A combined experimental and numerical study of the turbulent wake
Author Starke, A.R.
Title A combined experimental and numerical study of the turbulent wake
Conference/Journal PhD-thesis, Delft University of Technology
Month January
Year 2002

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.

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