Time-Domain Simulation of Large Amplitude Ship Roll Motions by a Chimera RANS Method. Hamn-Ching Chen and Tuanjie Liu. Texas A&M University. College ...
Proceedings of the Eleventh (2001) International Offshore and Polar Engineering Conference
Stavanger, Norway, June 17-22, 2001 Copyright © 2001 by The International Society of Offshore and Polar Engineers ISBN 1-880653-51-6 (Set); ISBN 1-880653-54-0(I/o1.111); ISSN 1098-6189 (Set)
Time-Domain Simulation of Large Amplitude Ship Roll Motions by a Chimera RANS Method Hamn-Ching Chen and Tuanjie Liu
Texas A&M University
College Station, TX, USA Erick T. Huang
Naval Facilities Engineering Service Center Port Hueneme, CA, USA
ABSTRACT
have been conducted for roll motions of floating bodies. Time-domain fully nonlinear simulations of parametric roll motions were studied by, among others, Cointe et al. (1990) and Tanizawa and Naito (1997, 1998). However, most of the numerical studies were using potential flow methods with the artificial damping terms added to dynamic and kinematic free surface boundary conditions. More recently, Yeung, Liao and Roddier (1998) and Yeung and Liao (1999) developed a free-surface randomvortex method for the simulation of floating cylinders in viscous fluid. Kang, Chen and Huang (1998) and Chen, Kang and Huang (1998) employed a chimera domain decomposition approach for the simulation of viscous nonlinear free surface flows induced by 2D ship sway, heave, and roll motions. In the present study, the chimera RANS method of Chen and Chen (1998), and Chen et al. (2000) was generalized for large amplitude roll simulations around practical ship and barge configurations. Calculations were performed first for a motor vessel under prescribed roll motions. The method was then extended for free decay roll simulation of a barge in calm water. Finally, the method was employed for time-domain simulation of a free-floating barge subject to large amplitude incident waves. A parametric study was performed to examine the resonance effects between the roll motion responses and incident wave conditions.
A Reynolds-Averaged Navier-Stokes (RANS) numerical method has been employed in conjunction with a chimera domain decomposition approach for time-domain simulation of large amplitude ship roll motions. For the simulation of arbitrary roll motions, it is convenient to construct body-fitted numerical grids for the ship and ambient flow domain separately. The ship grid block is allowed to roll with respect to its center of rotation under either forced or free roll conditions. The roll moments are computed every time step by a direct integration of the hull surface pressure and shear stresses obtained from the chimera RANS method. The simulations for prescribed roll motions of a full-scale motor vessel clearly show that the bilge keels at the mid-ship produced large roll damping but generated very little waves. On the other hand, the ship skag acts like a wavemaker during the roll motion and produced large wakes in the stem region. Time-domain simulations were also performed for a freefloating pontoon barge in free decay motions and under large amplitude incident waves. The simulation results successfully predicted the roll resonance when the incident wave coincides with the free decay period of the barge. KEYWORDS: Ship roll motion, Free decay simulation, Incident waves, Turbulent flow, Navier-Stokes. equations, Chimera domain decomposition.
NUMERICAL METHOD INTRODUCTION The present study is concemed with the roll motion of two- and three-dimensional ships with or without the presence of ambient waves. Simulations were performed first for prescribed roll motions in calm water to evaluate the general performance of the numerical method. The method was then extended to simulate free-floating bodies in ambient waves under various incident wave conditions.
The roll motions of ships and barges to incident waves are one of the primary concems in naval architecture and ocean engineering. For small amplitude wave and body motions, linear or perturbation theories are often used in frequency domain to predict the responses. During the past decade, several numerical and experimental studies
299
For viscous flow simulations, the chimera RANS method of Chen and Chen (1998) and Chen et al. (2000) has been employed for accurate resolution of the viscous free surface flow induced by ship roll motions. The method solves the nondimensional Reynolds-Averaged NavierStokes equations for incompressible flow in orthogonal curvilinear coordinates (x~, t): U ,i~ = 0
U.=V.=W.=O.
Ot
jk
U,ijk_~ 0
2 on z=~7
(4)
A more detailed description of the chimera RANS/freesurface method was given in Chen and Chen (1998) and Chen et al. (2000). RESULTS AND DISCUSSION
In the present study, the chimera RANS method is employed first for the calculation of a motor vessel shown in Figure 1 with prescribed roll motions. The ship length L is 57.3 m and the draft D is 3.58 m. Calculations were performed for a prescribed roll angle of +5 degrees and a roll period of 10.5 sec. A characteristic velocity Uo --- L/T = 5.46 m/s is used for the normalization of RANS equations. This gives a Reynolds number of 2.79 x 10~ and a Froude number of 0.23 based on the ship length. A 61 x 25 x 61 boundary fitted grid is used around the ship hull as shown in Figure 1. The ship grid is completely embedded in a 61 x 51 x 21 rectangular harbor grid. In the present chimera domain decomposition approach, the ship grid is allowed to roll with respect to the harbor grid during the simulation. The numerical grid for the ship and harbor blocks were regenerated every time step to conform to the submerged hull geometry and the free surface elevation. A grid-interface conservation technique (Chen and Chen, 1998) was employed to enforce the conservation of mass and momentum in the overlap region between the ship and harbor grid blocks.
(1)
. . . . + g ~ p , j _ ~ 1e g ~Ui t..uJu,ij +u,u.l,j
p=q/Fr
(2)
where ~ and u i represent the mean and fluctuating velocity components, and gO is the conjugate metric tensor, t is time p is pressure, and Re = UoL/v is the Reynolds number based on a characteristic length L, a reference velocity Uo, and the kinematic viscosity v. Equations (1) and (2) represent the continuity and mean momentum equations, respectively. The equations are written in tensor notation with the subscripts, ,j and ,jk, represent the covariant derivatives. In the present study, the two-layer turbulence model of Chen and Patel (1988) is employed to provide closure for the Reynolds stress tensor ui u j . The RANS equations have been employed in conjunction with a chimera domain decomposition technique for accurate and efficient resolution of body boundary layer and flow separation around ships in either prescribed or free roll motions. The method solves the mean flow and turbulence quantities on embedded, overlapped, or matched multiblock grids. Within each computational block, the finite-analytic method of Chen, Patel and Ju (1990) is employed to solve the RANS equations in a general, curvilinear, body-fitted coordinate system. The overall numerical solution is completed by the hybrid PISO/SIMPLER pressure solver to ensure that the equation of continuity is satisfied at each time step. The free surface boundary conditions for viscous flow consist of one kinematic condition and three dynamic conditions. The kinematic condition ensures that the free surface fluid particles always stay on the free surface. It can be expressed as
Figure 1. Numerical grid. ~7,+UTL+Vqy-W=O
on
z = r/
(3)
Figure 2 shows the computed hull surface pressure and velocity vector plots at t/T = 10.25 when the ship is at the maximum roll angle of 5 degrees. For completeness, the hull pressure contours for one complete roll cycle are also shown in Figure 3 to illustrate the complex threedimensional flow features induced by the prescribed roll motions. It is clearly seen that the bilge keels produced a pair of vortices in the opposite direction of the ship motion. The minimum pressure region was seen to occur just behind the bilge keels. Due to the large pressure
where 7?is the wave elevation and (U, V, W) are the mean velocity components on the free surface. The dynamic conditions represent the continuity of stresses on the free surface. When the surface tension and free surface turbulence are neglected, the dynamic boundary conditions can be obtained by extrapolation of the velocities from the inner fluid domain and maintaining a constant total pressure on the free surface. 300
differences between the front and back faces of the bilge keels, a large roll damping was observed near mid-ship sections. In the stern region, the skag also caused extensive flow separation and produced large resistance to the roll motions.
velocity vector plots at X/L = 0.1514, 0.2997, 0.5027 and 0.9213 to provide a more detailed assessment of the crosssectional geometry on roll damping. It is clearly seen that the bilge keels at X/L = 0.5027 induced strong vortices and local flow separations. However, the free surface at the mid-ship is nearly undisturbed except for a small region inside the boundary layer. On the other hand, the skag acts like a wavemaker and produced large vertical velocity components adjacent to the free surface. The stern waves generated by the skag motion are significantly higher than those observed in the bow and mid-ship sections. The propagation of the free surface wave due to the skag roll motions can be clearly seen from the pressure contour plots at X/L = 0.9213. ( A 1 ) X / L = 0 . 1 5 1 4 , t/I" = 9 2 5
0 t¢.0.05 -0.1 , I
. . -0.2
.
. Z0~l
0
-.
, 0.1
:o~--
0.2
0.3
0.2
...... 0 . 3
Y
Figure 2. Pressure contours and Velocity vector plots
~-0,05
"
-O,1 F
(a) P r e s s u r e C o n t o u r s : f i t = 10.00, Angl e = 0 d e g r e e
-0;2
..,0;1
0
=
0 Y
0;1
"
=
"
eq.O.05
-0.1 3 Y
(b) P r e s s u r e C o n t o u r s : t/T = 10.25, Angl e = 5 d e g r e e s [
o
(A4) X/L = 0.1514,
t/T = 10.00
e~-0.05 -0.1 I
-0.2
:0:i
0
0.1
0.2
" 0~3
Y
(e) P r e s s u r e C o n t o u r s : t/T = 10.50, Angl e = 0 d e g r e e 0 [
(B1) X/L=
0 . 2 9 9 7 , t/I" = 9 . 2 5
~0.05 -0.l .0.2
(d) P r e s s u r e C o n t o u r s : t/T = 10.75, A n g l e = -5 d e g r e e s
,o.1 0 Y (B~) X/L = 0.2997,
0.1
o".2
0~3
t/r = 9,50
o b,~-O.05
-0.1 ~
3 Y X/L = 0.2997,
0 ~
Figure 3. Pressure contours for motor vessel at 5 ° roll
A detailed examination of the mean velocity field for motor vessel indicated the presence of a strongly threedimensional flow field with large longitudinal velocity components. In order to ascertain the influence of crosssection geometries on roll damping characteristics, calculations were also performed for several twodimensional ship cross sections at 10 ° roll motions. Figure 4 shows the computed pressure contours and
i
-o.2
-o.1
-
o
t / r =, 9 . 7 5
o.1
o.2
~.3
Y o
=
*
=
0 Y
0~1
"
tq-0.05 -0.1 [
..0.2
:,0.I
"
.... 0~2 " - "JE~'O.3
Figure 4. Pressure contours for 2D ship sections at 1 0 ° roll motion: (A) X/L = 0.1514, 03) X / L = 0.2997. 301
o
=
°
=
/
°
It s h o u l d b e n o t e d that t h e r o l l m o m e n t
-0.1
-0.2
[
-0.1
0 Y (C~) X/L = 0.5027,
I
O.I
0
0;3
0.2
~.3
UT = 9.50
~o.o5° -o.1
[
-o.2
-
-
"
-o.l
o[
_
~ Y
....
~,I- "
(c3) X/L = 0.5027, t/T = 9.75
t~0.05
-0.1
.
.
.
.
.
.
.3
Y 0
=
"
=
"
t'~-0.05
-0.1
c o n s i s t s o f three
parts due to hydrostatic pressure, hydrodynamic pressure, and shear stresses. For clarity, we will present only the roll moments produced by the hydrodynamic pressure and shear stresses here since the roll motions were prescribed. The contributions due to the hydrostatic pressure will be included later for flee floating cases when the total roll moments due to both the hydrostatic and hydrodynamic pressures are needed for the prediction of roll motions. It is seen from Figure 5 that the roll moment is produced almost entirely by the hydrodynamic pressure gradients. The contributions due to shear stress is negligible except for the first station X/L = 0.1514 near the bow. Furthermore, there is a phase shift of about 40 ° between the roll motion and the induced roll moment. This phase shift is significantly smaller than the 180 ° phase lag for the hydrostatic pressure component. The phase differences between the hydrostatic and hydrodynamic pressure components are caused by viscous effects and flow separations.
t~0.05
3 Y
~
.
~
°
~ , 30
0 t,~-0.05
30 20 "~"
20
-0.1
3
,.- 10
Y
I
(D2) X/L = 0.9213, tel ` = 9.50
10 "o
0
0
•
t40.05
-
