Structure of Zero Pressure Gradient High Reynolds Number Turbulent Boundary Layers
Doctoral thesis, 2008
This thesis presents part of the large research program funded by the European Commission called
Wallturb: A European synergy for the assessment of wall turbulence. The main aim of this research
program is to create new experimental and numerical databases on the characteristics of turbulent wall-
bounded ﬂows, especially turbulent boundary layers. The goal is that these databases will be used to
gain more insight into the physical mechanisms governing the dynamics of these ﬂows. This knowledge
is deemed essential for the future development of efﬁcient and physical turbulence modeling strategies,
which are in turn crucial to aircraft and other industries for sustainable development, especially under
the pressure of high oil prices and operational costs.
The signature experiment of Wallturb was the multi-investigator, multi-system, multi-point investigation carried out in the 20m test section of the boundary layer research facility at LML Lille, France
in 2006. This thesis is focused primarily on the part of that investigation which utilized the 143 probe
hot-wire array belonging to the Turbulence Research Laboratory of Chalmers, and only on the two zero-
pressure gradient boundary layer experiments at Reθ of 9800 and 19 100.
A new hot-wire calibration method was developed and utilized for this investigation. The method is
based on a polynomial curve ﬁtting approximation which expresses the instantaneous velocity as a function of instantaneous voltage. The results showed that even a second order polynomial approximation
yields very good agreement between the measured proﬁles (or computed proﬁles after the calibration)
and the reference proﬁles used in the calibration. The method also provides an opportunity to do the
calibration on the ﬂy as long as the convergence of the high order voltage statistics can be satisﬁed.
The large scale motions of the turbulence were studied in detail using two-dimensional two-point
cross-correlations maps on different planes within the measurement domain. It was observed that the
elongated correlations exist at every wall-normal position above the buffer layer. These elongated structures were relatively more signiﬁcant in the log layer.
The investigation using the proper orthogonal decomposition showed that the POD (in conjunction
with Fourier analysis in the statistically homogeneous and stationary directions) can effectively represent
the total kinetic energy with a small number of modes. At both Reynolds numbers, it was possible to
recover almost 90% of the total turbulence kinetic energy within the entire boundary layer with only
four POD modes. The reconstructed velocity ﬂuctuations on the spanwise-wall-normal plane show how
organized motions of turbulence with signiﬁcant amounts of energy interact with each other across the
boundary layer. It was also possible to observe the interaction between the inner and outer layers of
turbulence using these reconstructed velocity ﬁelds.
proper orthogonal decomposition
large scale structures
Turbulent boundary layers
zero pressure gradient
high Reynolds number