Abstract
Catamarans continue to increase in size and application, with proposals circulating within the
shipbuilding industry for bigger and better designs than the present generation of catamarans. The present paper attempts to show a comparison of resistance calculation of a small fast catamarancarri ed out by experimental and CFD techniques. Experimental tests were carried out with a scaled model at the Towing Tank facilities at University Austral of Chile. CFD simulation using the RANSE code TDYN and Potential Flow code SHIPFLOW was used to calculate the resistance of a prototype catamaran for high-speed operation. The code includes automatic modfi cation ofthefree sii rface and therefore dynamic trim and sinkage changes are considered in the solution. Several published articles in well-known journals have detailed various proceda res to estimate the resistance characteristics of catamarans. Since few published articles are in existence regarding experimental data on catamarans, it is the aim of this research to undertake a CFD analysis to predict the wave resistance and ultimately the total resistance.
Experimental investigation appears to provide very good agreement as has been observed in the
resistance curves showing that CFD methods may adequately deal with the problem of wave
interference produced by both demihulls. A further conclusion by the authors is that panel density on free surface needs to be defined ade quately to capture the waves in the transom at higher Froudenumbers.
1. Introduction
The present paper presents a comparison between CFD and experimental methods in the prediction of calm water resistance of a small fast catamaran. The comparison is restricted to an existing hull form with fixed demihull separation:
therefore the results presented here are
not intended to be
representative of an optimization approach. Moreover the discussion should be viewed simply as a validation test on the reliability of CFD methods for this particular catamaran. Although it is possible to carry out a hydrodynamic optimization using purely numerical methods (López et al. 2000; Kim et al. 2000), is it considered much safer to compare CFD results against experimental data (Stern et al.
1998).
A multidisciplinary approach including CFD is thought to be the way forward in hydrodynamics optimization (Peri 2003, Maisonneuve et al. 2003), however the accuracy of CFD methods is still not completely reliable and current research is being devoted to validate CFD techniques (Mehta 1998, Coleman and Stern 1998). It is then necessary to be cautious when performance predictions are involved, although the necessary validation procedures are being developed (Stern et al. 1999; Larsson et al. 2003).
In order to evaluate and confront both experimental and theoretical results, two different CFD codes are used to calculate calm water resistance for a small fast catamaran. Both sets of numerical results are then compared to experimental results obtained for scaled model at the towing tank at University Austral of Chile.
Experimental and CFD Resistance Calculation
of a Small Fast Catamaran
M. Salas'; R. Luco'; P. K Sahoo2; N. Browne2 and M. López3 University Austral of Chile. msalas@uach.cl
2
Australian Maritime College. P.Sahoo@mte.amc.edu.au Nautatec, Spain. nautatec@nautatec.com
2. Catamaran main characteristics
The tested vessel corresponds to a small fast catamaran built by Aiwoplast in Chile. The hull, decks and bulkheads are sandwich panels made of composite materials with foam core. The structural configuration of this craft has been illustrated by Ojeda et al. (2004).
Main particulars of the vessel are given in Table 1 below whiles Figures 1 and 2 depict the built vessel and the hull geometry respectively:
Table 1: Geometrical Parameters of full scale vessel
Figure 1: The tested catamaran
3. CFD Method
From the mathematical point of view, the equations governing the fluid motion around a vessel are known since the 19th century. Although the equations have practical applications they cannot be solved analytically. In recent times Navier-Stokes equations have been solved using numerical algorithms. Nowadays contour elements or singularity methods are the base of most numerical algorithms used in the prediction of calm water resistance of ships.
3.1 RANSE code Tdyn
Primarily the CFD investigation was carried out using Tdyn (2004) CFD code. It is beyond the scope of this paper to show the mathematical details of the code. López et al. (2000) and García et al. (2002) have provided an extensive discussion on this aspect. However some general description of the solver algorithm may be of interest. The CFD code is based on the FEM and may use almost any type of element, but it is optimized for using linear tetrahedra. An unstructured grid is used to enhance geometry flexibility and to speed up the initial modeling time.
Figure 2: Hull geometry
Parameters Dimensions
Length over all 16.76 m Beam maximum 6.00 m
Depth 2.40 m
Draught 0.80 m
Displacement 19 tonnes Service Speed 22 knots
3.1.1 Free surface discretization
The discretization of a general three-dimensional computational domain into an unstructured assembly of tetrahedra is accomplished by means of an advancing front grid generation procedure. This procedure requires the geometry of the computational domain to be defined in terms of an assembly of surface patches. In this case the surface definition of a complete computational domain, consisting of hull and appendages surfaces, free surface, inflow plane, exit plane, and bottom and lateral surfaces is based on NURBS patches (Kim and Shin 2003).
3.1.2 Boundary conditions
Boundary conditions are allowed to be assigned directly on the geometrical entities and automatically transferred to the grid. This utility permits not to re-assign boundary conditions every time a new grid is generated. Furthermore, boundary conditions may be defined by analytic functions. This fact allows performing different drift angle analyses using the same grid, by changing the inflow condition. Other kind of phenomena like non-uniform flows may also be simulated in a similar way.
3.1.3 Control Volume
Finite element solution of a fixed control volume is in most cases accurate enough for design
purposes. However, a great quantitative performance of results may be obtained in some cases by updating the domain, taking into account free surface deformations and a dynamic sinkage and trim of the boat. The procedure used to update the domain is now summarized.The hull model is first considered in an estimated steady state position. A planar or quasi-planar surface is used as reference for free surface calculations. An automatic unstructured grid generator based on the advancing front technique is used to generate a surface mesh and a volume mesh. A steady state simulation is performed with the hull in this initial position.
The net heave force and trim moment acting on the hull are calculated from the previous converged solution. The sinkage and trim corrections required by the equilibrium of this force and moment are evaluated. Free surface is updated accordingly to previous results. This is made at CAD level, generating a new NURBS surface based on the previous triangulation of the free surface. A new domain is then created within the preprocessor, repositioning the hull and using the new free surface. This process is automatic, but if necessary may be controlled by the user by means of a wizard-type too]. Finally, a new mesh is automatically generated.
A steady state simulation is performed again in the new domain. A converged free surface is obtained for this given hull position at the end of the present step. This process should be repeated until a convergence of the results. Experience shows that one iteration is enough in most of the cases to obtain forces results within the uncertainty band.
The sinkage and trim corrections are expressed in terms of the net heave force and trim moment using the following relations:
=
_F
pgAM. pgl
& is a correction of the sinkage at a center of gravity, ¿a is a trim angle correction. F, and M, are a net heave force and a trim moment. A, is the water plane area, and Jy is the corresponding moment of inertia about the transverse y-axis. The heave force and the trim moment are defined in terms of the pressure p and the viscous stress tensor components r . which can be obtained directly from the flow
solver.
New free surface NURBS definition, taking the resulting deformation into account, is generated in I
NURBS Cartesian support grid of MxN points is created. M and N are calculated in terms of the number of local maximum in the X and Y axis directions.
Z coordinate of the points, representing the wave elevation, is interpolated into the grid. This interpolation is based on a weighted function of the nearest points. The nearest points are easily located by using a quad-tree structure.
Finally, the NURBS surface based on the support grid is generated. Boundaries of the NURBS are defined by projecting the original ones in the Z direction.
3.2 Potencial Flow code SHLPFLOW
Shipflow uses panel methods to calculate the co-efficient of wave resistance, and therefore it is necessary to define the grid of panels that will be used for the analysis. The module XMESH is used to define the groups/surfaces that are to be considered. To define the grid of panels representing the body, the number of stations to be used along the length of the hull and the number of points across each station must be specified.
Results of CFD simulations were then confronted with experimental measurements of hull resistance in order to validate the numerical predictions.
Flow
Zone 2
Boundary Layer Method
Figure 3: Zonal Approach in SHLPFLOW Solver
The theoretical wave resistance coefficient, C, is calculated by splitting the flow into three regions where an efficient approximation of the flow equations may be made and a complete flow calculation may be accomplished in a few hours using the potential flow, as described by Larsson (1993). Figure 3 represents the zonal approach or regions used by SHIPFLOW to maximise computational efficiency.
Flow in Zone I is calculated using a higher order panel method with linear or non-linear free surface boundary conditions.
Flow in Zone 2 is calculated using momentum integral methods for laminar and turbulent boundary layers.
Flow in zone 3 is calculated using the Reynolds-Average Navier-Stokes method with a k-epsilon turbulence model and a numerically generated body fitted coordinate system.
4. Model and Experimental Procedure
A FRP model, of scale factor . = 17, was built to carry out the towing tank tests. No appendages were installed on the model, and all the experiments were done to the full load displacement, of 19 tons. Experiments were conducted for the range speed of 8 to 28 Knots, corresponding to FN of 0.35 to 1.2. Tests were carried out in the towing tank of the Institute of Naval and Maritime Sciences at the University Austral of Chile. Tank dimensions are 45 m in length, 3 m width and 2 m water depth. Model was towed at the required speed (same full-scale Fn ) by a cable connected to a dynamometer where drag is measured and directly recorded into a computer. Models are free to trim and trim angles may be measured if required.
Zone i Zone 3
Results from model experiments were extrapolated to the full-scale craft using the IYFC extrapolation procedure and ITTC ship model correlation line, correlation allowance of A]ITC of 0.0004 over the friction coefficient of the prototype and zero over the friction coefficient of the model. All data presented in this investigation corresponds to the full-scale craft, floating in smooth, deep salt-water conditions, with a uniform standard temperature of 150 C.
To induce turbulent flow along the length of the model hull, 16 turbulence stimulator studs were placed at both demihull bows, as can be seen in Figure 4. No particular turbulence transition location was aimed with this stud configuration. Figure 5 shows the scaled model undergoing towing tank tests.
Figure 6: CFD wave height at 28 knots
_'Ø- .-: ...
L -. . ____ -- -a. - -. . - .-. -- .-- :.-
:--
.-.
-.Figure 7: Free surface at 16 knots
Finally resistance predictions from experimental tests and both CFD codes are presented in Figure 8. In Shipflow results wave resistance of the model has been calculated based on the regression equation developed by Sahoo et al. (2004).
Figure 4: The model fitted with studs Figure 5: Towing tank test
5. Results
Figures 6 and 7 depict the results of wave height and free surface obtained under different simulated speeds of Tdyn CFD.
00 0.2 0.4
Total Resistance Coefficient
s
£
.
Fn
Towing Tank --o- -Shipf low
.û Tdyn
Figure 8: CFD and Towing Tank resistance predictions Conclusions
In the low speed range both CFD codes predict higher CT than the towing tank. The disagreement may be due to trim angle being affected by pulling cable in the experimental tests. Between Fn 0.5 and Fn 0.9 Tdyn agrees closely with experimental results as both total resistance curves are almost identical. Shipflow resistance estimates are slightly higher than CFD Tdyn and Towing Tank resistance results in this speed range.
Both CFD codes. i.e. Tdyn and Shipflow, produce very close total resistance coefficients all over the speed range. CFD codes and experimental results are in remarkable good agreement above Fn 0.5 and upto Fn 1 .0, for higher speeds numerical results predict lower resistance than the towing tank. The difference is about 20% forFn 1.2
Acknowledgements
The authors would like to express their sincere gratitude to The University Austral of Chile and The Australian Maritime College, Australia for their support, encouragement and financial help rendered throughout the course of this research work.
References
Coleman, H.W. and Stern, F. (1998). "Uncertainties in CFD Code Validation". ASME J. Fluids Eng., Vol. 120, pp. 635-636.
García, J., Luco, R. Salas, M., López, M. and Oñate, E. (2002) "An Advanced finite element method
for fluid-dynamic analysis of America's Cup boat", Proc. of High Performance Yacht Design
Conference. pp. 21-29. Auckland, New Zealand. 4-6, Dec. 2002.0.025 o 0.020 15 0.0
I.-o
4
'S 0.010 -.5 5.-005 0 0.000 0.6 0.8 1.0 1.2Kim, B. and Shin Y. (2003). "A NURBS Panel Method for Three-Dimensional Radiation and
Diffraction Problems". Journal of Ship Research, VoI. 47. N°2. pp.1 77-1 86.Kim, W., Kim, D. and Van, S. (2000). "Development of wave and viscous flow analysis system for computational evaluation of hull forms" Ship and Ocean Technology, Sept. 2000, Vol. 4, N° 3, pp. 33-45.
Larsson L., Stern, F. and Bertram, V. (2003) "Benchmarking of Computational Fluid Dynamics for Ship Flows: The Gothenburg 2000 Workshop". Journal of Ship Research, Vol. 47, N°1, pp. 63-81. Larsson, L. (1993), "Resistance and Flow Predictions Using SHIPFLOW Code". 19thWEGEMNT School, Nantes, France.
López, M.; Garcfa, J. and Oñate, E. (2000) "Recreational craft optimization using a CFD code" (In Spanish) Barcelona, Spain. Technical workshop on sport craft.
Maisonneuve, J., Dauce, F. and Alessandrini, B. (2003). "Towards Ship Optimal Design Involving CFD'. Proc. of CFD 2003: C'omputational Fluid Dynamics Technology in Ship Hydrodynamics,
London pp. 3 1-41.
Mehta, U.B. (1998). "Credible Computational Fluids Dynamics Simulations". AIAA Journal, Vol. 36, pp. 665-667.
Ojeda, R.; Prusty, B. G. and Salas M.. (2004) "Finite Element Investigation on the Static Response of a Composite Catamaran under Slamming Loads". Ocean Engineering, Vol. 31. pp. 901-929
Peri, D and Campana, E. (2003). "Multidisciplinary Design Optimization of a Naval Surface
Combatant". Journal of Ship Research, Vol 47. N°1. pp. l-12.Sahoo, P.K., Browne, N.A. and Salas, M. (2004). "Experimental and CFD Study of Wave Resistance of High-Speed Round Bilge Catamaran Hull Forms". Proc. of the 4th International Conference on High Peiformance Marine Vehicles (to be published).
Stern,F., Longo, J., Abdel-Maksoud, M. and Suzuki, T. (l998)."Evaluation of Surface-Ship Resistance and Propulsion Model-Scale Database for CFD Validation". Proc.of ist Symposium on Marine Application of Computational Fluid Dynamics, 19-2 1 May 1998, McLean, VA.
Stern, F.. Wilson, R.V., Coleman, H. and Paterson, E. (l999)."Verification and Validation of CFD Simulations". Proc. of 3rd ASME/JSME Joint Fluids Engineering Conference, San Francisco, CA,
18-23 July 1999.
