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ative influences and respective merits of discretisation algorithms and turbulence models. It is why this database was chosen as one of the two test cases of the 1990 SSPA-CTH-IIHR Workshop on Viscous Flow held at Goteborg [2], and again selected for the 1994 CFD Workshop held at Tokyo [3].

The results obtained during the first workshop held at Goteborg [ 2], indicated that most of the methods based on Reynolds Averaged Navier-Stokes Equations were able to simulate the gross features of the flowfield and predicted the shape and location of the wake. However, neither the central region of the wake (the now famous “hook” shaped contours) nor the details of the wall flow were simulated by the methods used at that time. Actually, most of compared methods produced essentially the same too diffusive flow, particularly in the near wake region. Insufficient grid resolution, especially on such complex three-dimensional configurations, spatial discretisation errors, limited convergence on non-linearities are the usual reasons put forward to justify the bad performances of a numerical simulation. Even if these reasons are to be considered, and this paper will draw attention to another one (the influence of inlet conditions), the authors noticed [4] that the turbulence models used at that time were mainly responsible for the bad representation of longitudinal vortex. A systematic comparison of the respective influences of various discretisation schemes and grids was conducted and used to quantify the consequences of adhoc modifications of the turbulent viscosity in the central region of the wake. This systematic analysis established that the modifications of eddy-viscosity distribution were the only ones responsible of dramatic improvments of the iso- velocity contours. The aim of this previous study [4] was obviously not to promote such a-posteriori alterations, but rather to underline the likely weaknesses of an eddy-viscosity based turbulence closure for such a complex flow in order to stimulate the validation and assessments of more complex turbulence models in the context of complex geometries.

One year later, during the 1994 CFD Workshop held at Tokyo [3], a session was again devoted to the same test cases, namely the HSVA and Dyne Tankers. Although many contributors employed again algebraic zero equation models (Cebeci-Smith or Baldwin-Lomax models), the results were significantly improved since the “hook-shape” behaviour was often captured, at least to some extent, by an increased number of participants. Those results are somewhat difficult to understand since the same Baldwin-Lomax turbulence models used in 1990 and 1994 did not provide the same results. An analysis of eddy-viscosity contours in the near wake conducted by Sotiropoulos and Patel suggests that “the apparent success of methods using the Baldwin-Lomax model is mainly due to the arbitrary restriction of the computed eddy-viscosity level in the central part of the wake”. Therefore, this unexpected and undesirable consequence of [4] can be considered as a not-always-confessed illustration of the major role played by the turbulence closure in the representation of such complicated afterbody flows.

During this last workshop and for the first time in the context of naval hydrodynamics, two research teams tried to use second-moment turbulence closures ([5], [6]). Sotiropoulos & Patel [5] employed the near-wall second-moment transport closure of Shima [7]. Comparisons with results obtained with the two-layer k–ε turbulence model of Chen & Patel [8] revealed that the second-moment closure was able of reproducing most of the features observed in the measurements and particularly the S-like structure of the isovels in the central part of the wake. However, a closer examination of their results revealed that the longitudinal vorticity in the near wake was noticeably overestimated, the computed rate of decay of secondary motion in the wake being also slower than its measured counterpart. Chen et al. [6] employed a second-moment closure based on the pressure-strain correlations of Speziale, Sarkar and Gatski [9] in the fully turbulent flow regions whereas the low Re near-wall closure of Shima [10] was used to provide the necessary viscous damping in the laminar sublayer and buffer layer. Here again, their results clearly established the superiority of second-moment closures over simpler isotropic eddy viscosity models for this kind of applications, even if, on the contrary of the previous contributors, the longitudinal vorticity appeared to be slightly underestimated.

The objectives of the present study are twofold:

  • The analysis in the first part will be conducted under the general context of isotropic eddy viscosity turbulence closures. New turbulence closures based on the kω model and its recent variants developped in the aerodynamical context will be examined. The influence of inlet conditions will be examined in order to determine if full-body computations provide mechanisms for generating longitudinal vorticity that would be absent or underestimated when computations start at mid-body.

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