Numerical study on the hydrodynamic drag force of a container ship model

Alexandria Engineering Journal (2019) xxx, xxx–xxx

H O S T E D BY

Alexandria University

Alexandria Engineering Journal www.elsevier.com/locate/aej www.sciencedirect.com

ORIGINAL ARTICLE

Numerical study on the hydrodynamic drag force of a container ship model Ahmed G. Elkafas a,*, Mohamed M. Elgohary a, Akram E. Zeid b a Department of Naval Architecture and Marine Engineering, Faculty of Engineering, Alexandria University, 21544 Alexandria, Egypt b Department of Marine Engineering Technology, Faculty of Maritime Transport and Technology, Arab Academy for Science, Technology & Maritime Transport, 21937 Alexandria, Egypt

Received 6 May 2019; revised 7 July 2019; accepted 28 July 2019

KEYWORDS Computational fluid dynamics; ANSYS-CFX; Ship resistance; Holtrop method; Container ship; Hydrodynamic drag

Abstract In recent years, importance has been recognized increasingly for the reduction of fuel consumption of ships in a seaway to reduce green-house gas emissions from shipping. From a ship design viewpoint, it is of crucial importance to establish reliable prediction methods for ship’s resistance and propulsive power. The required power for the propulsion unit depends on the ship resistance and speed. There are three solutions for the prediction of ship resistance as follow analytical methods, model tests in tanks and Computational Fluid Dynamics (CFD). The rapid developments in computers and computational methods increased the opportunities of the CFD simulation to be used in the ship design process. The present paper aims at simulating ship resistance using CFD simulations method which is conducted using ANSYS-CFX software package. As a case study, Container ship scale model is investigated. The results show the ship resistance which calculated at various ship speeds and Froude number. Predicted results for resistance components at various Froude numbers were compared against Resistance results computed by using Holtop method. It is shown that the simulation results agree fairly well with the results computed from Holtrop method, and that ANSYS-CFX code can predict ship resistance. Ó 2019 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction In recent years, importance has been recognized increasingly for the reduction of fuel consumption of ships in a seaway to reduce green-house gas emissions from shipping. It is esti* Corresponding author. E-mail addresses: [email protected], [email protected] (A.G. Elkafas). Peer review under responsibility of Faculty of Engineering, Alexandria University.

mated that almost 90% of global trade is mobilized by shipping. In the process of carrying such an immense amount of goods, ships produce roughly 3% of global CO2 emissions, 14–15% NOX emissions and 16% of SOX emissions [1]. Increasing environmental concerns and adoption of different emission related regulations have motivated both shipbuilders and owners to opt for more efficient and environment-friendly vessels. From a ship design viewpoint, it is of crucial importance to establish reliable prediction methods for ship’s resistance and propulsive power for a range of operational speeds. With the development of power-driven vessels in the

https://doi.org/10.1016/j.aej.2019.07.004 1110-0168 Ó 2019 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: A.G. Elkafas et al., Numerical study on the hydrodynamic drag force of a container ship model, Alexandria Eng. J. (2019), https:// doi.org/10.1016/j.aej.2019.07.004

2 nineteenth century, Evaluation of ship hydrodynamic parameters and components of ship resistance began to be important. The resistance of a ship at a selected speed and displacement is the fluid force acting on the ship in the opposite direction of its forward motion [2]. It can be defined as the force required to move the ship at a particular speed [3]. There are three solutions for the prediction of ship resistance as follows analytical methods, model tests in tanks and Computational Fluid Dynamics (CFD). Towing tank model testing has been since early times, the most reliable method for power predictions, because of its high cost and demand for a fixed and given geometry it can be used only in the basic design stage when the design parameters related to the vessel’s hull geometry are fixed and serves as a final validation and benchmark to be used afterward in the conclusion of the shipbuilding process during sea trials [4]. On the other hand, the last decade has seen the exponential growth of computational fluid dynamic solvers that solve Reynolds Averaged Navier Stokes equations over the hull form in finite volume approaches [5]. Although originally the computational cost was penalizing its application in early design stages, the advances in computing hardware and software allowed the integration of Computational Fluid Dynamics (CFD) in the early ship hull form design and optimization [6]. For the last few decades computer technology has been exponentially evolving in an unrestrained manner bringing massive Central Processing Unit (CPU) power for acceptable price to the regular high-end users. Computational Fluid Dynamics (CFD) is greatly dependent on CPU power since the basis in solving a fluid flow of any kind is found in Navier-Stokes (NS) equations with extension. These require high computational effort to acquire a satisfactory solution. So that Computational Fluid Dynamic (CFD) approaches for studying the influence of hydrodynamic forces on ships are increasingly used in the marine field. CFD application is an easy and less time consuming application [7]. The accuracy of using CFD simulation is proven to be high and most naval architects use this method instead of towing tank experiment method which is tedious and time consuming [2]. CFD application has advanced in recent years and become one of the most important methods used in ship building industries [8]. CFD methods can analyze flow problems in resistance estimation. CFD techniques give practical results with less effort in cost and time. Viscous flow gives more accurate results of drag than potential flow [9,10]. Also, empirical or statistical methods are considered suited. The most prominent of these is the approximate resistance and power prediction method by Holtrop and Mennen together with its revision [11]. Although this methodology provides sufficient accuracy, the statistical sample of the hull forms on which it is based dates back to the 1970s and 1980s. Such hulls, although roughly similar, have some distinct deviations from modern commercial vessels. The Holtrop and Mennen method is currently considered as one of the most accurate and efficient methods for the estimation of the resistance and propulsion power requirements of conventional monohull vessels at the initial stages of design. In this paper, example of CFD simulation of ship resistance components is presented for Container ship model on calm water. The software used for computations was ANSYSCFX package which has implemented a RANS solver model. In this paper, CFD simulations of the hull would be conducted

A.G. Elkafas et al. with the different velocities of flows. Predicted results for resistance components at various Froude numbers were compared against resistance results computed by using Holtop method. The study presented herein aims to assess the deviation of the CFD simulation results when compared with the results of Holtrop Method. The detail information about the geometry of the model, boundary layer, boundary domain, meshing process, study conditions, testing installations would be presented on the following sections of the paper. Generally, it is shown that the simulation results agree fairly well with the results computed from Holtrop method, and that ANSYSCFX code can predict ship resistance 2. Theoretical background 2.1. Ship resistance and power Ship Resistance is the total force that opposes the forward motion of the ship at a corresponding speed in calm water. Alternately, the force required to tow a ship in calm water at a constant speed. In order to achieve a forward motion, vessel’s thrust must overcome the total resistance. The total resistance of ship consists of air and hydrodynamic resistances. Hydrodynamic resistance is affected by the wetted surface area of the ship hull. It can be divided into two main components according to two approaches. It is composed of either the frictional and residual resistances or the viscous and wave resistances [2]. Particularly, frictional resistance component plays an important role as it takes the largest portion of the total ship resistance for the majority merchant ships. For example, skin friction can account for up to 90% of the total resistance, for a slow-speed ship [12]. The total resistance of a vessel can be calculated by Eq. (1) [2]. RT ¼ RF þ RR Or RT ¼ RV þ RW

ð1Þ

where RT, RF, RR, RV and RW are the total resistance, friction resistance, residual resistance, viscous and wave making resistance respectively. All above components of resistance are calculated using the generic form [2]: 1 R ¼ qCAV2 2

ð2Þ

where C – The resistance coefficient q – The density of the medium A – Wetted Surface area V – The vessel speed For the current ship model, the total resistance in deep water can be calculated using Holtrop-Mennen method. The Holtrop method [11] is currently considered as one of the efficient methods for the estimation of the resistance and propulsion power requirements of conventional vessels. It is an empirical method consisting of equations for the various resistance components that derive from the statistical analysis and regression of a database with a large number of model test results. The model developed by Holtrop is a numerical description of the ship’s resistance, subdivided into components of different origin. Each component was expressed as a

Please cite this article in press as: A.G. Elkafas et al., Numerical study on the hydrodynamic drag force of a container ship model, Alexandria Eng. J. (2019), https:// doi.org/10.1016/j.aej.2019.07.004

Numerical study on the hydrodynamic drag force

3

function of the speed and hull form parameters. The application of Holltop’s method for the deep water resistance consist many ship types, one of them is specified for our case as discussed in [11]. The Holtrop-Mennen Method has acquired widespread recognition. Holtrop and Mennen tried to include physical aspects in their formulas, but used the experimental data for determining the coefficients. A summary of their method which is based on test results from 334 models of tankers, cargo ships, trawlers, ferries, etc., is given below. The resistance is split into viscous and wave resistance. For the viscous resistance, the standard formula is used as presented in Eq. (3). CV ¼ ð1 þ kÞCF

ð3Þ

where CF is obtained from the ITTC-57 formula. The form factor k is determined from a formula obtained statistically as follow.
 B T L L3 ; ; k¼f ; ; CP ; c ð4Þ L L LR r where c is a coefficient dependent on the shape of the after body and LR is the length of the after body. If LR or S are unknown, they may be obtained from other statistically derived formulas. The appendage resistance is considered as a correction to the form factor. For the wave resistance, Holtrop and Mennen use a theoretical expression attributed to Havelock (1913), obtained by replacing the hull by two pressure disturbances separated by the wave making length of the hull. The original expression is elaborated in the following equation. RW d ¼ C1 C2 C3 emFn þ m2 cosðkFn2 Þ W

ð5Þ

where W is the weight of the ship and C1, C2, C3, m, and m2 are coefficients, which are functions of the form parameters of the hull. Different coefficients are used for Fn = 0.40 and Fn = 0.55. In the intermediate range, the residuary resistance is obtained by an interpolation formula between the two limits. Holtrop and Mennen also suggest a formula for the roughness allowanceDCF and compute the total resistance as expressed in Eq. (6). 1 RW RT ¼ qV2 S½CF ð1 þ kÞ þ DCF  þ W 2 W

ð6Þ

After determining the resistances then the corresponding effective power (PE) which help vessels moving through in water with a determined speed can be calculated by Eq. (7). PE ¼ RT  V

ð7Þ

@q þ r  ðqUÞ ¼ 0 @t

ð8Þ

@ðqUÞ þ r  ðqU  UÞ ¼ rp þ r  s þ SM @t

ð9Þ

where the stress tensor, s is related to the strain rate as follow: 2 s ¼ lðrU þ ðrUÞT  dr  UÞ 3

ð10Þ

The Third governing equation of CFD is the total energy equation which can be presented in the following form. @ðqhhot Þ @q  þ r  ðqUhhot Þ ¼ rðkrTÞ þ rðU  sÞ þ U  SM þ SE @t @t ð11Þ

where htot is the total enthalby, related to the static enthalpy h (T, p) by: 1 htot ¼ h þ U2 2

ð12Þ

The term rðU  sÞ represents the work due to viscous stresses and is called the viscous work term. The term U  SM represents the work due to external momentum sources and is currently neglected. Generally, the Navier-stokes equations describe both laminar and turbulent flows without the need for additional information. However, turbulent flows at realistic Reynolds numbers span a large range of turbulent length and time scales. In general, turbulence models seek to modify the original unsteady Navier-stokes equations by the introduction of averaged and fluctuating quantities to produce the Reynolds Averaged Navier-Stokes (RANS) equations. Turbulence models based on RANS equations are known as statistical Turbulence models due to the statistical averaging procedure employed to obtain the equations [14]. The Reynolds averaged equations given below in Eqs. (13) and (14).  @q @  þ qUj ¼ 0 @t @xj

ð13Þ

 @ðqUÞ @  @p @ qUi Uj ¼  þ ðsij  qui uj Þ þ SM þ @t @xj @xj @xj

ð14Þ

where s is the molecular stress tensor (including both normal and shear components of the stress). The need of turbulence models for RANS simulation is to determine the Reynolds stresses. This process can be conducted by three categories of RANS turbulence.  Linear eddy viscosity

2.2. Computational fluid dynamics theory The proposed CFD model was developed based on the Reynolds-averaged Navier-Stokes (RANS) method for three dimensional unsteady viscous incompressible flow using ANSYS-CFX software package. The averaged continuity and momentum equations for incompressible flows may be given as in the following two equations [13]. The instantaneous equations of mass, momentum can be written as follows in Eqs. (8) and (9).

This is a turbulence models which using Reynolds stress that obtained from the Reynolds averaging from Navier stokes equations. This involves the relation between Reynolds stresses and mean strain. This models has disadvantages in flow situations, such as, over predict turbulence energy levels in stagnant regions, Misinterpretation of normal stresses and does not reproduce the asymmetry in the velocity profile  Nonlinear eddy viscosity models

Please cite this article in press as: A.G. Elkafas et al., Numerical study on the hydrodynamic drag force of a container ship model, Alexandria Eng. J. (2019), https:// doi.org/10.1016/j.aej.2019.07.004

4

A.G. Elkafas et al.

This turbulence model is more accurate than linear eddy viscosity model. It is due to the fact the turbulence is a highly nonlinear phenomena  Reynolds stress model (RSM) This turbulence model which is also referred as the second moment closure model is most complete turbulence model. In this turbulence model, the eddy viscosity is removed and Reynolds stress are directly computed. Referring to ANSYS-CFX, there are three type of turbulence model, which are k-epsilon, k-omega, and shear stress transport (SST) [15].

Table 1

Vessel and model particulars.

Symbol

Full-scale vessel

Scaled vessel model (1:100)

Unit

Length between perpendiculars (LPP) Breadth (B) Draught (D) Displacement Metacentric height (GM) Vertical centre of gravity (KG) LCG length (from aft perpendicular)

247

2.47

m

32 12 64,000 ton – –

0.32 0.12 63.4 kg 8.75 153

m m – mm mm

–

1160

mm

K-e Model The k-e model consists of k, kinetic energy and e, balance of dissipation along with the complete RANS equation. The k-e model works well away from the wall around the boundary layer edge and for fully turbulent flows in the high Reynolds regime. K-x Model The k-x model consists of k, kinetic energy and x, specific dissipation turbulent frequency. Works well within the low Reynolds regime and should have been applied for the transitional Reynolds for this simulation. The model predicts separation early and requires a mesh inflation layer near the wall. SST Model The shear stress transport SST model, which is applied in this simulation, gives high accuracy modelling of the boundary layer and is a combination of both k-e and k-x. The SST model gives accurate predictions of the onset and the amount of flow separation under opposing pressure gradients, where turbulence is present. By applying both previous models, it covers both regions of the boundary layer, close to the wall and far away from the wall close to the boundary layer limit and applies the Bradshaw relation for good separation prediction [16]. The shear stress transport (SST) model was used for this simulation to gain the longitudinal forces, resistance forces, acting on a container ship model, as it gives the best results for maritime engineering applications. 3. Methodology and setup 3.1. Model details The case study for this paper is selected to be a Container ship model. The vessel is a twin-propeller container ship [17]. A 1:100 scale model of this vessel was built in software. The general parameters of the model are listed in Table 1. The 3D model of the vessel is processed using Rhinoceros 5.0 and MAXSURF Modeler and Imported to Geometry Module of ANSYS Workbench version 19. Fig. 1 shows the bare hull of model built in Rhinoceros 5.

3.2. Fluid domain geometry The boundary domain is the area where flows (Air and Water) will influence the hull of the vessel. The boundaries of the fluid domain are designed to be placed with a sufficient distance from the area of investigation. This is to ensure the accuracy of the solution. The fluid domain for container ship model’s investigation was built based on the International Towing Tank Conference (ITTC)’s recommendation in order to prevent flow reflections [18]. The inlet and the exterior boundary such as top, bottom and side of wall whereby the flow is undisturbed usually occurred, they are required to be located around one or two total length of the object of investigation which in this case is the length between perpendiculars. As the outlet of the fluid domain is normally where the fluid is unsteady, it is required to be placed around three to five perpendicular length away from the ship to prevent the interference or reflection of the flow, where half of the body is modelled to decrease the computational domain size and time. The ship axis is located along the x-axis with the bow located at x = LBP and the stern at x = 0. The still water level lies at z = 0. The dimensions of the computational domain satisfy the well-known ITTC procedure. Detailed information about the principles of computational domain dimensions’ selection strategy can be found in [19] and [20]. Also a detailed description of the boundary conditions is given in [21]. The general view of the computational domain and the boundary conditions are shown in Fig. 2. Table 2 shows the selected dimension for the fluid domain which represented in ANSYS-CFX. 3.3. Mesh The meshing of the fluid domain and the model were conducted using ANSYS Meshing 19.0 with the CFD as the physic preference and the CFX as the solver. The size function for the mesh is set as curvature, the mesh will not change the shape of hull or resemblance the tendency of hull’s shape. While the minimum size of the mesh is set to be 1 mm such that the mesh is allowed to capture the curvature of the model [22]. Table 3 presents the finalized mesh criteria. In order to ensure that the mesh represents the actual body for analysis, refinement were made on the body of the fluid domain, face of Hull. The refinements were as below:

Please cite this article in press as: A.G. Elkafas et al., Numerical study on the hydrodynamic drag force of a container ship model, Alexandria Eng. J. (2019), https:// doi.org/10.1016/j.aej.2019.07.004

Numerical study on the hydrodynamic drag force

Fig. 1

Fig. 2

Table 2

5

Geometry of container ship model.

Boundary Domain Conditions.

Size of the fluid domain geometry.

Fluid domain entities

B.C

ITTC

Selected

Distance (m)

Rectangular

Inlet Outlet Top & Bottom wall Side wall

1–2 3–5 1–2 1–2

1 3 1 1

2.5 7.5 2.5 2.5

Table 3

LPP LPP LPP LPP

3.3.1. Body sizing

Mesh size and specification.

Criteria

Value

Nodes Body sizing (m) Face sizing (m) Inflation layer Growth rate Maximum thickness boundary layer (m)

239,385 0.3 0.008 5 1.2 0.05

Fig. 3

The body sizing is applied with unstructured tetrahedral element size of 0.3m. The aim of body sizing applied is such that the mesh size for both side of interface for the Box are same. This action allows the optimal interpolation between fluid domains [14]. 3.3.1.1. Face sizing. Further refinement is conducted on the face of the Hull. The element size applied on the face of the Hull was 0.008 m. The refinement is conducted so that the flow

Meshing of hull and fluid domain.

Please cite this article in press as: A.G. Elkafas et al., Numerical study on the hydrodynamic drag force of a container ship model, Alexandria Eng. J. (2019), https:// doi.org/10.1016/j.aej.2019.07.004

6

A.G. Elkafas et al. 3.4.2. Domain characteristic

behaviour around the Hull can be modelled with a higher mesh resolution which hence increase the accuracy of the results. Fig. 3 below shows Meshing and inflation layer around hull.

Table 4 presents the domain characteristics that being applied to the flow.

3.4. CFX pre solver

3.4.3. Boundary condition

The completed mesh in the previous module is then imported to the CFX Pre Solver of ANSYS CFX to define its analysis method, fluid flow characteristic and its boundary conditions. The details of the setup are as below: 3.4.1. Analysis setting  The turbulence model that is selected for the analysis is Shear Stress Transport (SST) Model.  The analysis is conducted based on steady state approached as RANS based CFD stimulation method is used.

Table 4

Domain characteristics.

Criteria

Value

Fluid type Fluid density (kg/m3) Temperature (°C) Kinematic viscosity (m2/s) Morphology Buoyancy model Gravity Z component (m/s2) Domain motion Reference pressure (atm) Turbulence model Turbulent wall functions

Water 997 25 8.9E7 Continuous fluid Buoyant 9.81 Stationary 1 SST Standard

Table 5

Table 5 presents the type of boundary conditions that being applied to the fluid domains and Fig. 4 shows the boundary condition. 3.4.4. Output control The main interested output of the analysis is the hydrodynamic performance of the Hull in term of drag force. In order to monitor the progress of the CFX-Solver, the hydrodynamic characteristic is expressed in the following expression [force_x()@Hull]. 3.4.5. Solver control Solver control is used to increase the efficiency of the computer resources and control the quality of the CFX solution; ensuring the result will converged to ensure the accuracy of the results. The solver input and the convergence criteria were defined in Table 6.

Table 6

Solver control inputs.

Convergence control Minimum iteration Maximum iteration Timescale control

200 1200 Auto

Convergence criteria Residual type Residual target

RMS 0.00001

Boundary condition setting specification. Boundary type

Settings

Inlet

Inlet

Outlet Top, Bottom and Side wall Symmetry Hull

Opening Walls Symmetry Wall

Velocity Range = 1–2 [m/s] Turbulence model: SST model Mass and momentum: Entrainment Static Pressure: 0 [Pa] Mass and momentum: Free slip wall – No Slip wall

Fig. 4

Boundary Condition on the Fluid Domain.

Please cite this article in press as: A.G. Elkafas et al., Numerical study on the hydrodynamic drag force of a container ship model, Alexandria Eng. J. (2019), https:// doi.org/10.1016/j.aej.2019.07.004

Numerical study on the hydrodynamic drag force

Fig. 5

7

Graph showing the convergence of the solution.

3.5. CFX solver

4. Independent study and results

The defined CFX-Pre files are imported into the CFX-Solver for analysis. The run mode of the CFX solver was set to be the Intel MPI Local Parallel with 2 partitions core and the computations are made on 4 CPU with 2.50 GHz, on windows Win10 system. Explanation of the numerical method can be found in [23]. During the simulation progress, inspections on the solution convergence is conducted and the results show a converge trend. Figs. 5 and 6 show CFX Solver when simulate the performance and reach the balance condition at results. The residual monitors in Fig. 5 demonstrate monotonic convergence, indicating a well-posed problem and a tightly converged solution. Fig. 6 shows the change in the monitor point(drag) values vs. iteration number. After approximately 100 iterations, the drag monitor point is within just a few percent of its final value. However, the drag value is still far from its final value, so stopping the analysis here could be misleading. As the residuals decrease further, the monitor values change less and less between iterations. Once the monitor point values have ‘‘flattened out”, so the solution is assumed to be converged.

4.1. Grid independence study In order to reach the results with high accuracy in CFD simulation, the mesh must divide elements as much as possible. However, the number of nodes of the simulated model directly depends on three main factors (Technology, Time and Cost) [24]. In this paper, Richardson’s extrapolation method for grid convergence could be a proper choice for estimation of the mesh error. To have a clear view of the method, the following section have an illustration about calculation of the drag coefficient, which is based on the Richardson’s extrapolation method [25] as shown in Fig. 7. The grid convergence study was conducted based on the ITTC, uncertainty analysis recommendation [4]. The convergence study was made based on three varying mesh resolution which were categorized into coarse, medium and fine mesh. The mesh were varied by the modification of the face sizing while keeping the body sizing with a constant element size. The inflation layer was kept constant throughout the analysis as the mesh resolution was based on the standard wall

Please cite this article in press as: A.G. Elkafas et al., Numerical study on the hydrodynamic drag force of a container ship model, Alexandria Eng. J. (2019), https:// doi.org/10.1016/j.aej.2019.07.004

8

A.G. Elkafas et al.

Fig. 6

Change of monitor point (drag) values vs. iteration number.

Fig. 7

Richardson Extrapolation method.

Please cite this article in press as: A.G. Elkafas et al., Numerical study on the hydrodynamic drag force of a container ship model, Alexandria Eng. J. (2019), https:// doi.org/10.1016/j.aej.2019.07.004

Numerical study on the hydrodynamic drag force Table 7

9

The coarse, medium and fine mesh details.

Detail

Coarse

Medium

Fine

Body sizing (m) Face sizing (m) Number of nodes Number of elements Drag force (N) Drag coefficient

0.3 0.008 248,863 781,248 5.13448 0.010107517

0.3 0.006 344,331 1,045,750 3 0.005905671

0.3 0.0046 503,421 1,496,670 2.334 0.004594612

Table 8

Results of meshing error estimation.

Outcome

Equation

Value

Change in solution (e32) Changes in solution (e21) Convergence ratio Order of convergence

e32 = C(h3)  C(h2) e21 = C(h2)  C(h1) Ri = e21/e32 q = ln(e32/e21)/ln (ri) d = e21/rpi  1 CR = C1 – d

0.004201 0.001311 0.312019 3.461470

Error of the finest grid Richardson extrapolated solution Relative error estimate (er)

0.000594 0.004000

er = Ci  CR/CR

0.012 Drag Coefficient

0.01

Drag Coefficient

CR 0.008 0.006 0.004 0.002 0

200

250

300

350

400

450

500

550

Number of Nodes(×1000)

Fig. 8

Number of nodes against Drag Coefficient.

Relave Error

10

1 100000

1000000

0.1

Number of Nodes

Fig. 9 nodes.

Drag’s Relative Error Estimation against the number of

calculation. It should be noted that there is a constant refinement ratio exists between the nodes count on every mesh that being conducted. Table 7 shows the details of the meshes used for the convergence studies and drag force calculated at each case at 1 m/s. Based on formulas at the used equation section, outcomes have been calculated and presented at Table 8. Figs. 8 and 9 show the Richardson Extrapolation convergence studies and the relative error estimation that conducted on the Hull to determine the mesh performance. It is expected that the simulations which have the higher number of nodes will be more accurate. The relative error estimation study is conducted on the convergence result to determine is the error between the results vary with number of nodes. The drag coefficient was converged based on the graphs which prove that the mesh is converged with different fineness of mesh. However, the fine mesh is still chosen for analysis as it provides a higher accuracy to the stimulation which hence minimizes the error of investigation. 4.2. Resistance results After installation of simulation for the hull and boundary domain in CFX-Pre, then simulations will run and export output data under tested conditions. It is the fact that this simulation only tests a half of the ship hull. Therefore, in order to obtain the full resistance of the whole hull, the generated result are doubled. Simulations presented in this study were performed for 8 selected test conditions for different Froude Number (Fn) and also different ship speeds as presented in Table 9 which show the selected test conditions. The resistance components resulted from CFD simulation are divided to skin friction resistance and pressure resistance component. The simulation results show that the skin friction resistance account up to 90% of the total resistance as shown in Fig. 10. In order to examine the accuracy of resistance results of the simulated ship model by using ANSYS-CFX solver, the simulation results for the tested Froude numbers are thoroughly validated by comparing directly with the resistance results from the Holtrop prediction method [11] in MAXSURF software. The comparison determines the accuracy of the programming and the computational implementation of the conceptual model in which it examines the mathematical errors. CFD simulation and Holtrop method are investigated similar test condition and Froude numbers to calculate the difference between both resistance components results. Fig. 11 shows the comparison of skin friction resistance results from CFD simulations to Holtrop skin friction resistance results. The comparison between two results is very good for the whole simulated conditions. Within the simulated range of Froude Number, the maximum error is 5.15% at Fn = 0.4. The model results from CFD simulation indicate that the computations predicted 3.125% lower skin friction resistance at Fn = 0.24 and 0.28, 4.2% lower skin friction resistance at Fn = 0.35 compared to the results from Holtrop. Generally, it is shown that the CFD simulation results agree fairly well with the results computed from Holtrop method, and that ANSYS-CFX code can predict ship resistance. Fig. 12 shows the comparison of pressure resistance results from CFD simulations to Holtrop form component results. Within the simulated range of Froude Number, the

Please cite this article in press as: A.G. Elkafas et al., Numerical study on the hydrodynamic drag force of a container ship model, Alexandria Eng. J. (2019), https:// doi.org/10.1016/j.aej.2019.07.004

10

A.G. Elkafas et al.

Table 9

The selected test conditions (Speed-Froude Number).

Speed (m/s)

1

1.2

1.4

1.6

1.7

1.8

1.9

2

Fn ¼ pVffiffiffiffiffiffi

0.20315

0.24378

0.28441

0.32504

0.345355

0.36567

0.385985

0.4063

gL

model results from CFD simulation indicate that the computations predicted greater results than those from Holtrop method.

18 Total Resistance

16

Skin Fricon Resistance

Resistance (N)

14

5. Conclusion and recommendation

Pressure Resistance

12 10 8 6 4 2 0 0.15

0.2

0.25

0.3

0.35

0.4

0.45

Froude Number (Fn)

Fig. 10 Resistance components values calculated by CFD simulation Versus Froude Number.

Skin Fricon Resistance (N)

16 CFD Simulaon

14

Holtrop Method 12 10 8 6 4 2 0 0.15

0.2

0.25

0.3

0.35

0.4

0.45

Froude Number(Fn)

Fig. 11 Comparison of Skin friction resistance between CFD simulation and Holtrop Method. 1.6

Resistance(N)

1.4 1.2

CFD pressure component

1

Holtrop Form component

0.8 0.6 0.4 0.2 0

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Froude Number (Fn)

Fig. 12 Comparison between CFD simulation’s pressure component and Holtrop’s form component.

In this paper, a Reynolds averaged Navier Stokes (RANS) method is presented to predict the resistance components results for a container ship model. The software used for computations was ANSYS-CFX package which has implemented a RANS solver model. The turbulence model that is selected for the analysis is Shear Stress Transport (SST) Model which gives high accuracy modelling of the boundary layer and is a combination of both k-e and k-x. To predict the resistance of ship with different running attitudes conveniently, a plenty of numerical simulations of ship advancing at different speeds and Froude numbers are carried out. After installation of simulation for the hull and boundary domain in CFX-Pre, then simulations will run and export output data under tested conditions. The resistance components resulted from CFD simulation are divided to skin friction resistance and pressure resistance component. The simulation results show that the skin friction resistance account up to 90% of the total resistance. Accuracy of the computations is evaluated by comparing with the results from Holtrop Method in MAXSURF software. First, computed skin friction resistance results from CFD simulation are compared with Holtrop skin friction resistance results. The comparison between two Results is very good for the whole simulated conditions. Within the simulated range of Froude Number, the maximum error is 5.15% at Fn = 0.4. Then, the comparison of pressure resistance results from CFD simulations to Holtrop form component results is presented. Within the simulated range of Froude Number, the model results from CFD simulation indicate that the computations predicted greater than results from Holtrop method. Generally, it is shown that the degree of agreement with Holtrop prediction method is satisfactory for resistance components. The present simulation seems to indicate the availability of ANSYS-CFX as a tool for the prediction of ship resistance and its application to the development of ship design. A grid convergence study has been conducted to determine the accuracy of the mesh and hence increase the accuracy of the predicted result. The grid convergence study done and the analysis conducted with Low Reynolds Wall Treatment, the stimulation result seem to be acceptable and further investigation can be conducted. In general, the CFD simulations by computer software, which would give us the results with high accuracy, timesaving and presented in visual images must be highly used. So that more and more CFD simulations would be applied on the whole fields simply because of its efficiency and reliability.

Please cite this article in press as: A.G. Elkafas et al., Numerical study on the hydrodynamic drag force of a container ship model, Alexandria Eng. J. (2019), https:// doi.org/10.1016/j.aej.2019.07.004

Numerical study on the hydrodynamic drag force The recommendations for a better future of this work can be concluded, the verification of the accuracy of CFD simulation results based on the results from Holtrop method. It is not really objectivity when evaluates the results of a software by another one’s. However, due to limitations of research which have led to not carry out simulations by the experimental model in towing tank in order to get data for validation purposes. Therefore, one of the future recommendations, the Results of CFD simulation must be compared with Experimental data generated from Towing tank or using another software in order to be more validated. For further investigation, it is necessary to solve the problem of nodes number limitation. The higher use of nodes number will increase the accuracy of result even though the simulation time will be longer.

11

[11] [12]

[13]

[14]

[15]

References [1] S. Sherbaz, W. Duan, Ship trim optimization: assessment of influence of trim on resistance of MOERI container ship, Sci. World J. 2014 (2014) 1–6, https://doi.org/10.1155/2014/603695. [2] A.F. Molland, S. Turnock, D. Hudson, in: Ship Resistance and Propulsion. Practical Estimation of Ship Propulsive Power, Cambridge University Press, New York, USA, 2011, https://doi. org/10.1017/CBO9780511974113. [3] L. Larsson, H.C. Raven, J.R. Paulling, Ship Resistance and Flow, Society of Naval Architects and Marine Engineers, Jersey City, N.J., 2010, http://app.knovel.com/hotlink/toc/id: kpPNASSRF2/principles-of-naval. [4] H. Jasak, V. Vukcˇevic´, I. Gatin, I. Lalovic´, CFD validation and grid sensitivity studies of full scale ship self propulsion, Int. J. Nav. Archit. Ocean Eng. 11 (2019) 33–43, https://doi.org/ 10.1016/j.ijnaoe.2017.12.004. [5] H. Schneekluth, V. Bertram, Ship propulsion, in: Sh. Des. Effic. Econ., second ed., Butterworth-Heinemann, Oxford, 1998, pp. 180–205. doi: 10.1016/B978-075064133-3/50006-2. [6] International Towing Tank Conference (ITTC), The specialist committee on computational fluid dynamics-Final report and recommendations to the 26th ITTC, in: Proc. 26th ITTC, 2011, pp. 337–377. [7] A.G. Elkafas, N.R. Ammar, M.M. Elgohary, A. Zeid, Prediction of shallow water resistance for a new ship model using CFD simulation: case study container barge, J. Sh. Prod. Des. 35 (2) (2019) 198–206, https://doi.org/10.5957/ jspd.11170051. [8] H. Abdelkhalek, D.F. Han, L.T. Gao, Q. Wang, Numerical estimation of ship resistance using CFD with different turblence model, in: Adv. Res. Struct. Mater. Eng. Inf. Technol. III, Trans Tech Publications Ltd, 2014, pp. 209–213. doi: 10.4028/ www.scientific.net/AMR.1021.209. [9] M.S. Tarafder, K. Suzuki, Computation of wave-making resistance of a catamaran in deep water using a potentialbased panel method, Ocean Eng. 34 (2007) 1892–1900, https:// doi.org/10.1016/j.oceaneng.2006.06.010. [10] K.A. Belibassakis, T.P. Gerostathis, K.V. Kostas, C.G. Politis, P.D. Kaklis, A.I. Ginnis, C. Feurer, A BEM-isogeometric

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

[24]

[25]

method for the ship wave-resistance problem, Ocean Eng. 60 (2013) 53–67, https://doi.org/10.1016/J. OCEANENG.2012.12.030. J. Holtrop, A statistical re-analysis of resistance and probulsion data (1984) 272–276. H. Lackenby, The thirty-fourth Thomas Lowe gray lecture: resistance of ships, with special reference to skin friction and hull surface condition, Proc. Inst. Mech. Eng. 176 (1962) 981–1014, https://doi.org/10.1243/PIME_PROC_1962_176_077_02. J.H. Ferziger, M. Peric, Computational methods for fluid dynamics/J.H. Ferziger, M. Peric., 2002. doi: 10.1007/978-3642-56026-2. J.D. Anderson, Computational Fluid Dynamics the Basics With Applications, first ed., McGraw-Hill Education, 1995. . F.R. Menter, Two-equation eddy-viscosity turbulence models for engineering applications, AIAA J. 32 (1994) 1598–1605, https://doi.org/10.2514/3.12149. F. Menter, M. Kuntz, R.B. Langtry, Ten years of industrial experience with the SST turbulence model, Heat Mass Transf. 4 (2003). Y. Wang, S. Chai, H.D. Nguyen, Modelling of a surface vessel from free running test using low cost sensors, in: 2017 3rd Int. Conf. Control. Autom. Robot., 2017, pp. 299–303. doi: 10.1109/ ICCAR.2017.7942707. International Towing Tank Conference (ITTC), Practical guidelines for ship CFD applications, in: Proc. 26th ITTC, 2011. . T. Tezdogan, Y.K. Demirel, P. Kellett, M. Khorasanchi, A. Incecik, O. Turan, Full-scale unsteady RANS CFD simulations of ship behaviour and performance in head seas due to slow steaming, Ocean Eng. 97 (2015) 186–206, https://doi.org/ 10.1016/j.oceaneng.2015.01.011. Y. Hakan Ozdemir, A. Dogrul, B. Barlas, T. Cosgun, A numerical application to predict the resistance and wave pattern of kriso container ship, Brodogradnja 67 (2016) 47–65. doi: 10.21278/brod67204. Y. Ozdemir, B. Barlas, T. Yilmaz, S. Bayraktar, Numerical and experimental study of turbulent free surface flow for a fast ship model, Brodogradnja 65 (2014) 39–54. Henk Kaarle Versteeg, W. Malalasekera, An introduction to computational fluid dynamics – the finite volume method, second, Pearson Education Limited, 1995. doi: 10.1017/ cbo9780511761348.011. ANSYS, CFX-solver theory GUIDE, (n.d.). . J. Tu, G. Yeoh, C. Liu, in: Computational Fluid Dynamics: A Practical Approach, third ed., Butterworth-Heinemann, 2019, https://doi.org/10.1016/C2015-0-06135-4. D. ZINGG, Viscous airfoil computations using Richardson extrapolation, in: 10th Comput. Fluid Dyn. Conf., American Institute of Aeronautics and Astronautics, 1991. doi: 10.2514/ 6.1991-1559.

Please cite this article in press as: A.G. Elkafas et al., Numerical study on the hydrodynamic drag force of a container ship model, Alexandria Eng. J. (2019), https:// doi.org/10.1016/j.aej.2019.07.004