Detailed analysis of the flow within the boundary layer and wake of a full-scale ship
Introduction
Experimental fluid dynamics towing tank tests have been traditionally used to evaluate the flow around the ship. The main principle of this technique is to test a scaled model of the ship in similar conditions to that of a fullscale one. This approach is expensive, time-consuming and most importantly carries significant limitations. Among them, due to Reynolds number differences, the full-scale boundary layer is generally thinner than in model scale. Also, the aft boundary layer is significantly different in model and full-scale. For applications such as ship resistance investigations, model to full-scale scaling limitations are usually overcome by the application of empirical correlation factors (Larsson and Raven, 2010). This is not the case for boundary layer investigations where a model to full-scale correlation approach is not yet fully established (ITTC, 2014a; ITTC, 2017).
An example of model scale assessments of the boundary layer and wake was conducted by Patel and Sarda (1990). This type of investigation has been beneficial to a better understanding of the flow behaviour on the ship aft end. Nevertheless, when an accurate picture of the full-scale aft end flow is required, a model scale investigation is not the most suitable option.
An alternative method to assess the near-wall flow of the ship relies on viscous flow Computational Fluid Dynamics (CFD). This method is based on the Navier-Stokes equations and allows numerical modelling of scenarios in full scale, therefore avoiding scaling issues. For full-scale ship hydrodynamic applications, Reynolds Averaged Navier–Stokes (RANS) is known to provide a quick solution as it does not require significant computational power. Full-scale self-propulsion studies revealed that RANS numerical model is able to provide good quality predictions of the propeller forces and moment (Ponkratov and Zegos, 2015; Jasak et al., 2019; Bakica et al., 2020). These investigations are in line with the results of the Lloyds Register First Full-scale Ship Hydrodynamics Workshop (Lloyds Register, 2016). However, RANS might not be recommended for scenarios when the flow is predominantly unsteady and/or hull flow separation is expected, this is particularly important for calculations of the bilge vortex that typically forms at the stern of medium to high block coefficient ships (ITTC, 2014a).
If flow separation is expected, one could consider the implementation of Large Eddy Simulation (LES) to model the turbulence contained in the flow. The principle of LES is to approach the modelling of turbulence by considering that the large vortical structures created by the geometry contain most of the energy within the bulk flow. LES resolves turbulent vortices everywhere in the flow domain down to the grid size. LES could provide more accurate predictions of the fluid flow than RANS; however, LES is still computationally unaffordable in full-scale ship hydrodynamics due to the high Reynolds number.
A most recent approach for the simulation of turbulent ship flows is based on a combination of RANS/LES, such as DES (Detached Eddy Simulation). This method combines the best features of LES and RANS by only using LES away from the wall where a high level of unsteadiness of the flow is expected (i.e. around the bilges, detached flow regions or in the wake) while RANS is applied in the near-wall region. This method is more computationally affordable in ship hydrodynamics than LES, allowing the study of complex unsteady flows in full-scale and being deemed as the best alternative to calculate wake parameters, especially behind medium to high block coefficient ships (Larsson et al., 2015). Full-scale flow predictions using a DES97 and its improved version, a DDES, were conducted by Xing et al. (2010). The authors established that both DES approaches improve the prediction of the total resistance and velocity distribution for most of the propeller plane; however, the authors also revealed that both models showed issues predicting the shear stress in the boundary layer region. Some of these issues might be attributed to the log-layer mismatch behaviour that the DES97 and DDES models exhibit (Spalart et al., 2006) which could be corrected using an IDDES approach and which represents an improved version of the DDES and DES97 approaches.
This paper presents a thorough analysis of the aft end boundary layer and wake of a full-scale ship. The numerical approach used during this analysis is based on an IDDES approach that was previously validated against sea trials torque data (Pena et al., 2020). Also, the computational mesh was tailored to allow for the resolution of the largest turbulent vortex that was expected to be shed from the hull: the bilge vortex. Nominal wake, resistance distribution and velocity fields were post-processed to assess the hydrodynamic performance of the ‘MV Regal’ (Lloyds Register, 2016), a full-scale general cargo ship.
Section snippets
Benchmark case study
The ‘Regal’ is a 138m single screw vessel (Fig. 1) with the following main particulars (Table 1):
Before the sea trials, the vessel was dry-docked, the hull was cleaned, and the propeller surface was polished. In this clean condition, the hull, rudder and propeller were 3D laser scanned to obtain an accurate geometric representation. The scanned geometry was directly imported into the CFD computations, thus ensuring high accuracy of the geometry CAD models.
The sea trials were conducted in a
Turbulence modelling strategy
This work used the Improved Delayed Detached Eddy Simulation (IDDES) turbulence modelling strategy and following the approach described in previous work (Pena et al., 2020). The IDDES belongs to the DES family, and it is based on the model developed by. In general, this model switches between the RANS SST k-ω model, which has demonstrated maturity and reliability calculating skin friction coefficients and steady flow features (Wilcox, 1993; Menter, 1994); and LES away from the wall, where it
Boundary layer analysis approach
As mentioned in the introduction section, this analysis required a higher definition of the boundary layer of the ship that was required to measure the velocity profiles across the 3D ship boundary layer of the. The boundary layer thickness was defined as the normal wall distance, , at which the velocity is equal to . Boundary layer parameters were calculated on spanwise cross-section planes at different 'frames' along the ship length (FRi). All planes were parallel to each other,
Ship resistance: calculated components
The bare hull total resistance, viscous resistance and pressure resistance were determined from the converged IDDES simulations. The drag forces were made dimensionless and represented by the total resistance coefficient (), pressure resistance coefficient () and the viscous resistance coefficient (). These coefficients were defined as , and , where , and are the total resistance, viscous resistance and pressure resistance, respectively, S
Time-step and spatial discretization
The Courant number (Cr) is used to represent the number of cells that the fluid travels through within a time step, and it is defined as Cr = (where is the local speed, the interval of time (time step) and the cell size in the direction of the flow). A mean Cr of 1 was implemented, ensuring the convergence and accuracy of the unsteady simulations. All simulations used a 2nd order spatial and temporal discretization for all equations.
Mesh
The mesh configuration was definied identically
Mesh performance analysis
A mesh independence study was conducted for the simulation set-up on four different grid resolutions by varying the mesh size input parameter while holding all other parameters constant and following recommended practices (ITTC, 2017). The uniform parameter refinement ratio was established as . As a result, four grids were generated as follows, the coarse grid (G.1) with 12.3 million cells, the medium grid (G.2) with 25.4 million cells, the fine grid (G.3) with 41.1 million cells and the
Results analysis
The numerical results of the flow around the hull are shown and discussed in terms of ship resistance coefficients, limiting streamlines, nominal wake and the boundary layer at the stern of the ship. The results of this assessment are referred to the following parameters:
- •
Distances (x, y and z) are dimensionalised as a function of the ship length (L), beam (B) and draught (T) as follows: x/L, y/B and z/T.
- •
The incoming flow, , is in the negative x-direction.
- •
The components of mean velocity in
Discussion and conclusions
The present research has numerically investigated the ship hydrodynamic performance of a full-scale general cargo ship using extensive flow data on the boundary layer and wake field. The assessment was conducted using an IDDES sophisticated numerical approach able to directly resolve from the Navier-Stokes equations any relatively large turbulent scale vortices contained in the flow.
Ship resistance per unit length measurements and pressure coefficient distribution confirmed a pressure
CRediT authorship contribution statement
Blanca Pena: Methodology, Writing - original draft. Ema Muk-Pavic: Writing - review & editing, Supervision. Patrick Fitzsimmons: Writing - review & editing, Supervision.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
The authors would like to acknowledge Giles Thomas for his invaluable contribution to this work. We would also like to recognize Siemens Star CCM+ and Lloyds Register team for their technical support.
References (30)
CFD validation and grid sensitivity studies of full scale ship self propulsion
International Journal of Naval Architecture and Ocean Engineering
(2019)- et al.
CFD based vortex generator design and full-scale testing for wake non-uniformity reduction
Ocean. Eng.
(2018) A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities
Int. J. Heat Fluid Flow
(2008)- et al.
Flow Dynamics Past a 30P30N three-element airfoil using improved delayed detached-eddy Simulation
AIAA J.
(2016) CFD simulation of loadings on circular duct in calm water and waves
Ships Offshore Struct.
(2020)Vortex interactions with walls
Annu. Rev. Fluid Mech.
(2002)- et al.
Formation mechanism of hairpin vortices in the wake of a truncated square cylinder in a duct
J. Fluid Mech.
(2010) ISO 15016:2015 Standard, Ships and marine technology — guidelines for the assessment of speed and power performance by analysis of speed trial data
ITTC proceedings of the 8th international conference
27th propulsion committee proceedings