Nobuyuki Shima

Prediction of a Shear-Driven Three-Dimensional Turbulent Boundary Layer.

A three-dimensional turbulent boundary layer formed when an initially collateral boundary layer encounters transverse wall motion is calculated using a second-moment closure applicable up to a wall. The numerical solutions are extensively compared with an experiment by Lohmann, including the distributions of all the Reynolds stress components. In the inner layer, the turbulence model produces reasonable shear stress components parallel to the wall. This leads to a good prediction of the magnitude and direction of the wall shear stress. In the outer layer, however, a very rapid growth of the transverse shear stress component found in the experiment is not reproduced by the model. A modification of the redistribution model whose effect is limited to the outer layer in developing flows would be desirable.

Preduction of a turbulent oscillating boundary layer with a second-moment closure.

The turbulent boundary layer under a free-stream whose velocity varies sinusoidally in time around a zero mean is calculated using a Reynolds stress model. Direct simulation (DS) data by Spalart and Baldwin are used to assess the performance of the turbulence model. The model is a full second-moment closure applicable right up to a wall, which was previously shown by the author to reproduce various turbulent flows. Extensive comparison between the DS data and the predictions is made on variations of the wall shear stress, the mean velocity profiles, and the distributions of all the Reynolds stress components. The agreement is generally excellent. In particular, a laminarization during the acceleration phase and a succeeding retransition are reproduced well by the model calculation.

Prediction of a three-dimensional turbulent boundary layer created by a rotating free-stream velocity vector.

A direct simulation (DS) by Spalart of a three-dimensional turbulent boundary layer created by a rotating free-stream velocity vector offers a standard test case for turbulence models. The flow situation is calculated here using a second-moment closure applicable up to a wall, which was previously shown to reproduce various two-dimensional flows. The numerical solutions are extensively compared with the DS results including the distributions of all the Reynolds stress components. The agreement is generally satisfactory, showing the wide applicability of the turbulence model. The rather close alignment of the Reynolds stresses with the mean shear in the flow suggests a need for a separate test on more strongly three-dimensional boundary layers.

A reynolds-stress model for near-wall regions.

The Reynolds stress model for high Reynolds numbers by Launder et al, is extended to near-wall regions oFlow Reynolds numbers. In the development of the model, particular attention is given to the high anisotropy of turbulent stresses in the immediate vicinity of a wall and to the behavior of the exact stress equation at a wall. A transport model for the turbulence energy dissipation rate is also developed by taking into account its compatibility with the stress model at a wall.