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CFD assessment of the wind loads on an LNG carrier and floating platform models
Ocean Engineering 97 (2015) 30–36
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CFD assessment of the wind loads on an LNG carrier and floating platform models A.D. Wnęk, C. Guedes Soares n Centre for Marine Technology and Engineering (CENTEC), Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
art ic l e i nf o
a b s t r a c t
Article history: Received 3 May 2014 Accepted 10 January 2015
Numerical analysis of the wind forces acting on a floating LNG platform and an LNG carrier models is performed with a computational fluid dynamics (CFD) code and compared with experimental results obtained in a wind tunnel. The results are represented in the form of coefficients of the wind force components in X and Y directions and yaw moment for various angles of wind attack. The numerical study based on a CFD code started by performing several tests with different type and resolution of the mesh. The results were also compared with two empirical methods as well as additional experimental measurements of similar LNG carrier. Reasonable agreement of the numerical and experimental results was reached. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Wind loads CFD LNG carrier LNG floating platform
1. Introduction Wind loads on ships as the one of the crucial factors in their manoeuvrability have been studied for a long time using several methods. Wind can vary randomly in its velocity and direction, decreasing the manoeuvring capability of ships, especially at low speeds as occurs in approaches to quays for example. Paulauskas et al. (2009) made an investigation on safety of the ships in open sea ports, looking at the possible cases of wind direction that can cause dangerous situations or at least difficulties for moored ships in open ports. Since many years the analysis of the wind forces acting on the ships, has been studied using different techniques. Isherwood (1972) used previously published experimental data to propose a new expression for the force and moment coefficients derived from multiple regression analysis of the results. Blendermann (1996), using his own collection of wind load data, derived expressions for the wind load coefficients which are the function of the drag coefficients, the angle of attack, the frontal and transverse areas of the ship, the cross-force parameter and the coordinates of the centre of ship area. Both methods can be used for several types of ship. These two methods were also considered in the comparisons in the current work of the analysis of wind forces acting on a floating LNG platform and an LNG carrier. Haddara and Guedes Soares (1999) selected four methods (Isherwood, Blendermann, Gould, OCIMF) to determine and compare wind loads on large tanker in the loaded and ballast conditions.
n
Corresponding author. Tel.: þ 351 218 41 7607. E-mail address: [email protected] (C. Guedes Soares).
http://dx.doi.org/10.1016/j.oceaneng.2015.01.004 0029-8018/& 2015 Elsevier Ltd. All rights reserved.
Application of computational fluids dynamics (CFD) is becoming increasingly widespread in several fields including wind effects in marine structures. CFD analysis has many advantages compared with wind tunnel results, which however remain the reference for validation purposes (Palmer et al., 2003). Flexibility in the model design, duration of the analysis and comprehensive visualization of the results are only some of the good sides of CFD. Nevertheless, the results of this method are much dependent on the mesh adopted as well as the proper user inputs into the software like boundary conditions, turbulence model, time-step. Brizzolara and Rizzuto (2006) have also applied CFD for prediction of wind pressure on superstructures of large commercial ships, in particular the suction area on the main deck caused by the presence of a negative pressure field. The results were compared with the data obtained by the formulations based on the stability standards and showed some discrepancy with the formulation in existing rules. The difference between the results could be caused by the lack of the suction effect on the deck portion close to the upwind edge in the present rules. The methodology for the ship aerodynamic forces determination with CFD application has been presented by Kaup (2006) and the results were verified by experimental measurements. Wind tunnel tests have been performed in use of the ferry boat model and the results were presented in a form of nondimensional coefficients. Both, numerical and experimental results gave good agreement. Yelland et al. (2002) provided validation of CFD model simulations. The air flow simulations over research ships were performed at various wind speeds and different wind directions. Results were compared with wind tunnel experiments. Applications to the assessment of aerodynamic behaviour of sails have also been done
A.D. Wnęk, C. Guedes Soares / Ocean Engineering 97 (2015) 30–36
Nomenclature cx cy cN Fx Fy N V u v w LOA B H AF AL Rn yþ
longitudinal force coefficient lateral force coefficient yaw moment coefficient longitudinal force component parallel to the lateral area of the ship lateral force component perpendicular to the lateral area of the ship yaw moment wind velocity velocity component in x-direction velocity component in y-direction velocity component in z-direction length overall of the ship beam height frontal projected wind area of the ship lateral projected wind area of the ship Reynolds number nondimensional wall distance
for example by Clauss and Heisen (2005) and by Ciortan and Guedes Soares (2007), who compared their predictions with the experiments of Yoo and Kim (2006). The current paper presents a CFD analysis of the wind forces acting on a floating LNG platform and an LNG carrier at full incidence of wind attack, comparing with the experiments reported in Wnęk et al. (2015). An initial numerical and experimental study of those two ship models has been already presented by Wnęk et al. (2009, 2010). Results in a form of coefficients of the wind force components in X and Y directions and yaw moment were at reasonable agreement with experimental measurements. In order to improve the numerical results, additional computations have been performed using different mesh type and resolution. Comparison of the results has also been made with additional data of Isherwood (1972) and Blendermann (1996) as well as wind loads on a similar LNG carrier obtained in a wind tunnel and reported by WaveSpec (2007).
2. Experimental measurements The experimental tests have been performed in an open-jet wind tunnel (Fig. 1) of Instituto Superior Técnico (IST) in Lisbon
y ρ RANS k ε ω h r μt F1, F2 Cμ σk σε σω β βn κ γ CDkω Ω
31
distance to the nearest surface air density Reynolds-averaged-Navier–Stokes equations turbulent kinetic energy turbulent dissipation rate the specific dissipation rate height of cylindrical computational domain radius of cylindrical computational domain eddy viscosity blending functions model constant model constant model constant model constant model constant model constant model constant model constant cross-diffusion term absolute value of the vorticity
(Wnęk et al., 2015). The tunnel has a rectangular closed working section with characteristics given in Table 1. The maximum wind velocity that the tunnel was able to attain was 15 m/s, but in practice the average speed in all tests was around 10 m/s. A strain gauge load cell (BS50-C sensor) was mounted under the tunnel’s floor, connected to the model and was able to measure the forces and moments along three Cartesian axes. The gap between the model and the floor was 0.005 m. Two models made of wood (Fig. 2) represents a floating LNG platform and an LNG carrier in the 1/400 scale with characteristics given in Table 2. All tests were performed three times for each case on different days by different researchers. This procedure makes the results independent on each other and allows the quantification of the uncertainty, which turned out to be small. Measurements were performed in various angles of incidence. Each isolated model was rotated repeatedly starting from 01 angle with 101 step until reproduces the full incidence: 3601 in case of LNG carrier and 1801 in case of the floating platform, which is symmetric in relation to the Y axis. Only the horizontal forces and yaw moment were measured and the results were presented in the form of dimensionless coefficients: cx ¼
Fx 1=2ρAF V 2
;
cy ¼
Fy 1=2ρAL V 2
;
cN ¼
N 1=2ρAL LOA V 2
:
ð1Þ
where Fx, Fy are the wind force components (parallel, perpendicular to the lateral area of the model, respectively, Fig. 3) and N is a yaw moment with positive up Z axis. AF, AL, LOA present the models’ characteristics (Table 2), V the average wind velocity equal to 10 m/s and ρ is the air density 1.2 kg/m3.
Table 1 Wind tunnels’ characteristics. Cross-section area h b (m2) Length of the measurement zone (m) Maximum wind speed (m/s) Fig. 1. Wind tunnel.
1.3 2 3 15
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A.D. Wnęk, C. Guedes Soares / Ocean Engineering 97 (2015) 30–36
Fig. 2. Physical models of floating platform and LNG carrier.
Table 2 Models’ characteristics. Characteristic
floating platform
LNG carrier
Length overall LOA (m) Beam B (m) Frontal projected wind area AF (m2) Lateral projected wind area AL (m2) Reynolds number Rn
0.916 0.15 0.00683 0.05275 6.2 105
0.725 0.115 0.01051 0.05011 4.9 105
V, wind velocity angle of attack
N, yaw moment
Fx, longitudinal force oZ
X
FY, lateral force Y Fig. 3. Coordinate system, wind forces and moment.
halves of the cylinder) were adopting different positions. Kaup (2006) has chosen similar methodology and created similar computation domain for the determination of ship aerodynamic forces, with only one mesh for all computations. His results obtained by numerical analysis presented very good agreement with experimental measurements. Initially, for the floating platform, a multi-block structured hexahedral mesh was generated with 1.3 106 cells (Wnęk et al., 2009). The first layer thickness on the hull’s surface (“CFDhexa”) was proportional to the dimensionless wall distance yþ equal to 5, that was imposed for the calculation of the first layer thickness. To determine the proper resolution of the mesh is usually a problematic issue in CFD. Problems arise with complex geometries or with details of a simple geometry, when using structured mesh generation, because it is not automatic in ANSYS ICEM CFD software, which can be a big challenge (Werner et al., 2007). Therefore, the unstructured grids are expedient for all complex geometries, which still are not trivial to generate and require additional mesh convergence studies. Another mesh generated for the floating platform is a tetrahedral mesh with 3.2 106 cells without any prismatic layers on a surface (“CFDtetra”). To capture the boundary layers effects along the walls of the model, it is actually necessary to generate accurate prism layers on a model. A third mesh was generated with 5.2 106 tetrahedral elements and 20 prism layers on the model’s surface (CFDtetra_y þ). The first layer thickness was proportional to the wall distance yþ , which was close to 1. The computational mesh for the LNG carrier used by Wnęk et al. (2010) was a tetrahedral one with 4.5 106 cells without prismatic layers on a model’s surface, denoted here as “CFDtetra”. All those earlier computations have been repeated here with another mesh (“CFDtetra_y þ”) of 6.2 106 tetrahedral elements with 5 prismatic layers (Fig. 6). The first layer thickness on the surface is proportional to yþ, which is close to 0.1.
Fig. 4. Models of floating platform and LNG carrier.
3. Numerical study The study addresses the models of an LNG carrier and of a floating platform (Fig. 4), which were performed in Rhinoceros 4.0 software to represents the geometric characteristics of the physical models (Table 2) with their geometric details. The models were exported to ANSYS ICEM CFD software, where the computational domain and mesh generation took place as the next procedure of CFD pre-processing.
Fig. 5. Computational domain.
3.1. Computational domain and grid generation The computational domain has been created in a form of cylinder (Fig. 5), with dimensions: h¼ 1.6LOA, r ¼ 3.7LOA for the floating platform and h ¼1.5LOA, r ¼ 3.5LOA for the LNG carrier, where h is the height and r is the radius of the cylinder. Due to the required series of computations for different angles of incidence, this shape of the domain significantly decreased the computing time. Only one universal mesh was generated for all simulations in which only the walls of the inlet and outlet (two
Fig. 6. Tetrahedral mesh.
A.D. Wnęk, C. Guedes Soares / Ocean Engineering 97 (2015) 30–36
F 1 ¼ tanhðarg41 Þ:
3.2. Boundary conditions The same boundary conditions have been implemented on the models of the floating platform and of the LNG carrier. The no-slip condition was applied on the hulls (wall friction on the wall), that is, for the viscous flow, the velocity of the fluid particles on the boundary face is equal to the velocity of the face or, in another words, the fluid particles on the boundary surface move with the velocity of this surface: u ¼ Ux;
v ¼ V y;
33
w¼0
ð2Þ
arg1 ¼ min max
ð10Þ ! ! pffiffiffi k 500ν 4ρσ ω2 k ; 2 ; βωy y ω CDkω y2
ð11Þ
where CDkω is the cross-diffusion term: 1 ∂k ∂ω CDkω ¼ max 2ρσ ω2 ; 10 20 ω ∂xj ∂xj
ð12Þ
where F2 is a second blending function expressed as follows: F 2 ¼ tanhðarg22 Þ:
The free-slip condition was imposed on the imitation of still water free surface (floor of the domain), which is no friction on the wall. The top of the domain was treated as a symmetry plane. The wind velocity at the inlet was set to be uniform as taken from the wind tunnel tests (Eq. (3)). U x ¼ 10 m=s;
V y ¼ 0;
Wz ¼ 0
ð3Þ
At the outlet zero pressure was imposed.
ð6Þ
and Sij is a mean component of deformation rate of a fluid element in a turbulent flow. The model constants are C μ ¼ 0:09, σ k ¼ 1:00, σ ε ¼ 1:30, C 1ε ¼ 1:44, C 2ε ¼ 1:92. This standard k–ε model, widely used nowadays, has one particular disadvantage. It fails in a near wall layer and the shear stresses in adverse pressure gradient flows are often over predicted. The model was replaced by a shear stress transport (SST) model developed by Menter (1993). This is a combination of two common turbulence models: k–ε, which is accurate in the outer part of the boundary layer and Wilcox k–ω, which is more accurate in the near wall region. The transport equations are: ∂k ∂ρk ∂ðρui kÞ ∂u ∂ þ ð7Þ ¼ τij i βn ρωk þ μ þ σ k μt ∂t ∂xi ∂xj ∂xj ∂xj ∂ω ∂ρω ∂ðρui ωÞ γ ∂ui ∂ 1 ∂k ∂ω þ 2ρð1 F 1 Þσ ω2 ¼ τij βρω2 þ μ þ σ ω μt þ ∂t ∂xi υt ∂xj ∂xj ∂xj ω ∂xj ∂xj
ð8Þ where the kinematic eddy viscosity is equal to (9) a1 k maxða1 ω; ΩF 2 Þ
ð15Þ
where φ1 : σ k1 ¼ 0:85, pffiffiffiffiffi σ ω1 ¼ 0:5, β1 ¼ 0:075, a1 ¼ 0:31, β ¼ 0:09, γ 1 ¼ β1 =βn σ ω1 κ2 = βn , κ ¼ 0:41, and φ2p : ffiffiffiffiffi σ k2 ¼ 1:0, σ ω2 ¼ 0:856, β2 ¼ 0:0828, βn ¼ 0:09, γ 2 ¼ β2 =βn σ ω2 κ 2 = βn , κ ¼ 0:41. The SST model was also particularly examined in aerodynamic flow computations by Peng et al. (2007). The sensitivity of the results to the code settings as the application of different turbulence models has been presented in Wnęk and Guedes Soares (2012). Computations have been performed in ANSYS CFX code on 8 CPUs, Intels Xeons CPU E5420 @2.50 GHz, 16 GB of RAM. The average time of analysis for one angle of wind attack was about 5 h. The physical timescale was 0.005 which gave the best convergence.
4. Results
2
νt ¼
where Ω is the absolute value of the vorticity and y is a distance to the nearest surface. The set of all constants φ comes from the following relation, well described in Menter (1993):
ð5Þ
where dynamic turbulent viscosity is: k ε
ð14Þ
n
Initially, the air flow around the floating platform has been computed using the two-differential equations k–ε turbulence model (Hargreaves and Wright, 2007). At present this is one of the most universal non-algebraic turbulence models used in CFD, which is the simplest in use and well established within fluid dynamics (Versteeg and Malalasekra, 2007). The standard transport equations for turbulent kinetic energy k and turbulent dissipation rate ε can be expressed as follows ∂ðρkÞ ∂ ρuj k ∂ μ ∂k þ þ 2μt Sij Sij ρε ¼ μþ t ð4Þ ∂xj ∂t ∂xj σ k ∂xj
μt ¼ ρC μ
! pffiffiffi k 500ν ; 2 βωy y ω
ϕ ¼ F 1 ϕ1 þ ð1 F 1 Þϕ2 :
3.3. Turbulence model
∂ðρεÞ ∂ ρuj ε ∂ μ ∂ε ε ε2 þ þ 2C 1ε μt Sij Sij C 2ε ρ ¼ μþ t ∂t ∂xj k ∂xj σ ε ∂xj k
arg2 ¼ max 2
ð13Þ
ð9Þ
where F1 is a blending function that is one in the near wall region (k–ω) and zero far away from the surface (k–ε) and is expressed as follows:
4.1. Floating LNG platform Fig. 7 presents a comparison between wind force coefficients determined in the wind tunnel and by numerical analyses using three computational grids (Table 3), as well as the two empirical methods of Isherwood (1972) and Blendermann (1996). Blendermann’s data were based on a rectangular block with the dimension’s ratios length/breadth ¼6.67 and height/breadth ¼0.3, while for the floating platform these ratios are L/B ¼6.1 and H/B¼ 0.26. The platform was symmetric with respect to the centreplane and the aerodynamic loads were determined only at half incidence. Wind forces obtained by the first numerical computations (CFDhexa) have not achieved a perfect match with the experimental measurements (EXP). The additional computations (CFDtetra, CFDtetra_y þ) significantly improved the results, which are mostly observed for lateral forces. Comparing these new computations with CFDhexa, lateral force coefficients cy increased by more than 50% for the 80–1001 incidence when the platform is located sideways to the wind forces while CFDtetra_y þ presents a significant growth of the forces at full incidence of wind attack. An interesting occurrence took place between the results of CFDtetra_yþ and the Blendermann’s block. The numerical results achieved almost a perfect match with Blendermann’s data, except the incident of 60–801 for longitudinal forces, in which CFDtetra presents better agreement. Significant discrepancies in the mentioned range could be caused by the biggest area of the flow detachment in which designation of the pressure field by RANS
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A.D. Wnęk, C. Guedes Soares / Ocean Engineering 97 (2015) 30–36
1.5 1.0
Cx
0.5 0.0 EXP CFDhexa CFDtetra CFDtetra_y+ Blend. Isher.
-0.5 -1.0 -1.5 -2.0 0
20
40
60
80
100
120
140
160
180
Angle [deg] 0.2 EXP CFDhexa CFDtetra CFDtetra_y+ Blend. Isher.
0.0
Cy
-0.2
Fig. 8. Wall shear vectors and pressure distribution for 601 incidence.
-0.4 2
-0.6
EXP
1.5
-0.8
CFDtetra CFDtetra_y+
1 0.5
0
20
40
60
80
100
120
140
160
180
Cx
-1.0
Angle [deg]
0 -0.5 -1
0.2
-1.5
0.1
-2 0
CN
0.1
30
60
90 120 150 180 210 240 270 300 330 360
Angle [deg]
0.0
2.0
EXP CFDhexa CFDtetra CFDtetra_y+ Blend. Isher.
-0.1 -0.1
EXP
0
20
40
60
80
100
120
140
160
180
Cy
-0.2
Angle [deg]
1.5
CFDtetra
1.0
CFDtetra_y+
0.5 0.0 -0.5
Fig. 7. Longitudinal force, lateral force and yaw moment coefficients for floating LNG platform.
-1.0 -1.5
0
Table 3 Type of mesh for the floating platform. Platform No of elem. y þ imposed
60
90 120 150 180 210 240 270 300 330 360
Angle [deg]
CFDhexa
CFDtetra
6
6
1.3 10 5
30
3.2 10 No prism lay.
CFDtetra_y þ 5.2 10 1
0.2
6
0.1
model is not very precise. Fig. 8 presents pressure distribution on the hull for 601 angle of incidence. Data of Isherwood and numerical results agreed only for some angles of incidence.
CN
0.1 0.0 -0.1
EXP CFDtetra
-0.1
CFDtetra_y+
-0.2
4.2. LNG carrier
0
30
60
90
120 150 180 210 240 270 300 330 360
Angle [deg]
Results for the LNG carrier are presented in Fig. 9. Since the model is asymmetric with respect to the centreplane, all angles of incidence were taken into consideration. The comparison of numerical and experimental results shows reasonable agreement, which is evident mostly for yaw moments. Although the first numerical results (CFDtetra) under predicted the wind tunnel measurements (EXP) by about 50% for longitudinal forces, the consistency has been remained good.
Fig. 9. Longitudinal force, lateral force and yaw moment coefficients for LNG carrier.
Additional computations (CFDtetra_y þ ) demonstrated some improvements of the results. The magnitude of the forces has increased and the consistency of the curves was improved, which is mostly visible for longitudinal forces and yaw moments.
A.D. Wnęk, C. Guedes Soares / Ocean Engineering 97 (2015) 30–36
35
Fig. 10. Pressure contours on LNG carrier at the angle of 301 (left-CFDtetra, right-CFDtetra_y þ ).
Table 4 Type of mesh for the LNG carrier. LNG carrier No of elem. y þ imposed
Table 5 Wind force coefficients according to different thickness of first prism layer. CFDtetra 6
4.5 10 No prism lay
CFDtetra_y þ 6.2 10 0.1
6
Fig. 10 presents the pressure contours on the LNG model at an angle of incidence of 301. The maximum pressure obtained by the first CFD computation (CFDtetra) is equal to 64.75 Pa, while the maximum pressure obtained by CFDtetra_y þ is equal to 70.88 Pa. This apparent growth of the pressure was caused by the additional prismatic layers (Table 4) on the model’s surface, which counted 5 layers and the first layer thickness on the surface was proportional to yþ close to 0.1. The first prism layer thickness corresponding to the nondimensional wall distance y þ was analysed by Wnęk and Guedes Soares (2012) only for 501 angle of incidence. Table 5 presents results determined by the wind tunnel and CFD code using tetrahedral mesh with various thicknesses of the first prism layer. In comparison to the experimental measurements, the numerical data varied slightly. The most reasonable result occurred for yþ ¼0.1. The significant difference in magnitude of the forces between wind tunnel tests (EXP) and CFDtetra_y þ results by about 40% for some angles of incidence has not a clear explanation. Numerical and experimental results were compared with the aerodynamic data of Isherwood (1972) and Blendermann (1996) as well as wind loads on similar LNG carrier provided by technical report of WaveSpec (2007). These complementary data refer only to a half incidence of wind attack (1801) and only that incidence is compared. The schematic view of the models is presented in Fig. 11. It is observed that the longitudinal force coefficients obtained by CFD code follows the Blendermann’s data as well as the WaveSpec results (Fig. 12). Moreover, the lateral forces obtained by WaveSpec match perfectly the CFDtetra_y þ data. A significant divergence is observed between data of Isherwood and longitudinal and lateral force coefficients obtained by CFD, while the yaw moments are in a reasonable agreement for some angles of incidence. Given the above agreement of the numerical results with the data obtained by the two empirical methods as well as the data of WaveSpec, the difference between the numerical and experimental results suggests that there might have been some deficiencies of the experiment associated with the relatively low wind speed in the tunnel, which were apparent in some conditions, while in others good results were obtained as discussed earlier. The curvature consistency (Fig. 9) is well reproduced, but there is a difference in the magnitude of the forces with the experimental measurements over predicting the numerical results. The ambient
EXP CFD (no prism) CFD (yþ ¼ 0.05) CFD (yþ ¼ 0.1) CFD (yþ ¼ 0.5) CFD (yþ ¼ 1) CFD (yþ ¼ 2) CFD (yþ ¼ 10) CFD (yþ ¼ 30)
cx [–]
cy [–]
cN [–]
1.1 0.54 0.49 0.5 0.5 0.48 0.45 0.5 0.54
1.1 0.68 0.8 0.76 0.69 0.69 0.7 0.69 0.68
0.054 0.047 0.06 0.053 0.05 0.05 0.05 0.046 0.04
Fig. 11. Schematic view of LNG carrier (current LNG, Blendermann’s model, WaveSpec).
conditions of the tunnel like for example temperature, humidity did not have significant matter on the results accuracy due to tests repetitions by different researchers on different days. The most probable cause of difference in the magnitude of the results was the error associated with the low wind speed which creates too small forces making it difficult for the load cell to be accurate as it might be prone to limitations in the range of measured values or in its sensitivity to the parameter changes.
5. Conclusions Wind loads on two isolated ship models (floating LNG platform and LNG carrier) have been studied. Wind forces were obtained by numerical analysis (CFD) and compared with experimental measurements performed in the wind tunnel. Additional comparison of the results has been carried out using data of Blendermann and Isherwood as well as other wind tunnel measurements performed on similar LNG model by WaveSpec.
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A.D. Wnęk, C. Guedes Soares / Ocean Engineering 97 (2015) 30–36
angles of incidence, but showed a similar dependency of the results with the angle of attack.
1.5 EXP CFDtetra CFDtetra_y+ Blend. Isher. Wave Spec
1 0.5
Cx
0
Acknowledgments
-0.5 -1 -1.5 -2 0
20
40
60
80
100
120
140
160
180
Angle [deg]
The study was carried out within the project “SAFEOFFLOAD” (Safe Offloading from Floating LNG Platforms) funded by the European Commission through the GROWTH program under contract TST4-CT-2005-012560. The first has been financed by The Portuguese Foundation for Science and Technology (Fundação para a Ciência e a Tecnologia) under contract numbers SFRH/BD/ 67070/2009.
0.2 EXP CFDtetra CFDtetra_y+ Blend. Isher. Wave Spec
0.0 -0.2
Cy
-0.4
References
-0.6 -0.8 -1.0 -1.2 -1.4
0
20
40
60
80
100
120
140
160
180
Angle [deg] 0.2 EXP CFDtetra CFDtetra_y+ Blend. Isher. Wave Spec
0.1
CN
0.1 0.0 -0.1 -0.1
0
20
40
60
80
100
120
140
160
180
Angle [deg] Fig. 12. Longitudinal force, lateral force and yaw moment coefficients for LNG carrier compared with empirical methods and WaveSpec data.
The first numerical results for the floating platform (CFDhexa) were in reasonable agreement with experimental measurements. However, discrepancies for some angles of incidence provoked additional computations with emphasis on mesh convergence study. It was observed that for cylindrical domain like also for small details of the model, tetrahedral mesh was more reasonable to use, instead of structured mesh. The differences are visible in the magnitude of the forces like also in the consistency of the curves. Additional prismatic layers on the model’s surface also improved the results, which confirm the statement that they are important to capture the boundary layers effects along the walls of the model, which is also noticeable for LNG carrier. Additional data of wind loads on similar models, earlier determined by Blendermann presented a good agreement with numerical results. Moreover, an almost a perfect match of the lateral force coefficients has been achieved for the floating platform. Furthermore, another supplementary experimental data, obtained by WaveSpec on similar model of LNG carrier, showed very good agreement with numerical results of lateral force coefficients, where lateral forces perfectly match each other. Experimental measurements performed in a wind tunnel on the identical models over predicted numerical results in some
Blendermann, W., 1996. Wind Loading of Ships—Collected Data from Wind Tunnel Tests in Uniform Flow (Report No. 574). Institut für Schiffbau der Universität Hamburg. Brizzolara, S., Rizzuto, E., 2006. Wind heeling moments on very large ships. Some insights through CFD results, In: Proceedings of the Ninth International Conference of Ships and Ocean Vehicles, Rio de Janeiro, Brasil, pp. 781–793. Ciortan, C., Guedes Soares, C., 2007. Computational study of sail performance in upwind condition. Ocean Eng. 34, 2198–2206. Clauss, G.F., Heisen, W., 2005. CFD analysis on the flying shape of modern yacht sails. In: Guedes Soares, C., Garbatov, Y., Fonseca, N. (Eds.), Maritime Transportation and Exploitation of Ocean and Coastal Resources. Taylor & Francis, London, pp. 87–94. Haddara, M.R., Guedes Soares, C., 1999. Wind loads on marine structures. Mar. Struct. 12, 199–209. Hargreaves, D.M., Wright, N.G., 2007. On the use of the k–ε model in commercial CFD software to model the neutral atmospheric boundary layer. J. Wind Eng. Ind. Aerodyn. 95, 355–369. Isherwood, R.M., 1972. Wind resistance of merchant ships. Trans. Roy. Inst. Naval Architects 114, 327–338. Kaup J., 2006. Guidelines for Numerical Calculations of Ship Aerodynamic Forces. In: Proceedings of the Fourth International Scientific Conference, EXPLO-SHIP 2006, Zeszyty Naukowe Nr. 11(83) Akademii Morskiej w Szczecinie, pp. 131–140 (in polish). Menter, F.R., 1993. Zonal two equations k-turbulence models for aerodynamic flows. In: Proceedings of the 24th AIAA Computational Fluid Dynamics Conference, AIAA Paper 93-2906, Orlando, FL. Palmer, G., Vazquez, B., Knapp, G., Wright, N., 2003. The practical application of CFD to wind engineering problems. In: Proceedings of the Eighth International IBPSA Conference, Eindhoven, The Netherlands, pp. 995-999. Paulauskas, V., Paulauskas, D., Wiffels, J., 2009. Ships safety in open ports. Comput. Modell. New Technol. 13 (2), 48–55. Peng, S.-H., Eliasson, P., Davidson, L., 2007. Examination of the shear stress transport assumption with a low-Reynolds number k-omega model for aerodynamic flows, In: Proceedings of the 18th AIAA Computational Fluid Dynamics Conference, AIAA-2007-3864, Miami, FL. Versteeg, H., Malalasekra, W., 2007. An Introduction to Computational Fluid Dynamics: The Finite Volume Method. Pearson Education Ltd., Harlow, England. WaveSpec, 2007. Prediction of Wind Loads on Large Liquefied Gas Carrier. Society of International Gas Tanker & Terminal Operators Ltd. (SIGTTO), pp. 1–28. Werner, S., Pistidda, A., Larsson, L., Regnstrom, B., 2007. Computational fluid dynamics validation for a fin/bulb/winglet keel configuration. J. Ship Res. 51 (4), 343–356. Wnęk A.D., Paço A., Zhou X-Q., Guedes Soares C., 2009. Numerical and experimental analysis of the wind forces acting on a floating LNG platform. In: Proceedings of the 13th Congress of International Maritime Association of the Mediterranean (IMAM 2009); Istanbul, Turkey, pp. 697–702. Wnęk A.D., Paço A., Zhou X-Q. Guedes Soares, C., 2010. Numerical and experimental analysis of the wind forces acting on LNG carrier. In: Pereira, J.C.F, Sequeira, A., (Eds.), Proceedings of the Fifth European Conference on Computational Fluid Dynamics, (ECCOMAS CFD2010), Lisbon. Wnęk, A.D., Guedes Soares, C., 2012. Numerical analysis of the shadow effect of an LNG floating platform on an LNG carrier under wind conditions. In: Rizzuto, E, Soares, C. Guedes (Eds.), In: Sustainable Maritime Transportation and Exploitation of Sea Resources. Taylor and Francis Group, UK, pp. 117–122. Wnęk, A.D., Paço, A., Zhou, X-Q., Sutulo, S., Guedes Soares, C., 2015. Experimental study of aerodynamic loads on an LNG carrier and floating platform. Appl. Ocean Res. (accepted for publication). Yelland, M.J., Moat, B.I., Pascal, R.W., Berry, D.I., 2002. CFD model estimates of the airflow distortion over research ships and the impact on momentum flux measurements. J. Atmos. Oceanic Technol., 1477–1499. Yoo, J., Kim, T.H., 2006. Computational and experimental study on performance of sails of a yacht. Ocean Eng. 33, 1322–1342.
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Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng
CFD assessment of the wind loads on an LNG carrier and floating platform models A.D. Wnęk, C. Guedes Soares n Centre for Marine Technology and Engineering (CENTEC), Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
art ic l e i nf o
a b s t r a c t
Article history: Received 3 May 2014 Accepted 10 January 2015
Numerical analysis of the wind forces acting on a floating LNG platform and an LNG carrier models is performed with a computational fluid dynamics (CFD) code and compared with experimental results obtained in a wind tunnel. The results are represented in the form of coefficients of the wind force components in X and Y directions and yaw moment for various angles of wind attack. The numerical study based on a CFD code started by performing several tests with different type and resolution of the mesh. The results were also compared with two empirical methods as well as additional experimental measurements of similar LNG carrier. Reasonable agreement of the numerical and experimental results was reached. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Wind loads CFD LNG carrier LNG floating platform
1. Introduction Wind loads on ships as the one of the crucial factors in their manoeuvrability have been studied for a long time using several methods. Wind can vary randomly in its velocity and direction, decreasing the manoeuvring capability of ships, especially at low speeds as occurs in approaches to quays for example. Paulauskas et al. (2009) made an investigation on safety of the ships in open sea ports, looking at the possible cases of wind direction that can cause dangerous situations or at least difficulties for moored ships in open ports. Since many years the analysis of the wind forces acting on the ships, has been studied using different techniques. Isherwood (1972) used previously published experimental data to propose a new expression for the force and moment coefficients derived from multiple regression analysis of the results. Blendermann (1996), using his own collection of wind load data, derived expressions for the wind load coefficients which are the function of the drag coefficients, the angle of attack, the frontal and transverse areas of the ship, the cross-force parameter and the coordinates of the centre of ship area. Both methods can be used for several types of ship. These two methods were also considered in the comparisons in the current work of the analysis of wind forces acting on a floating LNG platform and an LNG carrier. Haddara and Guedes Soares (1999) selected four methods (Isherwood, Blendermann, Gould, OCIMF) to determine and compare wind loads on large tanker in the loaded and ballast conditions.
n
Corresponding author. Tel.: þ 351 218 41 7607. E-mail address: [email protected] (C. Guedes Soares).
http://dx.doi.org/10.1016/j.oceaneng.2015.01.004 0029-8018/& 2015 Elsevier Ltd. All rights reserved.
Application of computational fluids dynamics (CFD) is becoming increasingly widespread in several fields including wind effects in marine structures. CFD analysis has many advantages compared with wind tunnel results, which however remain the reference for validation purposes (Palmer et al., 2003). Flexibility in the model design, duration of the analysis and comprehensive visualization of the results are only some of the good sides of CFD. Nevertheless, the results of this method are much dependent on the mesh adopted as well as the proper user inputs into the software like boundary conditions, turbulence model, time-step. Brizzolara and Rizzuto (2006) have also applied CFD for prediction of wind pressure on superstructures of large commercial ships, in particular the suction area on the main deck caused by the presence of a negative pressure field. The results were compared with the data obtained by the formulations based on the stability standards and showed some discrepancy with the formulation in existing rules. The difference between the results could be caused by the lack of the suction effect on the deck portion close to the upwind edge in the present rules. The methodology for the ship aerodynamic forces determination with CFD application has been presented by Kaup (2006) and the results were verified by experimental measurements. Wind tunnel tests have been performed in use of the ferry boat model and the results were presented in a form of nondimensional coefficients. Both, numerical and experimental results gave good agreement. Yelland et al. (2002) provided validation of CFD model simulations. The air flow simulations over research ships were performed at various wind speeds and different wind directions. Results were compared with wind tunnel experiments. Applications to the assessment of aerodynamic behaviour of sails have also been done
A.D. Wnęk, C. Guedes Soares / Ocean Engineering 97 (2015) 30–36
Nomenclature cx cy cN Fx Fy N V u v w LOA B H AF AL Rn yþ
longitudinal force coefficient lateral force coefficient yaw moment coefficient longitudinal force component parallel to the lateral area of the ship lateral force component perpendicular to the lateral area of the ship yaw moment wind velocity velocity component in x-direction velocity component in y-direction velocity component in z-direction length overall of the ship beam height frontal projected wind area of the ship lateral projected wind area of the ship Reynolds number nondimensional wall distance
for example by Clauss and Heisen (2005) and by Ciortan and Guedes Soares (2007), who compared their predictions with the experiments of Yoo and Kim (2006). The current paper presents a CFD analysis of the wind forces acting on a floating LNG platform and an LNG carrier at full incidence of wind attack, comparing with the experiments reported in Wnęk et al. (2015). An initial numerical and experimental study of those two ship models has been already presented by Wnęk et al. (2009, 2010). Results in a form of coefficients of the wind force components in X and Y directions and yaw moment were at reasonable agreement with experimental measurements. In order to improve the numerical results, additional computations have been performed using different mesh type and resolution. Comparison of the results has also been made with additional data of Isherwood (1972) and Blendermann (1996) as well as wind loads on a similar LNG carrier obtained in a wind tunnel and reported by WaveSpec (2007).
2. Experimental measurements The experimental tests have been performed in an open-jet wind tunnel (Fig. 1) of Instituto Superior Técnico (IST) in Lisbon
y ρ RANS k ε ω h r μt F1, F2 Cμ σk σε σω β βn κ γ CDkω Ω
31
distance to the nearest surface air density Reynolds-averaged-Navier–Stokes equations turbulent kinetic energy turbulent dissipation rate the specific dissipation rate height of cylindrical computational domain radius of cylindrical computational domain eddy viscosity blending functions model constant model constant model constant model constant model constant model constant model constant model constant cross-diffusion term absolute value of the vorticity
(Wnęk et al., 2015). The tunnel has a rectangular closed working section with characteristics given in Table 1. The maximum wind velocity that the tunnel was able to attain was 15 m/s, but in practice the average speed in all tests was around 10 m/s. A strain gauge load cell (BS50-C sensor) was mounted under the tunnel’s floor, connected to the model and was able to measure the forces and moments along three Cartesian axes. The gap between the model and the floor was 0.005 m. Two models made of wood (Fig. 2) represents a floating LNG platform and an LNG carrier in the 1/400 scale with characteristics given in Table 2. All tests were performed three times for each case on different days by different researchers. This procedure makes the results independent on each other and allows the quantification of the uncertainty, which turned out to be small. Measurements were performed in various angles of incidence. Each isolated model was rotated repeatedly starting from 01 angle with 101 step until reproduces the full incidence: 3601 in case of LNG carrier and 1801 in case of the floating platform, which is symmetric in relation to the Y axis. Only the horizontal forces and yaw moment were measured and the results were presented in the form of dimensionless coefficients: cx ¼
Fx 1=2ρAF V 2
;
cy ¼
Fy 1=2ρAL V 2
;
cN ¼
N 1=2ρAL LOA V 2
:
ð1Þ
where Fx, Fy are the wind force components (parallel, perpendicular to the lateral area of the model, respectively, Fig. 3) and N is a yaw moment with positive up Z axis. AF, AL, LOA present the models’ characteristics (Table 2), V the average wind velocity equal to 10 m/s and ρ is the air density 1.2 kg/m3.
Table 1 Wind tunnels’ characteristics. Cross-section area h b (m2) Length of the measurement zone (m) Maximum wind speed (m/s) Fig. 1. Wind tunnel.
1.3 2 3 15
32
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Fig. 2. Physical models of floating platform and LNG carrier.
Table 2 Models’ characteristics. Characteristic
floating platform
LNG carrier
Length overall LOA (m) Beam B (m) Frontal projected wind area AF (m2) Lateral projected wind area AL (m2) Reynolds number Rn
0.916 0.15 0.00683 0.05275 6.2 105
0.725 0.115 0.01051 0.05011 4.9 105
V, wind velocity angle of attack
N, yaw moment
Fx, longitudinal force oZ
X
FY, lateral force Y Fig. 3. Coordinate system, wind forces and moment.
halves of the cylinder) were adopting different positions. Kaup (2006) has chosen similar methodology and created similar computation domain for the determination of ship aerodynamic forces, with only one mesh for all computations. His results obtained by numerical analysis presented very good agreement with experimental measurements. Initially, for the floating platform, a multi-block structured hexahedral mesh was generated with 1.3 106 cells (Wnęk et al., 2009). The first layer thickness on the hull’s surface (“CFDhexa”) was proportional to the dimensionless wall distance yþ equal to 5, that was imposed for the calculation of the first layer thickness. To determine the proper resolution of the mesh is usually a problematic issue in CFD. Problems arise with complex geometries or with details of a simple geometry, when using structured mesh generation, because it is not automatic in ANSYS ICEM CFD software, which can be a big challenge (Werner et al., 2007). Therefore, the unstructured grids are expedient for all complex geometries, which still are not trivial to generate and require additional mesh convergence studies. Another mesh generated for the floating platform is a tetrahedral mesh with 3.2 106 cells without any prismatic layers on a surface (“CFDtetra”). To capture the boundary layers effects along the walls of the model, it is actually necessary to generate accurate prism layers on a model. A third mesh was generated with 5.2 106 tetrahedral elements and 20 prism layers on the model’s surface (CFDtetra_y þ). The first layer thickness was proportional to the wall distance yþ , which was close to 1. The computational mesh for the LNG carrier used by Wnęk et al. (2010) was a tetrahedral one with 4.5 106 cells without prismatic layers on a model’s surface, denoted here as “CFDtetra”. All those earlier computations have been repeated here with another mesh (“CFDtetra_y þ”) of 6.2 106 tetrahedral elements with 5 prismatic layers (Fig. 6). The first layer thickness on the surface is proportional to yþ, which is close to 0.1.
Fig. 4. Models of floating platform and LNG carrier.
3. Numerical study The study addresses the models of an LNG carrier and of a floating platform (Fig. 4), which were performed in Rhinoceros 4.0 software to represents the geometric characteristics of the physical models (Table 2) with their geometric details. The models were exported to ANSYS ICEM CFD software, where the computational domain and mesh generation took place as the next procedure of CFD pre-processing.
Fig. 5. Computational domain.
3.1. Computational domain and grid generation The computational domain has been created in a form of cylinder (Fig. 5), with dimensions: h¼ 1.6LOA, r ¼ 3.7LOA for the floating platform and h ¼1.5LOA, r ¼ 3.5LOA for the LNG carrier, where h is the height and r is the radius of the cylinder. Due to the required series of computations for different angles of incidence, this shape of the domain significantly decreased the computing time. Only one universal mesh was generated for all simulations in which only the walls of the inlet and outlet (two
Fig. 6. Tetrahedral mesh.
A.D. Wnęk, C. Guedes Soares / Ocean Engineering 97 (2015) 30–36
F 1 ¼ tanhðarg41 Þ:
3.2. Boundary conditions The same boundary conditions have been implemented on the models of the floating platform and of the LNG carrier. The no-slip condition was applied on the hulls (wall friction on the wall), that is, for the viscous flow, the velocity of the fluid particles on the boundary face is equal to the velocity of the face or, in another words, the fluid particles on the boundary surface move with the velocity of this surface: u ¼ Ux;
v ¼ V y;
33
w¼0
ð2Þ
arg1 ¼ min max
ð10Þ ! ! pffiffiffi k 500ν 4ρσ ω2 k ; 2 ; βωy y ω CDkω y2
ð11Þ
where CDkω is the cross-diffusion term: 1 ∂k ∂ω CDkω ¼ max 2ρσ ω2 ; 10 20 ω ∂xj ∂xj
ð12Þ
where F2 is a second blending function expressed as follows: F 2 ¼ tanhðarg22 Þ:
The free-slip condition was imposed on the imitation of still water free surface (floor of the domain), which is no friction on the wall. The top of the domain was treated as a symmetry plane. The wind velocity at the inlet was set to be uniform as taken from the wind tunnel tests (Eq. (3)). U x ¼ 10 m=s;
V y ¼ 0;
Wz ¼ 0
ð3Þ
At the outlet zero pressure was imposed.
ð6Þ
and Sij is a mean component of deformation rate of a fluid element in a turbulent flow. The model constants are C μ ¼ 0:09, σ k ¼ 1:00, σ ε ¼ 1:30, C 1ε ¼ 1:44, C 2ε ¼ 1:92. This standard k–ε model, widely used nowadays, has one particular disadvantage. It fails in a near wall layer and the shear stresses in adverse pressure gradient flows are often over predicted. The model was replaced by a shear stress transport (SST) model developed by Menter (1993). This is a combination of two common turbulence models: k–ε, which is accurate in the outer part of the boundary layer and Wilcox k–ω, which is more accurate in the near wall region. The transport equations are: ∂k ∂ρk ∂ðρui kÞ ∂u ∂ þ ð7Þ ¼ τij i βn ρωk þ μ þ σ k μt ∂t ∂xi ∂xj ∂xj ∂xj ∂ω ∂ρω ∂ðρui ωÞ γ ∂ui ∂ 1 ∂k ∂ω þ 2ρð1 F 1 Þσ ω2 ¼ τij βρω2 þ μ þ σ ω μt þ ∂t ∂xi υt ∂xj ∂xj ∂xj ω ∂xj ∂xj
ð8Þ where the kinematic eddy viscosity is equal to (9) a1 k maxða1 ω; ΩF 2 Þ
ð15Þ
where φ1 : σ k1 ¼ 0:85, pffiffiffiffiffi σ ω1 ¼ 0:5, β1 ¼ 0:075, a1 ¼ 0:31, β ¼ 0:09, γ 1 ¼ β1 =βn σ ω1 κ2 = βn , κ ¼ 0:41, and φ2p : ffiffiffiffiffi σ k2 ¼ 1:0, σ ω2 ¼ 0:856, β2 ¼ 0:0828, βn ¼ 0:09, γ 2 ¼ β2 =βn σ ω2 κ 2 = βn , κ ¼ 0:41. The SST model was also particularly examined in aerodynamic flow computations by Peng et al. (2007). The sensitivity of the results to the code settings as the application of different turbulence models has been presented in Wnęk and Guedes Soares (2012). Computations have been performed in ANSYS CFX code on 8 CPUs, Intels Xeons CPU E5420 @2.50 GHz, 16 GB of RAM. The average time of analysis for one angle of wind attack was about 5 h. The physical timescale was 0.005 which gave the best convergence.
4. Results
2
νt ¼
where Ω is the absolute value of the vorticity and y is a distance to the nearest surface. The set of all constants φ comes from the following relation, well described in Menter (1993):
ð5Þ
where dynamic turbulent viscosity is: k ε
ð14Þ
n
Initially, the air flow around the floating platform has been computed using the two-differential equations k–ε turbulence model (Hargreaves and Wright, 2007). At present this is one of the most universal non-algebraic turbulence models used in CFD, which is the simplest in use and well established within fluid dynamics (Versteeg and Malalasekra, 2007). The standard transport equations for turbulent kinetic energy k and turbulent dissipation rate ε can be expressed as follows ∂ðρkÞ ∂ ρuj k ∂ μ ∂k þ þ 2μt Sij Sij ρε ¼ μþ t ð4Þ ∂xj ∂t ∂xj σ k ∂xj
μt ¼ ρC μ
! pffiffiffi k 500ν ; 2 βωy y ω
ϕ ¼ F 1 ϕ1 þ ð1 F 1 Þϕ2 :
3.3. Turbulence model
∂ðρεÞ ∂ ρuj ε ∂ μ ∂ε ε ε2 þ þ 2C 1ε μt Sij Sij C 2ε ρ ¼ μþ t ∂t ∂xj k ∂xj σ ε ∂xj k
arg2 ¼ max 2
ð13Þ
ð9Þ
where F1 is a blending function that is one in the near wall region (k–ω) and zero far away from the surface (k–ε) and is expressed as follows:
4.1. Floating LNG platform Fig. 7 presents a comparison between wind force coefficients determined in the wind tunnel and by numerical analyses using three computational grids (Table 3), as well as the two empirical methods of Isherwood (1972) and Blendermann (1996). Blendermann’s data were based on a rectangular block with the dimension’s ratios length/breadth ¼6.67 and height/breadth ¼0.3, while for the floating platform these ratios are L/B ¼6.1 and H/B¼ 0.26. The platform was symmetric with respect to the centreplane and the aerodynamic loads were determined only at half incidence. Wind forces obtained by the first numerical computations (CFDhexa) have not achieved a perfect match with the experimental measurements (EXP). The additional computations (CFDtetra, CFDtetra_y þ) significantly improved the results, which are mostly observed for lateral forces. Comparing these new computations with CFDhexa, lateral force coefficients cy increased by more than 50% for the 80–1001 incidence when the platform is located sideways to the wind forces while CFDtetra_y þ presents a significant growth of the forces at full incidence of wind attack. An interesting occurrence took place between the results of CFDtetra_yþ and the Blendermann’s block. The numerical results achieved almost a perfect match with Blendermann’s data, except the incident of 60–801 for longitudinal forces, in which CFDtetra presents better agreement. Significant discrepancies in the mentioned range could be caused by the biggest area of the flow detachment in which designation of the pressure field by RANS
34
A.D. Wnęk, C. Guedes Soares / Ocean Engineering 97 (2015) 30–36
1.5 1.0
Cx
0.5 0.0 EXP CFDhexa CFDtetra CFDtetra_y+ Blend. Isher.
-0.5 -1.0 -1.5 -2.0 0
20
40
60
80
100
120
140
160
180
Angle [deg] 0.2 EXP CFDhexa CFDtetra CFDtetra_y+ Blend. Isher.
0.0
Cy
-0.2
Fig. 8. Wall shear vectors and pressure distribution for 601 incidence.
-0.4 2
-0.6
EXP
1.5
-0.8
CFDtetra CFDtetra_y+
1 0.5
0
20
40
60
80
100
120
140
160
180
Cx
-1.0
Angle [deg]
0 -0.5 -1
0.2
-1.5
0.1
-2 0
CN
0.1
30
60
90 120 150 180 210 240 270 300 330 360
Angle [deg]
0.0
2.0
EXP CFDhexa CFDtetra CFDtetra_y+ Blend. Isher.
-0.1 -0.1
EXP
0
20
40
60
80
100
120
140
160
180
Cy
-0.2
Angle [deg]
1.5
CFDtetra
1.0
CFDtetra_y+
0.5 0.0 -0.5
Fig. 7. Longitudinal force, lateral force and yaw moment coefficients for floating LNG platform.
-1.0 -1.5
0
Table 3 Type of mesh for the floating platform. Platform No of elem. y þ imposed
60
90 120 150 180 210 240 270 300 330 360
Angle [deg]
CFDhexa
CFDtetra
6
6
1.3 10 5
30
3.2 10 No prism lay.
CFDtetra_y þ 5.2 10 1
0.2
6
0.1
model is not very precise. Fig. 8 presents pressure distribution on the hull for 601 angle of incidence. Data of Isherwood and numerical results agreed only for some angles of incidence.
CN
0.1 0.0 -0.1
EXP CFDtetra
-0.1
CFDtetra_y+
-0.2
4.2. LNG carrier
0
30
60
90
120 150 180 210 240 270 300 330 360
Angle [deg]
Results for the LNG carrier are presented in Fig. 9. Since the model is asymmetric with respect to the centreplane, all angles of incidence were taken into consideration. The comparison of numerical and experimental results shows reasonable agreement, which is evident mostly for yaw moments. Although the first numerical results (CFDtetra) under predicted the wind tunnel measurements (EXP) by about 50% for longitudinal forces, the consistency has been remained good.
Fig. 9. Longitudinal force, lateral force and yaw moment coefficients for LNG carrier.
Additional computations (CFDtetra_y þ ) demonstrated some improvements of the results. The magnitude of the forces has increased and the consistency of the curves was improved, which is mostly visible for longitudinal forces and yaw moments.
A.D. Wnęk, C. Guedes Soares / Ocean Engineering 97 (2015) 30–36
35
Fig. 10. Pressure contours on LNG carrier at the angle of 301 (left-CFDtetra, right-CFDtetra_y þ ).
Table 4 Type of mesh for the LNG carrier. LNG carrier No of elem. y þ imposed
Table 5 Wind force coefficients according to different thickness of first prism layer. CFDtetra 6
4.5 10 No prism lay
CFDtetra_y þ 6.2 10 0.1
6
Fig. 10 presents the pressure contours on the LNG model at an angle of incidence of 301. The maximum pressure obtained by the first CFD computation (CFDtetra) is equal to 64.75 Pa, while the maximum pressure obtained by CFDtetra_y þ is equal to 70.88 Pa. This apparent growth of the pressure was caused by the additional prismatic layers (Table 4) on the model’s surface, which counted 5 layers and the first layer thickness on the surface was proportional to yþ close to 0.1. The first prism layer thickness corresponding to the nondimensional wall distance y þ was analysed by Wnęk and Guedes Soares (2012) only for 501 angle of incidence. Table 5 presents results determined by the wind tunnel and CFD code using tetrahedral mesh with various thicknesses of the first prism layer. In comparison to the experimental measurements, the numerical data varied slightly. The most reasonable result occurred for yþ ¼0.1. The significant difference in magnitude of the forces between wind tunnel tests (EXP) and CFDtetra_y þ results by about 40% for some angles of incidence has not a clear explanation. Numerical and experimental results were compared with the aerodynamic data of Isherwood (1972) and Blendermann (1996) as well as wind loads on similar LNG carrier provided by technical report of WaveSpec (2007). These complementary data refer only to a half incidence of wind attack (1801) and only that incidence is compared. The schematic view of the models is presented in Fig. 11. It is observed that the longitudinal force coefficients obtained by CFD code follows the Blendermann’s data as well as the WaveSpec results (Fig. 12). Moreover, the lateral forces obtained by WaveSpec match perfectly the CFDtetra_y þ data. A significant divergence is observed between data of Isherwood and longitudinal and lateral force coefficients obtained by CFD, while the yaw moments are in a reasonable agreement for some angles of incidence. Given the above agreement of the numerical results with the data obtained by the two empirical methods as well as the data of WaveSpec, the difference between the numerical and experimental results suggests that there might have been some deficiencies of the experiment associated with the relatively low wind speed in the tunnel, which were apparent in some conditions, while in others good results were obtained as discussed earlier. The curvature consistency (Fig. 9) is well reproduced, but there is a difference in the magnitude of the forces with the experimental measurements over predicting the numerical results. The ambient
EXP CFD (no prism) CFD (yþ ¼ 0.05) CFD (yþ ¼ 0.1) CFD (yþ ¼ 0.5) CFD (yþ ¼ 1) CFD (yþ ¼ 2) CFD (yþ ¼ 10) CFD (yþ ¼ 30)
cx [–]
cy [–]
cN [–]
1.1 0.54 0.49 0.5 0.5 0.48 0.45 0.5 0.54
1.1 0.68 0.8 0.76 0.69 0.69 0.7 0.69 0.68
0.054 0.047 0.06 0.053 0.05 0.05 0.05 0.046 0.04
Fig. 11. Schematic view of LNG carrier (current LNG, Blendermann’s model, WaveSpec).
conditions of the tunnel like for example temperature, humidity did not have significant matter on the results accuracy due to tests repetitions by different researchers on different days. The most probable cause of difference in the magnitude of the results was the error associated with the low wind speed which creates too small forces making it difficult for the load cell to be accurate as it might be prone to limitations in the range of measured values or in its sensitivity to the parameter changes.
5. Conclusions Wind loads on two isolated ship models (floating LNG platform and LNG carrier) have been studied. Wind forces were obtained by numerical analysis (CFD) and compared with experimental measurements performed in the wind tunnel. Additional comparison of the results has been carried out using data of Blendermann and Isherwood as well as other wind tunnel measurements performed on similar LNG model by WaveSpec.
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angles of incidence, but showed a similar dependency of the results with the angle of attack.
1.5 EXP CFDtetra CFDtetra_y+ Blend. Isher. Wave Spec
1 0.5
Cx
0
Acknowledgments
-0.5 -1 -1.5 -2 0
20
40
60
80
100
120
140
160
180
Angle [deg]
The study was carried out within the project “SAFEOFFLOAD” (Safe Offloading from Floating LNG Platforms) funded by the European Commission through the GROWTH program under contract TST4-CT-2005-012560. The first has been financed by The Portuguese Foundation for Science and Technology (Fundação para a Ciência e a Tecnologia) under contract numbers SFRH/BD/ 67070/2009.
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The first numerical results for the floating platform (CFDhexa) were in reasonable agreement with experimental measurements. However, discrepancies for some angles of incidence provoked additional computations with emphasis on mesh convergence study. It was observed that for cylindrical domain like also for small details of the model, tetrahedral mesh was more reasonable to use, instead of structured mesh. The differences are visible in the magnitude of the forces like also in the consistency of the curves. Additional prismatic layers on the model’s surface also improved the results, which confirm the statement that they are important to capture the boundary layers effects along the walls of the model, which is also noticeable for LNG carrier. Additional data of wind loads on similar models, earlier determined by Blendermann presented a good agreement with numerical results. Moreover, an almost a perfect match of the lateral force coefficients has been achieved for the floating platform. Furthermore, another supplementary experimental data, obtained by WaveSpec on similar model of LNG carrier, showed very good agreement with numerical results of lateral force coefficients, where lateral forces perfectly match each other. Experimental measurements performed in a wind tunnel on the identical models over predicted numerical results in some
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