Computing Added Resistance in Waves Rankine Panel Method vs RANSE Method Heinrich Söding, TU Hamburg-Harburg, Hamburg/Germany, h.soeding@tu-harburg.de Vladimir Shigunov, Germanischer Lloyd SE, Hamburg/Germany, vladimir.shigunov@gl-group.com Thomas E. Schellin, Germanischer Lloyd SE, Hamburg/Germany, thomas.schellin@gl-group.com Ould el Moctar, Germanischer Lloyd SE, Hamburg/Germany, moct@gl-group.com Sebastian Walter, Universität Duisburg, Duisburg/Germany, presently Meyer Werft GmbH, Papenburg/Germany, sebastian.walter@meyerwerft.de 1 Introduction Ship design is usually performed on the basis of powering requirements in calm water without detailed consideration of actual operating conditions. The effect of seaway is included using an experience-based allowance on the required power called sea margin. This practice can lead to either unnecessary excessive power reserves or to underpowered ships. Reliable prediction of the propulsion power increase in waves is important for both ship designers (selection of the propulsion system) and operators (establishing time schedules, estimating service speed and fuel consumption, optimising speed and course). 2 Model tests Model tests for added resistance in waves use either self-propelled or towed models. Selfpropelled models eliminate the influence of the towing equipment on model motions; however, the influence of motions and waves on the thrust deduction factor (required to estimate the added resistance) remains a factor of uncertainty. Towed models have either restrained surge motion or they are connected by soft springs to the towing carriage. Restraining the surge motion may influence added resistance, especially if it interferes with pitch and heave motions; thus the arrangement with springs appears more appropriate. The model set-up should ensure that springs do not influence ship motions; for instance, the natural frequency of the springs must differ from the encounter frequency as much as possible. Another difficulty with experiments for added resistance in waves is that added resistance (average longitudinal force over time) is small compared to the amplitude of force variations. Thus, errors in measuring these forces might be comparable to or even exceed the average force itself. Further, added resistance is sensitive to the quality of wave generation and wave measurement, especially in short waves, because, unlike linear reactions, added resistance depends on wave amplitude squared. 3 RANSE solvers CFD methods might, in principle, directly address the problem of power increase in irregular waves (if combined with an engine model). However, both long waves (leading to large ship motions) and short waves (which contribute to added resistance by wave diffraction) have to be resolved simultaneously, which would increase significantly the required grid size, number of cells and computational time. Therefore, CFD methods have so far been applied only to the problem of added resistance in regular head waves in a restricted range of wave frequencies. CFD methods provide total resistance, i.e., calm water resistance and added resistance in waves. The calm-water contribution has to be calculated separately on the same grid used to
predict total resistance and subtracted from the total resistance. To accurately compute calmwater resistance, fine grids are required to resolve the turbulent boundary layer on the hull and the steady wave system. Much coarser grids suffice for the resolution of (medium and longer) incoming, radiated and diffracted waves that are relevant for added resistance. Predictions of ship motions and added resistance in medium and long waves agree well between fine and coarse grids (Fig. 1). This suggests that added resistance in medium and longer waves can be computed on grids which resolve the waves, but not the boundary layer. To obtain total resistance, an additional calculation on a fine grid is necessary. 4 Potential flow codes Because CFD methods require too much computer resources to study the influence of various parameters on added resistance, potential flow methods are applied predominantly. Linear seakeeping analysis describes ship response (motions, sectional forces and moments, hull pressures, etc.) as time-periodic sinusoids, neglecting effects that depend nonlinearly on wave height. Time averages of linear responses are zero. However, waves generate also forces and moments that are non-zero when averaged over a wave encounter period. The lowest non-zero order of these forces and moments is two, i.e., they are proportional to wave amplitude squared. In a regular wave of encounter frequency ω e, any second-order effect consists of a part which oscillates with frequency 2ω e and has the average zero, and of a stationary part. Only the latter is of interest here. It can be determined without knowing the second-order oscillating flow potential; that simplifies the solution. But even the remaining potential flow problem is so complicated that certain terms (e.g. those containing third-order space derivatives of the stationary potential) have to be neglected. Within the second-order framework, effects like wave breaking or the hull shape above the stationary waterline cannot be accounted for. (Model tests and numerical simulations showed that bow sharpness above the calm-water waterline influences added resistance.) When considering the energy balance, increased resistance in waves is caused by (a) wave radiation due to ship motions and (b) diffraction of incident waves by the ship hull. The radiation-induced added resistance is large when ship motions are large, i.e., in longer waves. The diffraction of incident waves produces a diffraction-induced component of added resistance, which depends weakly on wave frequency and thus becomes the dominant component in shorter waves, where ship motions are small. In short waves, say for waves shorter than 1/4 to 1/3 of ship length, added resistance is difficult to predict accurately by any method. Instead of considering this energy balance to compute added resistance, we prefer to use the pressure distribution on the hull. The second-order stationary force follows from the expression F 2 = all panels (p 0 f2 +p 1 f1 +p 2 f0 ) + waterline panels ˆp 2 s ( f 0 s ) 4ρg ( f 0 s ) 3. (1) Indices 0 to 2 indicate the order (with respect to wave amplitude), whereas index 3 designates the vertical component. Here, p is pressure at a hull-fixed location, ρg is the statical downward pressure gradient, f is the panel area vector (inward normal direction in inertial coordinates), and s is a vector along the stationary waterline contour. An overbar designates a time average, and the hat symbol indicates amplitude. The first sum designates the second-order force on the hull up to the stationary waterline; the last term takes account of the variable hull immersion including dynamic swell-up. 5 Potential flow code GL Rankine Here a new panel method is applied to compute added resistance in waves. Code GL Rankine is based on the theory described in Söding (2011). Söding et al. (2012a,b) give more GL Rankine
Table I: Main particulars of WILS containership L pp 321.00m KG 21.296m B 48.40 m GM 2.000 m T 15.00m k xx 19.073m C B 0.6016 k yy = k zz 77.228m applications for other ships (Wigley hull and KVLCC2 tanker). The frequency-domain panel method is based on Rankine sources. Like in other Rankine source seakeeping codes, the flow potential is taken as the sum of the parallel flow due to forward speed, the steady disturbance potential φ 0, and the time harmonic flow potential due to the incoming wave, its diffraction at the hull and due to ship motions: φ = ux+φ 0 ( x)+re(ˆφe iωet ). (2) One distinctive feature of our code is the steady disturbance potential: It is taken to be constant in the ship-fixed coordinate system, not in the inertial system as usual. Both assumptions are physically correct, but they lead to different boundary conditions for ˆφ and thus to different amplitudes ˆφ. The so-called m terms, which are difficult to determine accurately, appear in our formulation not in the hull boundary condition, but in the free surface boundary condition, where they can be determined more accurately and where inaccuracies have less influence on the pressure force on the hull. Other features in which our method differs from other Rankine source methods are: No second derivatives of the steady potential appear in determining the first-order hull pressure. (These terms should be present in the usual Rankine source method, but are mostly ignored.) A transom condition is satisfied, which states that, at an immersed transom, the water surface hight oscillates just as that of the transom. The term involving f 2 in (1) is ignored in other methods; the same holds for some terms in the complicated expression for p 2. 6 Test case As a test case, the WILS containership designed by the Maritime and Ocean Engineering Research Institute (MOERI) is used. The model was tested in two wave directions at two Froude numbers at scale 1/60 under the Joint Industry Project WILS II. Table I lists main particulars of the ship. Two experimental techniques provided the average longitudinal force in waves. One technique relied on the sum of the spring forces; the other, on the relative surge displacement of the model with respect to the carriage. The resistance in calm water was subtracted from the post-processed resistance to obtain added resistance in waves. Here, the test in head waves at the Froude number 0.183 was used for validation. Both GL Rankine and the RANSE code Comet were used to compute added resistance for the full-scale ship. The RANSE simulations were performed on two different grids. The fine grid resolved the turbulent boundary layer and the steady ship wave system. The coarse grid was chosen to only resolve incoming waves and wave-induced ship motions, but it did not accurately resolve the calm-water ship wave system and the calm-water resistance. On both grids, separate simulations in calm water obtained the calm-water component of resistance, which was then subtracted from the time-averaged value of total resistance in waves, computed on the same grid, to obtain added resistance.
Figure 1 plots the non-dimensional added resistance coefficient C aw = R aw ρgζ 2 ab 2 WL /L pp (3) as a function of the non-dimensional wave frequency ω = ω L pp /(2πg) = L pp /λ. (4) Results of GL Rankine (curve) are compared with experimental data (filled markers) and with results of Comet on fine and coarse grids (light markers). Note the large difference between results of the two test evaluations, especially in short waves. The two RANSE predictions are quite similar to each other and to the results of the potential code in medium and long waves, whereas they show gross relative errors in the high-frequency region. This demonstrates the inherent difficulty to obtain reliable estimates of added resistance in short waves. Results of GL Rankine end at about ω = 1.4 because for higher frequencies more than the upper limit of about 22000 panels (due to the hardware used) would have been required. C aw 7.0 8.0 Fr=0.183 6.0 5.0 4.0 3.0 2.0 1.0 GL Rankine exp.-spr. exp.-displ. CFD-fine CFD-coarse 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Figure 1: WILS containerschip. GL Rankine results (curve) compared to measurements based on different evaluation techniques and to computations with Comet on a fine and a coarse grid. ω 7 Conclusion Because of the agreement between results of RANSE calculations and of the potential flow code GL Rankine at medium and large wave lengths, we conclude that both methods can give accurate results for added resistance in this frequency range. Experimental results deviate substantially from computed ones and appear less reliable. In the high-frequency range, on the other hand, neither computational nor experimental results appear both feasible and correct. For large ships, these relatively short waves are most interesting because they are generated by moderate and, thus, more frequently occuring wind speeds. Formulae given in the relevant literature for added resistance at the high frequency limit appear also not correct, at least in the practically important frequency range between about ω = 1.4 and 2. Our attempts to establish better approximations for this case were unsuccessful.
Thus, for higher frequencies than about ω = 1.4 (depending a little on Froude number and wave heading) we use a simple extrapolation of C aw : Beyond the highest ω for which reliable calculations are possible, C aw is increased by a factor depending on the ratio of ship draft (for head waves: in the forebody) to incident wave length. The reason is that only waves shorter than about twice the draft are fully reflected by a long floating body. 8 References SÖDING, H. (2011), Recent progress in potential flow calculations, Proc. 1st Int. Symp. on Naval Architecture and Maritime, Istanbul, Turkey SÖDING, H.; GRAEFE, A. von; EL MOCTAR, O.; SHIGUNOV, V. (2012a), Rankinesource method for seakeeping predictions, 31st Int. Conf. on Ocean, Offshore and Arctic Eng. OMAE, Rio de Janeiro SÖDING, H.; SHIGUNOV, V.; SCHELLIN, T.; EL MOCTAR, O. (2012b), A Rankine panel method for added resistance of ships in waves, 31st Int. Conf. on Ocean, Offshore and Arctic Eng. (OMAE), Rio de Janeiro HONG, S. Y. (2011), Wave Induced Loads on Ships, Joint Industry Project-II, MOERI Technical Report No. BSPIS503A-2207-2, Daejeon, Korea (confidential) WALTER, S. (2011), Analysis of an approach to the definition of the added resistance of ships due to waves with RANSE methods, Dipl. Thesis, Univ. Duisburg-Essen (in German)