A combined experimental and numerical study of the turbulent wake
The main objective of the present investigation is to gain a better understanding of the flow in the far and near wake of a flat plate. To realize this objective a study is made of three flow configurations. First, the asymptotic far wake is studied, where, according to classical theory, properly scaled flow quantities become independent of the strearnwise distance. Experimental data available in the literature are used to validate numerical simulations of the far wake using two algebraic turbulence models and two two-equation models (k - E and k - w). Furthermore, new experimental data are obtained in the near wake of a flat plate that is subjected to a nominally zero pressure gradient. These experimental results are compared with numerical simulations using both a k - E turbulence model and a differential Reynolds-stress model. Finally a similar experimental and numerical investigation is made of the effects of curvature of the mean streamlines on the wake of the plate. In the numerical investigation of the far wake a study is made of the self-similar solutions obtained with various turbulence models for a wake subjected to a zero pressure gradient. In order to calculate these solutions, the boundary-layer equations are further simplified using the conditions on the existence of similarity solutions. As a result, the partial differential equations that describe the flow in a wake simplify to ordinary differential equations, which are solved numerically. The calculations show that both investigated two-equation models have discontinuous solutions at the interface between the wake and the surrounding free stream. This is confirmed analytically by a power-law approximation of the solution near this interface. The analysis also shows that the discontinuity is directly related to the relative magnitudes of the model constants in the diffusive terms of the turbulence equations. The numerical simulations of the far wake are furthermore used to study the strong dependency of the results obtained with the k - w model on the free-stream boundary condition for ta, With respect to the experimental investigation of the far wake it is noted that based on earlier studies by other researchers it has generally been assumed that the quantities in the far wake are independent of the wake-generating body. Recently, however, some critical observations have been added to this theory. The present study shows, on the basis of various experimental results available in the literature, that both the approach towards self-similarity and the self-similar state of a wake itself, vary between different wake-generating bodies. This has serious consequences for numerical simulations based on the similarity equations, since it is not possible to reproduce this experimental result numerically with the turbulence models used in the present investigation; each of the investigated models gives only one solution (with a given set of model constants) in the far wake, irrespective of the wake-generating body. In the study of the wake subjected to a nominally zero pressure gradient, a threecomponent LDA system is used to acquire data on mean velocities and Reynolds stresses. A clear influence is observed of the tapered trailing edge of the plate on the near wake. This creates an internal favourable pressure gradient in the near wake and a corresponding decrease of the momentum-loss thickness in downstream direction. The change-over of the wall-bounded flow on the plate into the wake causes a pronounced increase in the level of the transverse normal-stresses in the near wake. The experimental results are used for a detailed comparison with numerical simulations based on the steady, incompressible Reynolds-averaged Navier-Stokes equations. In these computations two turbulence models are used: a k - e model and a differential Reynoldsstress model. Both models give good results for the mean velocities, the turbulent kinetic energy and the shear stresses. The anisotropy of the normal-stress components in the near wake is furthermore predicted fairly accurately by the Reynolds-stress model, although the experimentally observed increase in the level of transverse normal-stresses along the centreline in the near wake is not reproduced. The final subject is the effect of curvature of the mean streamlines on the turbulence in the wake. In the experimental study curvature is induced by placing one of the adjustable side walls of the test section at a diverging angle with respect to the centreline of the wind tunnel, while the opposite wall is placed parallel to this line. As a result a lateral pressure gradient across the wake causes the wake to curve towards the diverging test-section wall. The three-component LDA system is used to acquire data on mean velocities and Reynolds stresses. The strongest curvature effects are observed close to the trailing edge of the plate. Comparison with computations shows good agreement with the experiments at not too large distances from the plate. However, further downstream a considerable underestimation of the transverse shift of the wake is predicted, which is found to be very sensitive to small variations in the applied pressure boundary conditions.