Trans RINA, Vol 157, Part A3, Intl J Maritime Eng, Jul-Sep 2015


ranged from 0 at the bottom of the domain to 4 in close proximity of the hull. Cell size is approximately 2% of vessel length at cell level 0 and the density increased eight- fold with each cell level. The mesh was generated at a 1:4 longitudinal geometric compression and finally stretched to the original aspect ratio to allow the originally cubical cells to be stretched in the flow direction to reduce the cell count. Cubical cells enabled the best performance of snappyHexMesh for mesh refinement and surface layer around the hull. Four prismatic layers with 1 mm cell height for the first layer and a 20% cell expansion was used to capture the boundary layer flow, allowing values of y+ ≈ 50 at model-scale and y+ ≈ 10,000 at full-scale. The total cell count was chosen to assure computational efficiency, accurate results, adequate surface layers and trouble-free meshing.


To keep the mesh comparable between the different hulls of constant length, but different draft and beam, the background mesh was altered to assure a similar number of cells relative to the draft and width. This resulted in an increased cell size for the slenderer hull as the number of cells in the longitudinal direction increased with the aim to achieve cubical cells. between 600k – 800k cells.


Full-scale Reynolds numbers were achieved by altering the viscosity of the fluid while the geometric properties remained at the model-scale. If the resulting shear force was in good agreement with empirical data it was assumed that the resulting total drag force is physically adequate.


2.2 (c) Experimental Validation at Model-scale


The 130 m hull was the base model of this hull form family and it had previously been tested in the Australian Maritime College towing tank with results presented previously [2], [14]. For this study the drag force at Froude numbers of Fr = 0.28, 0.37 and 0.45 was compared to the experimental results at a light and heavy displacement, respectively. These three speeds represent consecutive hump, hollow and hump in the resistance curve with the latter one being the main hump.


3. The total mesh count varied RESULTS


The following section includes the results of the validation of the novel method for full-scale CFD as well as the outcomes from the design space exploration. A discussion follows in section 4.


3.1 VALIDATION


Good agreement was seen for the drag force determined in simulations at model-scale Reynolds numbers when compared to the measurements in model test experiments for the speeds under consideration. The relative deviation was defined by


Figure 2: Mesh setup cell density expressed by cell level. Dark shade indicates high mesh density.


2.2 (b) Validation Approach for Full-scale CFD


This numerical study used a hybrid approach based on experimental and empirical data to validate a full scale prediction. Firstly the computational model was validated at model-scale against experimental data to assure that the flow characteristics at model-scale Froude and Reynolds number were successfully replicated.


It was assumed that the accuracy of pressure and wave- making related resistance is independent of Reynolds number and only depends on the size of the cells relative to the length of the hull. The resistance due to shear was compared to established ship-model correlations lines such as ITTC ‘57 and Grigson [23], where an acceptable agreement was assumed to indicate the adequate decomposition of the total drag force into normal and tangential stresses.


  Texp


=RR R


exp


 


Texp  cfd 


// /


Tcfd exp


A deviation of ε < 5% was observed with the numerical prediction generally below the experimental result. For the heavy displacement at Fr = 0.28 the numerical value exceeded the experimental result by 7%, which may be due to the partially ventilated transom at this condition. The shear force coefficient for all three cases was well within the correlation lines of ITTC and Grigson.


Figure 3 shows the absolute values of relative deviation between numerical


and experimental (DTMB 5415) to include


values are compared with the median total uncertainties for an unconventional fast displacement hull of 3 m length


a measure for


experimental uncertainty. This data was determined by model test data from different model test facilities and analysed for ITTC [24] and reached 4 – 6% for the speeds under consideration.


results. These


A-164


©2015: The Royal Institution of Naval Architects


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