIMULATION WITH A DISCRETIZED PROPELLER
A comparison between towing tank testing and full-scale CFD simulations is presented at three different target speeds. For the current self-propulsion simulation, the self-propulsion point was obtained using polynomial interpolation. The studies of boundary layer thickness, a basic grid uncertainty assessment and verification were performed to give some confidence of grid application to current self-propulsion simulation. All simulations are performed using a commercial CFD software STAR-CCM+. It is concluded that with high-fidelity numerical methods, it's possible to treat hull roughness and directly calculate full-scale flow characteristics, including the effects of the free surface, none-linearity, turbulence and the interaction between propeller, hull and the flow field. The authors declare no conflicts of interest.
NAVAL ARCHITECTURE
Б01: 10.24937/2542-2324-2021-4-398-15-23 УДК 629.5.018.12+629.5.035:532.51
Жанг Кингшан*' **, Чен Веймин*' **, Ду Юнлонг*' **, Донг Гуаксианг*' **
Государственная ведущая техническая лаборатория навигации и безопасности, Шанхайский научно-исследовательский институт судостроения и судоходства, Шанхай, Китай Ведущая лаборатория морской техники, Шанхайский научно-исследовательский институт судостроения и судоходства, Шанхай, Китай
МОДЕЛИРОВАНИЕ САМОХОДНЫХ ХАРАКТЕРИСТИК НАТУРНОГО СУДНА С ДИСКРЕТНЫМ ГРЕБНЫМ ВИНТОМ
Представлено сравнение испытаний в буксировочном бассейне и моделирование методами вычислительной гидродинамики (СЕБ) натурного судна при трех различных заданных скоростях. Для текущего моделирования режим самохода был получен с помощью многочленной интерполяции. Были проведены исследования толщины пограничного слоя, оценка неопределенности основной сетки и верификация для обеспечения уверенности в использовании сетки в данном моделирований самоходных характеристик. Все моделирование выполнено с помощью коммерческого ПО СЕБ - STAR-CCM+. Делается вывод о том, что с помощью высокоточных численных методов можно учесть шероховатость корпуса и непосредственно вычислить характеристики натурного течения, включая эффекты свободной поверхности, нелинейности, турбулентности и взаимодействия ГВ, корпуса и поля течения.
Авторы заявляют об отсутствии возможных конфликтов интересов.
For citations: Zhang Qingshan, Chen Weimin, Du Yunlong, Dong Guoxiang. Full-scale self-propulsion simulation with a discretized propeller. Transactions of the Krylov State Research Centre. 2021; 4(398): 15-23.
Для цитирования: Жанг Кингшан, Чен Веймин, Ду Юнлонг, Донг Гуаксианг. Моделирование самоходных характеристик натурного судна с дискретным гребным винтом. Труды Крыловского государственного научного центра. 2021; 4(398): 15-23.
Introduction
Введение
Traditionally, the engineering significance features in marine hydrodynamic flow at full scale are deduced from the model-ship extrapolation. Moreover, it is well known that it exceeds the practical limitations of matching both Reynolds and Froude scales simultaneously in towing tanks. In contemporary engineering practice, these limitations are reliably circumvented by the vast practical experience and unique extrapolation procedures for standard hull forms. In recent years, the International Maine Organization (IMO) has introduced new regulations to reduce the negative impact of ships on the natural environment, leading to the increment of worldwide research in marine hydrodynamics. Nowadays, an increasingly popular way with a full-scale simulation using Computational Fluid Dynamics (CFD) becomes an alternative option to estimate the ship performance, eliminating the scale effect and the need for extrapolation.
Prediction of the self-propulsion point of the ship is one of the main practical problems in marine hydrodynamics. Although full-scale simulation avoids the shortcomings in model-scale, its high time-consuming and uncertainties have brought doubts to ship-owners and ship designers and hindered the application and promotion of this method in the shipbuilding industry. Up to now, most of the full-scale numerical simulations are performed in universities and research institutions and are rarely used in engineering projects despite improvement in numerical algorithms and computer gain in power. Carrica et al. [1] applied a discretized propeller with dynamic overset mesh in self-propulsion simulation with a speed controller. They utilized this method in the evaluation of three ship hulls: the singlepropeller KVLCC1 tanker appended with a rudder, the twin-propeller fully appended surface combatant model DTMB 5613, and the KCS container ship without a rudder. The agreement between their results and experimental data illustrates the feasibility of numerical simulation of self-propulsion in full-scale. Castro et al. [2]
Table 1. Main particulars of ship and propeller Таблица 1. Основные характеристики судна и ГВ
carried out full-scale self-propulsion computations using discretized propeller for the KRISO container ship KCS, revealing that the propeller operates efficiently in full-scale and is subject to smaller load fluctuations. Ponkratov and Zegos [3] described the procedure of sea trial experiment and validated full-scale CFD self-propulsion simulation with sea trial data. Based on this procedure, the world's first workshop on full-scale hydrodynamic computer simulations was held by Lloyds Register of Shipping in 2016, where many participants validated their CFD simulation results against sea trial data. Subsequently, Jasak et al. [4] performed CFD validation and grid sensitivity studies of full-scale ship self-propulsion and compared their results with seal trial measurements. They applied an actuator disc model to replace a discretized propeller and a speed controller to control the rotating propeller rate during the simulations. Their results demonstrate the possibility of using high-fidelity numerical methods to calculate ship scale flow characteristics directly. Sun et al. [5] have also performed full-scale self-propulsion to analyze the full-scale ship self-propulsion performance and conducted a comparison with the statistical sea trial results. Unlike Jasak [4], they utilized a discretized propeller in their full-scale self-propulsion simulations. Their results show good agreement with the seal trail data, especially for cases that have considered both roughness and free surface effects.
This article aims to compare the results of self-propulsion point prediction between full-scale simulation and model test. Moreover, a bulk carrier's self-propulsion simulations in full-scale with a discretized propeller were performed at three different target speeds of 13.5 kn, 15.0 kn and 16.5 kn. Furthermore, the corresponding self-propulsion point was obtained by polynomial interpolation separately. In order to improve the confidence of the calculation results, the grid convergence and verification studies were carried out based on the unpropelled case with a smooth surface condition. And the influence of hull roughness was analyzed by two methods: Holtrop-Mannen and CFD simulation.
Ship Propeller
Length between perpendicular Lpp [m] 314.6 Diameter D [m] 9.6
Beam B [m] 52.5 Pitch P/D [-] 0.7409
Draft T [m] 18.1 Blade number Z [-] 4
Displacement V [m3] 253083.5 Rotating direction [-] Right-hand
Wetted surface S [m2] 24462.4
Fig. 1. Geometry for full-scale self-propulsion
Рис. 1. Геометрия натурного судна для прогнозирования самоходных характеристик
Ship particulars
Характеристики судна
A bulk carrier was selected as a case study ship, a 230,000 DWT bulk carrier designed to operate on the East Pacific and the South China Sea. The principal particulars of the ship are present in Table 1. The simplified geometric model of the ship is shown in Fig. 1.
Numerical modeling
Численное моделирования Governing equations
The numerical method applied to solve discretized governing equations of mass, momentum and energy conservation in the current study is an Unsteady Reynolds-Averaged Navier-Stokes (URANS) method. These governing equations were solved by the commercial CFD software STAR-CCM+. For incompressible flows, the averaged continuity and momentum equations may be written as:
d
(p U ) д --- +—
dt дх
-(putuj + pu\u'j) :
dp + dTtL
dxt dXj
)(pul )
dxt
= 0,
(1)
(2)
where ut refers to the time-averaged velocity components and p is the time-averaged pressure. p is the density of the fluid. The item Tj is the mean Reynolds stress tensor component. This viscous stress for a Newtonian fluid can be expressed as
dut du j -+ —-
dx L dxt
è j 1 0
(3)
The solver uses a finite volume method which discretizes the governing equations. A second-order upwind numerical scheme was used for the convection term, and a first-order scheme was applied for temporal discretization. The flow equations were solved in a segregated manner, and the continuity and momentum equations were linked with a predictor-corrector approach. To capture the interface between multi-phases, Volume of Fluid (VOF) scheme introduces an additional transport equation for the unknown variable a that represents the volume fraction of water inside each finite volume cell, which is defined as follows:
— + V-(aU) = 0.
dt
(4)
In order to complete the URANS equations, the turbulence model was selected as realizable k-e with all y+ wall treatment model in our simulations. It offers a good compromise between robustness and accuracy, which is also a common choice from other research fellows [6-8].
A Dynamic Fluid Body Interaction (DFBI) scheme was applied with the ship free to move in heave and pitch directions to simulate ship motions. Although in deep waters, the combined effect of sinkage and trim is known to be small on resistance and may even be neglected in some cases [9].
Computational setup
The setup of the computational domain is shown in Fig. 2 (on the color insert). The computational domain's basic size was specified, and the ship was placed in a suitable position to avoid reflection from the Left, Right and Outlet boundaries. Additionally, to minimize the reflections of the wave on Left, Right and Outlet boundaries, numerical wave damping was applied with a wave damping length of \Lpp.
For capturing the Kelvin wave pattern and flow around the ship, the ITTC recommended discretization of the volume was applied with standard refinements in the areas of free surface and near hull, especially the wake in Fig. 3 (on the color insert). Mesh solution in the region of the ship's boundary results in a value of y+ within a range of 30-300. In order to carry out a grid sensitivity study and predict the CFD uncertainties, systematic studies were performed applying the unpropelled cases with a smooth surface condition. An approach with a symmetry plane was applied on the
Fig. 2. Setup of the computational domain
Рис. 2. Схема вычислительной области
Fig. 3. Volume mesh Рис. 3. Объемная сетка
Fig. 4. Variation of the velocity profile within the boundary layer as a function of the Reynolds number for a fully developed flow in a plane channel simulated by DNS [20]
Рис. 4. Изменение профиля скорости в пограничном слое в функции числа Рейнольдса для полностью развитого течения в плоском канале, моделируемом DNS [20]
—г"!-1-
Channel flow ReT = 5200 2000 1000 550
Extent of log-law region
C/+ = 2.51n(y+)+5.2
Right boundary, and the total volumetric cell number was equal to 5.51 M. Based on the Generalized Richardson Extrapolation Method [10], the verification studies were performed for the speed of 15 kn for two coarser meshes with a total volumetric cell number of 1.28 M and 2.64 M and one finer mesh with a total volumetric cell number of 13.21 M. Base size of the element was systematically varied by the factor V2 in X, Y and Z direction in each mesh. The difference in the obtained value of total resistance between the base and the finer mesh was 0.45 %. Thus, the current base mesh with a total volumetric cell number of 5.51 M was applied instead of the finer mesh. The verification study results were presented in Table 2-4, where mesh 1 represents the fine mesh, while mesh 3 corresponds to the coarse mesh.
Treatment of hull roughness
In many cases, the hull roughness is usually not taken into account in the numerical simulation of ship performance, especially for model scale simulations. However, for a full-scale simulation, a good example can be a comparative analysis of hull roughness's influence on calm water resistance. The 19th ITTC [11] recommended that if roughness measurements are available, then the Bowden-Davison formula should be replaced by Townsin's formula. In the current described case, the hull roughness measurements are unavailable. Therefore, the effect of the hull roughness was calculated based on the Bowden-Davison formula:
AC/ =
1
105
è Lwl
- 0.64
x10-
(5)
in the study of the influence of the hull roughness on calm water resistance [2, 7, 14, 15]. The effect of the flow around the rough surface is an increase in turbulence. According to the study of Millikan [16], the two-point wall function model is implemented, where the velocity at the first node away from the wall is computed based on the following formula:
U + = -ln(y+ ) + B-DU+ к
(6)
where k is the von Karman constant, y+ is the non-dimensional normal distance from the boundary, B is the smooth wall intercept and AU+ is the roughness function. In STAR-CCM+, Eq. (6) is defined as:
1
*trb
ln( E'y + ),
(7)
where E = Elf and the default value of the coefficients are k = 0.42 and E = 9.0. The roughness function f is a slightly expanded version of the expression that was given by Cebeci and Bradshaw [17], which is defined as follows:
/ =
1
B
R - R+
R+ - R+
rough smooth
+ CR+
for
R +£ R+
i
for
(8)
D+ < D+ < D+
smooth rough
B + CR+
for R+ > R.
'smooth
where the exponent a is expressed as:
a = sin
П log(R + / RSmooth )
According to ITTC [12], hull roughness, which has no measured data, was assumed to be ks = In this article, two kinds of approaches were applied to investigate the effect of hull roughness. For the simplified method, the simulations of calm water resistance were run with the assumption that the hull surface is hydraulically smooth. Furthermore, the roughness allowance was computed based on the formula proposed by Holtrop and Mennen [13]. According to this formula, the increase of friction resistance was equal to ACf = 0.176x10 ^, which was speed independent. Therefore, the appropriate increase in total resistance due to each speed's roughness was obtained by multiplying ACf by 0.5pSSFs2. For the complicated method, the simulations of calm water resistance were run with a roughness model. The same method was applied
2 log(Rrough / ^smooth )
The parameter R+ is expressed as follows:
R+ =■
v
(9)
(10)
where r is the equivalent sand-grain roughness height, and the default values of the coefficients are given by Cebeci and Bradshaw [17]: B = 0, C = 0.253, R+smooth = 2.25, R+rough = 90. According to the study of Demirel, Turan [18], the roughness characteristics and roughness functions for the coated surfaces can be built into the wall functions of commercial CFD software. Therefore, Coefficients B and C in Eq. (8) were modified into 0.2 and 0.22, respectively, to fit the roughness function.
Taking hull roughness into account when simulating full-scale self-propulsion, Castro, Carrica [2] estab-
*
lished a relationship between hull roughness height and sand-grain equivalent roughness height. They calculated the friction coefficient of a full-scale ship with the formula Cfs = Cfos + ACf, which is an estimate for the KCS hull and corresponds to a flat plate of length Lpp. As proposed by White [19], the drag coefficient for a flat plate in a fully rough regime is
=
1.89 + 1.62log
10
L
s\-2-5
PP
(11)
00
where CD is the drag coefficient, Lpp is the length of a rough flat plate and e is the sand-grain roughness height. By making CD = Cfs, the sand-grain roughness height e is calculated. It can be noted that the sand-grain roughness height is much smaller than hull roughness height, which was applied to the equivalent sand-grain roughness height r in STAR-CCM+ for full-scale simulations.
Method of obtaining self-propulsion point
With the self-propulsion simulations results, three rotating rates of the propeller were applied for extrapolating the propulsion point at a single target speed. For each rotating rate N of the propeller, the total ship resistance R, propeller thrust T and propeller torque Q were obtained from the mean value of the last 100 physical seconds. Assuming that the rotating rate and the monitoring variable (ship total resistance, propeller thrust and propeller torque) satisfies a polynomial relationship, it can be expressed as y = Ax2 + Bx + C. With these three sets of data, three different polynomial equations with respect to the rotating rate N can be obtained. By making R = T, the rotating rate N for propulsion point was calculated. Thus, with this new obtained value N, ship total resistance R, propeller thrust T and propeller torque Q were finally calculated.
Results and discussion
Результаты и дискуссия
The CFD simulation results for the current study ship are present in this section and directly compared to those determined by towing tank testing and extrapolated to a full-scale using the "ITTC-78 model-ship correlation line" based on the two-dimensional method, rather than introducing the form factor. In addition, the studies of boundary layer thickness, a basic grid uncertainty assessment and verification were carried out based on the unpropelled case, giving some confidence that the grid size is appropriate for the current study.
Boundary layer thickness and mesh generation
Whenever possible, it is good to apply the low-Re approach to resolve the boundary layer. Therefore, a suitable mesh with many prism layers (approximately 20) near the ship's body surface is required. Meanwhile, given the grid quality requirement, the grid needs to be refined in a wall-tangential direction to lower the aspect ratio of these prism layer cells. For the reasons mentioned above, a high cell count is inevitable. For the model scale, the total cell number is about 2 million for a half ship, while it is increased to approximately 10 million, which might be only suitable for academic research.
In the current study, the URANS method was applied to solve discretized governing equations of mass, momentum and energy conservation. For wall treatment, a realizable k - e with all y+ wall treatment model was selected in our simulations. At the model scale, the grid only resolves the logarithmic part of the boundary layer, leaving the viscous sublayer and the buffer layer unresolved, as shown in Fig. 4 (on the color insert). There is enough data from towing tank testing to validate that good results can be obtained in model scale simulation when the dimension-less distance of the first cell center from the wall, the so-called y+, is set to be between 50 and 100. As shown in Fig. 4, the logarithmic range in velocity profiles starts at approximately the same value of y+ almost independent of changes in Reynolds number. Also, as the Reynolds number increases, it extends to higher values. At full scale, the Reynolds number is approximately three orders higher than that in model scale, wherefore there is no reason to require the same value of y+ in both model scale and full scale. Siemens PLM Software [20] have deduced that if one takes a point in the same relative position within the boundary layer in full scale and in model scale, then the dimensionless value y+ satisfies the following formula:
У full
ymodel.
(12)
It is no doubt that as long as it falls within the logarithmic range, one can use grids with a lower value of y+. For example, a grid that resolved the viscous sublayer in model scale, if scaled up to full-scale size, would lead to y+ values in the range around 200, which would be perfectly suitable provided the grid is sufficiently refined in tangential direction over curved surfaces [20].
Grid sensitivity study
To carry out a grid sensitivity study and to predict the CFD uncertainties, systematical studies were performed applying the bulk carrier appended with a rudder with a smooth surface condition. Furthermore, for observing the effect of volumetric cell number on the total resistance coefficient Ct, the computational domain was discretized in three different resolutions, and the simulations were run for each configuration. The grid refinement factor rG was chosen to be V2. The total resistance coefficients for each mesh configuration were computed at a design speed of 15 knots and are given in Table 2. The total resistance coefficient was overestimated by 0.45 % compared with that of finer mesh. Thus, the fine mesh configuration was chosen for all subsequent computations.
Verification study
In order to detect and show the predictive capability of the CFD method, a verification study was carried out to assess the spatial uncertainties of the simulation. The Grid Convergence Index (GCI) method based on Ri-
chardson's extrapolation [21, 22] was applied to estimate the discretized numerical uncertainties, which was used by many authors [23-25]. Three significantly different sets of grid were selected, recording the values of representative grid size, grid refinement factor and the key variables relevant to the objective of the simulation study. In this paper, the key variables were chosen to be the frictional resistance coefficient Cf and the total resistance coefficient Cfe. Immediately after that, the apparent order of the method p was calculated using the expression
p = —) M £32/ £21!+q(p)|; (13)
ln(r21 )
œ
q(p) =ln
rp - s è r32 - S 0
(,
s = 1 • sign
°32 è e21 0
(14)
(15)
where r21 and r32 are grid refinement factor, i.e., V2 in this paper, and e32 = - e21 = - is the key variable, i.e., Cf, Cs in this paper, on the kh grid.
Table 2. Cts results at different mesh configurations for full-scale simulation at 15 kn (Relative difference, D (%), is based on the Cs value using finer mesh data)
Таблица 2. Результаты Cts при разных конфигурациях сетки для моделирования самоходных характеристик натурного судна при 15 уз (Относительная разница, D (%), основана на значении Cts с более сгущенной сеткой)
Mesh configuration No. of Cells C ts (CFD) D (%)
Fine 5.51 M 0.001956 0.45
Medium 2.64 M 0.001960 1.85
Coarse 1.52 M 0.001988 2.04
Table 3. Calculation of the discretization error for Cf values Таблица 3. Вычисление ошибки дискретизации значений Cf
N1 n2 N3 ru Г32 ф1 ф2
5.51 M 2.64 M 1.28 M S S 0.001514 0.001506
Ф3 P Ф„ 2 e2 e 21 eext GCIfine21
0.001486 2.643856 0.001533 0.5284 % 1.2596 % 1.5964 %
Table 4. Calculation of the discretization error for Cts values Таблица 4. Вычисление ошибки дискретизации значений Cts
N1 n2 N3 Г21 r32 ф1 ф2
5.51 M 2.64 M 1.28 M Я 0.001956 0.001960
ф3 p Фех t21 ea21 e 21 ext GCIfine21
0.001988 5.614710 0.001946 0.2045 % 0.4962 % 0.6171 %
The extrapolated values are obtained using the expression
Ф21 =:
rP - 1 '21 1
(16)
The approximate relative error ea and extrapolate
relative error eext are then obtained by
ф1 - ф2
21
фехг - ф1
ф£
(17)
(18)
Finally, culated by
the fine-grid convergence index is cal-
gcile =
1.25e2
1
(19)
Table 3 and Table 4 illustrate this calculation procedure for three selected grids. As shown in Table 3 and Table 4, the numerical uncertainty in the fine-grid solution was reported as 1.5964 % and 0.6171 % for the frictional resistance coefficient Cf and the total resistance coefficient Cto respectively.
Roughness allowance
In this article, two kinds of approaches were applied to investigate the effect of the hull roughness, which are the Holtrop-Mennen method and the roughness model proposed by Demirel, Turan [18]. As shown in Table 5, it was more noticeable that the increase in total resistance coefficient due to hull roughness predicted employing CFD simulations is much smaller than that calculated according to the Holtrop-Mennen method. It seems that the CFD simulation with the prediction of hull roughness using Demirel et al.'s method is much accurate than that using the
Holtrop-Mennen method. Therefore, Demirel et al.'s method was applied for all subsequent computations of self-propulsions.
Full-scale self-propulsion simulaitons
Computations for self-propulsion at full scale were carried out at three different target speeds with a rough surface condition using Demirel et al.'s method. Moreover, the self-propulsion point was obtained utilizing polynomial interpolation for each target speed.
The above-mentioned grid sensitivity study and verification study shows that the fine mesh can provide accurate calculation results. Meanwhile, it can also capture more detailed flow field information, such as free surface elevation and downstream tip vortex of the propeller. Fig. 5 (on the color insert) displays the wave patterns obtained during towing tank testing and by full-scale CFD simulation at the speed of 15 kn. It allowed assessing the predicted free water surface elevation qualitatively. The Kelvin waves on the starboard side of the ship and wrinkle waves upstream of the bow can be noticeably observed. Fig. 6 (on the color insert) shows the resolved flow around the propeller. Tip vortices are well resolved in the refinement region, but only the strong hub vortex survives the translation to a coarse grid.
The capture of the detailed flow field information further improves the confidence of numerical calculations of full-scale self-propulsion. Table 6 presents the results of self-propulsion at three different target speeds. Two kinds of hull roughness values were introduced during the simulations: One with no measured data was assumed to be 150^m according to the 1978 ITTC performance prediction method [12] for a new-built ship. The other one was obtained from the shipyard based on the statistical regression, which is 100^m. The variation of hull roughness reveals that as the hull roughness increases, the thrust of the propeller increases, indicating that the hull roughness leads to incensement of ship resistance and energy
Table 5. Calculated differences in ship total resistance predictions obtained by towing tank testing and full-scale CFD simulations based on the Cte value at 15 knots
Таблица 5. Вычисление отличий в прогнозах полного сопротивления, полученных в буксировочном бассейне и при моделировании CFD на основании значения Cte при 15 уз
EFD Full-scale CFD inc. ACf acc. to H-M Full-scale CFD inc. ACf acc. to Demirel, Turan [18]
Total resistance coefficient Cts 1.9766 2.1364 1.9976
D (%) - 8.09 1.06
21
е
ext
Г
21
Table 6. Results of full-scale self-propulsion Таблица 6. Результаты натурных самоходных испытаний
Speed = 13.5 kn
Hull roughness Om) Propeller Thrust (kN) Propeller Torque (kNm) Propeller RPM Sinkage (m) Trim (deg)
100 1615.844 1644.713 65.402 -0.2088 0.1008
150 1620.086 1651.209 65.46 -0.2097 0.1015
Speed = 15 kn
100 1859.211 1943.909 72.002 -0.2692 0.1244
150 1892.993 1986.023 72.408 -0.2696 0.1247
Speed = 16.5 kn
100 2378.34 2533.923 81.28 -0.3354 0.1533
150 2388.299 2547.617 81.3978 -0.3364 0.1536
Ship Sinkage: "+" - trim by bow; "-" - trim by stern.
consumption. During the simulations, the ship motion in heave and pitch directions were also recorded. As the target speed increases, the sinkage of the ship varies from -0.2097m to -0.3364m while ship trimmed from 0.1015 degrees to 0.1536 degrees, revealing that the faster the ship runs, the deeper the ship sinks and the more significant angle the ship trims by bow.
Fig. 7 (on the color insert) shows the difference of thrust, torque and rotating rate of propeller between CFD simulation and towing tank testing at three different target speeds. As the target speed increases, the difference in propeller thrust is gradually getting smaller. Meanwhile, the difference in the rotating rate of the propeller varied within a small range of 0.48 % to 2.22 %. However, the ignored phenomenon is that the difference of propeller torque varied from -6.24 to -11.48, maintaining a negative value. This might be caused by the tetrahedral mesh type in the rotating region for the propeller.
Conclusion
Заключение
This work presents the feasibility of a CFD prediction of self-propulsion in full scale. To give some confidence that the grid size is appropriate for current self-propulsion, the studies of boundary layer thickness, a basic grid uncertainty assessment and verification were performed. Moreover, two kinds of approaches were applied to treat ship hull roughness. Then, the simulations of self-propulsion with a discretized pro-
peller were carried out at three different target speed with a rough surface condition. Moreover, the self-propulsion point was obtained utilizing polynomial interpolation for each target speed.
By performing grid sensitivity studies for an unpropelled case with a smooth surface condition, we estimated the grid uncertainty to be reasonably low: approximately 0.45 % at a speed of 15 kn. A strict verification study to assess the spatial uncertainties of the simulation was carried out. With the investigation of the effect of the hull roughness, a sand-grain equivalent roughness compatible with CFD wall-function model represents exceptional accuracy than the Holtrop-Mennen method. Although the predicted values of the propeller torque for three different target speeds were slightly unsatisfactory, the predicted thrust and rotating rate of the propeller consistent with those extrapolated from the "ITTC-78 model-ship correlation line" based on the two-dimensional method. This will essentially enhance our confidence to apply full-scale simulation in the prediction of the ship's self-propulsion performance in future ship designs.
As seen from Fig. 7, the preliminary work to improve the accuracy of the predicted torque of the propeller is encouraging. Also, to make it possible for industrial applications, a lot of scientific and industrial effort must be investigated, such as macros-routine to select the required rotation frequency of propeller to obtain self-propulsion point, reduction of consumption of computational resources and comparison with sea-trial date, etc.
Fig. 5. Wave pattern recorded during towing tank test (up) and calculated by CFD simulation (down) at a speed of 15 kn
Рис. 5. Волновой профиль, записанный во время испытаний в буксировочном бассейне (верх) и вычисленный в ходе моделирования CFD (низ) при скорости 15 уз
Fig. 6. Vorticity downstream of the propeller for self-propulsion at a speed of 15 kn
Рис. 6. Сбегающие вихри ГВ при самоходных испытаниях при скорости 15 уз
1 Speed = 13.5 kn VI Speed = 15.0 kn ut W Speed = 16.5 kn II
: Thrust 1 1 ore 1 14 e RPM 1" Thrust T га orq F U г RPM Thrust 1 II orqu ■ Diffftom EFD (%) 100ц»» ■ Diffftom EFD (%) 150цт e RPM
Fig. 7. Difference from towing tank testing results
Рис. 7. Разница по сравнению с результатами испытаний в буксировочном бассейне
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Received / Поступила: 13.09.21 Accepted / Принята в печать: 28.10.21 © Group of the authors, 2021
