It can be seen that the predicted vortex formation compares favorably with the experiment when three different turbulence models are used, as presented by A. Rizzi & J.Vos (AIAA Journal, Vol. 36, May 1998) and shown below:


Wall damping function is usually constructed by using one of the three parameters: y+=yuτ/ν, and Rτ=k2/(νε). In the authors’ opinion, it is not desirable to use a wall related parameter which changes during temporal or nonlinear iteration, such as uτ. Compared with Rτ, Ry is a more representative wall-distance indicator. Models based on Ry are usually more stable that those based on Rτ. Although the wall normal distance is difficult to determine exactly for complex geometries, a numerical approximation is easy to implement. The authors use a body-fitted multi-block solver that is capable of computing the wall normal distance for any given grids. More complex geometries such as the HSVA tanker have been treated without changing anything with the same code. The authors do not feel the need to replace Ry in the wall damping function for the application in complex geometries. However, when using a moving grid, the computation of wall-normal distance may become very time consuming. In this case, models based on Rτ will become attractive.

One of the most important contributions of the Reynolds stress transport model to the prediction of the wing-body junction flow is a better description of normal stress anisotropy and the exact description of the convection effect of Reynolds stress which is found to be very important in front of the wing. Results shown by the discussers are very interesting. It indicates that by taking into account the normal stress anisotropy with a nonlinear two-equation model, one can improve prediction of the horse-shoe vortex. However, the nonlinear two-equation models which are deduced from a Reynolds stress transport model by using local equilibrium assumption, are obviously unable to account for the convection effect. Consequently, other important features such as the distinction of high shear stress and low shear stress regions, the position of the pigment accumulation line, etc., captured by the Reynolds stress transport model, are unable to be predicted with nonlinear models.

Predictions with a Reynolds stress transport model given by A.Rizzi are not representative. They are probably obtained with a wall function approach, which suggests that wall function approach should not be used for complex three-dimensional flow prediction. In the present studies, the authors use a low Reynolds number model where wall reflection terms need to be added. Unfortunately, just like the wall function approach, the wall reflection terms are calibrated with simple boundary layer flow. The present study shows that they are not valid for separated flows. The shape of the horse-shoe vortex predicted by the Reynolds stress transport model is presented in the following figure. It is less satisfactory than the result obtained by the discussers with a nonlinear two-equation model, which indicates that the improvement provided by an exact description of convection effect is smaller than the deterioration introduced by the wall reflection terms.

Velocity vectors in the vertical symmetry plane.

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