International Conference on Computational and ...

International Conference on Computational Experimental Marine Hydrodynamics MARHY 2014 3-4 December 2014, Chennai, India.

CFD SIMULATION OF SHIP MANEUVERING K Ravindra Babu, NSTL, Defence Research and Development Organisation, India VF Saji, NSTL, Defence Research and Development Organisation, India HN Das, NSTL, Defence Research and Development Organisation, India

ABSTRACT International Maritime Organization (IMO) sets the standard for ship maneuverability. Naval ships needs even better maneuverability. Accurate prediction of ship’s maneuverability is very important even at the early stage of design. Basic step towards finding the maneuvering characteristic of any vessel is to find the hydrodynamic derivatives. There are many methods available for hydrodynamic derivatives prediction such as free running model test, captive model test etc. However these methods are expensive and time consuming. Predictions based on semi-empirical or empirical methods are not accurate. Whereas, accurate estimation of hydrodynamic derivatives is essential for evaluation of maneuverability and directional stability. RANS based CFD code are becoming popular as an alternative method to determine hydrodynamic derivatives. This paper presents prediction of hydrodynamic derivative for static maneuvers using SHIPFLOW software. CFD results in terms of hydrodynamic forces, moments and derivatives are compared with experimental results for a naval vessel and showed good agreement. 1. INTRODUCTION Predictions of ship-maneuvering performance have been one of t he most challenging topics in ship hydrodynamics. Due to the lack of analytical methods for predicting ship maneuverability, maneuvering predictions have traditionally relied on either empirical method or experimental model tests. Recently, computational fluid dynamics (CFD) based methods have shown promise in computing complex hydrodynamic forces for steady and unsteady maneuvers. Significant progress has been made towards this goal by applying Reynolds-averaged Navier-Stokes (RANS) based CFD codes to static maneuvers and dynamic maneuvers with generally good agreements with experimental data. The CFD simulations provide more insight into the entire flow structure around the hull, and the simulation results can be used to compute the forces and moment acting on the hull and also to determine hydrodynamic derivatives of the ship hull. Although RANS methods are considered promising, many difficulties associated with time accurate schemes, 6 DOF ship motions, implementations of complex hull appendages, propulsors and environmental effects such as wind, waves, and shallow water remain challenges.

set up and are time consuming, whereas in practices, both time and cost are limited. Thus the execution of extensive model tests for every ship is practically beyond possibility. Results of semi-empirical or empirical methods are not very accurate. RANS based CFD are hence becoming popular for calculation of derivatives. Present work employs a RANS based CFD tool (SHIPFLOW 5.1) for the calculation of hydrodynamic derivatives. 2. SIMULATION OF SHIP MANEUVERS Two simulations corresponding to straight line test and rotating arm test have been performed using the SHIPFLOW software for finding derivatives. An actual ship has been considered for this purpose. Fig 1 shows the model of the ship. Total length of the ship is 151.5m with beam 17.71m. For this analysis 4.9m of draft was used. Derivatives calculated using forces and moments obtained by SHIPFLOW are compared with experimental results.

Captive model test and free running test require large

© 2014: The Royal Institution of Naval Architects and IIT Madras

Fig 1 Ship model

International Conference on Computational Experimental Marine Hydrodynamics MARHY 2014 3-4 December 2014, Chennai, India. For a bare model without propellers or rudders, the Abkowitz’s mathematical models for hydrodynamic forces and moment can be reduced to eqn (2.1) and (2.2) by dropping the terms related to rudder angle (δ ). For the straight line test (static drift):

X  X  X vv 2 Y  Yv  Yvvv 3 N  N v  N vvv 3 (2.1) Fig 2 Grids of domain around the ship hull

For the rotating arm test (steady pure yaw):

X  X  X rr r 2 Y  Yr r  Yrrr rv 3 N  N r r  N rrr r 3 (2.2) 3. CFD MODELING To solve the flow around the hull two different approaches, i.e. global and zonal approaches are available in SHIPFLOW. A global approach means that the Navier-Stokes equations are solved in the whole flow domain. A zonal approach means that the flow domain is divided into different zones based on the flow characteristics inside. Global approach has been used here. Experimental results are already available for a model scale of 1:19.2 [5]. The present simulations are also carried out for same model scale, so that the results can be compared and validated. 3.1 MESH GENERATION The total number of elements generated was 858400. The total number of panels generated was 2834 and nodes generated were 3086. For potential flow calculations, required mesh was generated by XMESH module and for RANS calculations, grids were created by XGRID module. The mesh was generated automatically by giving XMAUTO in XMESH. The type of the mesh used in XGRID was medium. Figure 2 & 3 shows generated mesh on ship hull body.

Fig 3 Mesh 3.2 FLOW SOLUTION The potential flow analysis was carried out under the XPAN module of SHIPFLOW. This estimates the wave resistance. However flow near the stern end is completely viscous. Therefore a RANS solver XCHAP is used to resolve viscous effects. XCHAP has been used in the analysis. It is a finite volume code that solves the Reynolds Averaged Navier Stokes equations. 4 RESULTS 4.1 POST PROCESSING OF RESULTS USING SHIPFLOW Pressure distribution for Froude number of 0.23 is shown in fig 4. The wave height variation along the length of the ship is plotted. This is obtained from the potential flow analysis done in SHIPFLOW. The variation in the wave height at Froude number (Fn) =0.23 can be clearly visualized from the fig 5 and 6 shown below.


International Conference on Computational Experimental Marine Hydrodynamics MARHY 2014 3-4 December 2014, Chennai, India. Where the negative sign arises because of the sign convention adopted. A straight line test was carried out in a towing tank to determine the sway velocity dependent derivative. The test condition is simulated for a naval ship model using SHIPFLOW software at different drift angles. Hydrodynamic derivatives are calculated using the forces and moments obtained by SHIPFLOW.

Fig 4 Pressure Distribution

Fig 7 Straight line test Hydrodynamic Derivatives Hydrodynamic derivatives are calculated using the least square method using forces and moment obtained by SHIPFLOW. These hydrodynamic derivatives are compared with experimental results and presented in Table 1.

Derivative

Computed value

Experimental value

Fig.5 Wave height along hull (from free surface) for a

-Y’v

0.003

0.00285

velocity 1.646m/s

-N’v

0.0092

0.017

Plots of Y’ vs. v’ and N’ vs. v’ are presented (Fig 8 and Fig 9 respectively) Table 1 Non-dimensionalised sway force & yaw moment

Yv' Fig.6 Free surface elevation for a velocity 1.646m/s 4.2 SIMULATION OF STRAIGHT LINE TEST The velocity-dependent derivatives Yv and Nv of a ship at any draft and trim can be determined from measurements on a model of the ship, ballastard to a geometrically similar draft and trim, towed in a conventional towing tank at a constant velocity, V, corresponding to a given ship Froude number, at various angles of attack, to the model path shown in fig 7 V = -V sinβ

0.00045

y = 0.0030x - 0.0000

0.00035 Y' Yv'

0.00025 0.00015


0.06

0.11

v’

0.16

Fig 8 Y’ vs. v’ plot

0.21

International Conference on Computational Experimental Marine Hydrodynamics MARHY 2014 3-4 December 2014, Chennai, India. Table 2 Non-dimensionalised sway force

Nv'

0.0014

& yaw moment

y = 0.0092x - 0.0001

0.0012

Computed

Experimental

value

value

Y’r

0.0206

0.026

N’r

0.065

0.069

Derivative

0.001 N’ 0.0008

Nv'

0.0006 0.0004 0

0.05

0.1 v’

0.15

0.2 Yr'

Fig 9 N’ vs. v’ plot 0.0089 4.3 SIMULATION OF ROTATING ARM TEST

0.0069

This is carried out to measure the rotary derivatives Yr and Nr on a model, a special type of towing tank and apparatus called a rotating-arm facility is occasionally employed. An angular velocity r given by

r

y = 0.0206x - 0.0015

u R

The only way to vary r at constant linear speed is to vary R. The derivatives Yr and Nr are obtained by evaluating the slopes at r = 0. Because of ship symmetry, the values of Yr and Nr at the negative values of r are a reflection of their values at positive r but with opposite sign. This test condition is simulated using SHIPFLOW software for different radius of rotation. Hydrodynamic derivatives are calculated using the forces and moments obtained by SHIPFLOW.

Y’

Yr'

0.0049 0.0029 0.0009 0.05

0.25 r’

0.45

Fig 11 Y’ vs. r’ plot

Nr' 0.0325 y = 0.065x - 0.0049

0.0275 0.0225 N’ 0.0175

Nr'

0.0125 0.0075 0.0025 0

0.2

r’

0.4

0.6

Fig 12 N’ vs. r’ plot

Fig 10 Rotating arm test Hydrodynamic Derivatives Hydrodynamic derivatives are calculated using least square method using forces and moment obtained by SHIPFLOW. These hydrodynamic derivatives are shown in Table 2. Graph has been plotted between Y’ vs. r’ and N’ vs. r’ which shown in Fig 11 and Fig 12 respectively.

4.4 TURNING CIRCLE SIMULATION Introduction Sea trial and free running model tests are straightforward methods to obtain IMO maneuverability criteria. However the free running model test is not practical due to limitations of towing tank and it is also expensive. Computational simulations are advantageous than free running model tests for assessing vessel controllability and maneuvering performance. Once


International Conference on Computational Experimental Marine Hydrodynamics MARHY 2014 3-4 December 2014, Chennai, India. the hydrodynamic derivative are calculated using the captive model test or theoretical method or using RANS based CFD, almost any maneuver or ship operation can be simulated without additional model tests. The simulation model can be readily and economically modified to determine the effect of changes, such as increasing of rudder size. The linear equations of motion have only limited use. If a vessel is straight - line stable, they can be used, in principle, for maneuvering prediction, if the considered maneuvers are not too tight. If they are tight, the result will not be accurate enough, as contributions of nonlinear terms become significant and they could no longer be ignored. If a vessel is path-unstable, the linear system of equations cannot be applied at all, as the solution will have a tendency of unlimited increase and only nonlinear terms could stop its growth. A nonlinear system is derived from nonlinear terms in the Taylor series expansion of usually it is expanded up to the third power, as the terms of higher order are small in most cases. In general, which terms will be retained is determined by both theoretical consideration and practical experience. Numerical values of hydrodynamic derivatives come from model tests with planar motion mechanism (PMM), rotating arm, a free running model, empirical formulas or RANS based CFD. There are numerous formulations of the nonlinear equations, but the most common are the cubic and quadratic nonlinearity. The quadratic nonlinearity be used here because of the availability of a complete set sample data. However, cubic nonlinearity may also be used.

Fig 11 Turning circle plot The steady turning diameter has been found to be 27.615m Calculation of tactical diameter according to abs guidelines

V TD STD  0.910  0.424 S  0.675 L L L (4.1) Eqn 4.1 shows the calculation of tactical diameter Where, TD

=

tactical diameter in m,

Vs

=

test speed in knots

Simulation Program The system of equations used here is given in ABS Rule for Vessel maneuverability, which is a more simplified form. The system of equation is integrated with respect to time using MATLAB (2012 b) software to get the trajectory for turning circle maneuvers. In the input block, the code will read the input data such as rudder angle and hydrodynamic coefficients. These input data will then be used in the process block in order to calculate the hull, rudder and propeller forces. Hull modules are divided into three sub-blocks called surge, sway and yaw sub-block. Surge, sway and yaw acceleration are calculated using the nonlinear equation. The equation of motion was double integrated to obtain the translation of motion in the x and y direction. Fig 11 shows the predicted turning circle.

L

=

STD

=

length of the vessel in m, measured between perpendiculars, standard tactical diameter in m

Tactical Diameter = 35.27 m < 5L. Hence IMO criteria have been satisfied. Table 3 gives the comparison between turning circles calculated in different ways. Table 3 Comparison of tactical diameter in ship’s length Parameter

ABS guidelines

Present result

Sea trial result

Tactical diameter in ship’s length (m)

5

4.47

3.8


International Conference on Computational Experimental Marine Hydrodynamics MARHY 2014 3-4 December 2014, Chennai, India. The difference between computational and sea trial results may be attributed to the nonlinear terms of hydrodynamic coefficients, which were neglected in the present analysis. In spite of the inaccuracy of present linear analysis, the predicted tactical diameter qualifies the ABS criteria in a very similar way as the actual sea trial result does . 5

CONCLUSIONS • In view of the present state of art, successful analysis for computational estimate of Tactical Diameter for ship, as reported in the present work is very encouraging. • Velocity dependent variables were calculated using static maneuvers. •

Stability condition was checked.

• Turning circle maneuver has been simulated using ABS guideline for maneuverability. Results agreed well with sea-trial observations. • As the results obtained are in good agreement with the sea-trial results, RANS based CFD tool can be used for calculation of turning circle/hydrodynamic derivative calculation at early design stage to predict maneuvering characteristic of vessel.

6

REFERENCES 1. American Bureau of Shipping, 2006, Guide for Vessel manoeuvrability, American Bureau of Shipping. 2. Fossen, T. I., 1999, Guidance and Control of Ocean Vehicles, University Of Trondheim, Norway. 3. Lewis, E. V., 1988, Principles of Naval Architecture, The Society of Naval Architects and Marine Engineers, Jersey city, NJ. 4. SHIPFLOW 5.0 Users Manual, 2013, Flowtech International AB, Sweden. 5. NSTL Report Number NSTL/HR/HSTT/203 A “Hydrodynamic Model Tests For P-15 VesselMar 2008.
