  We apply a data-based, linear dynamic estimator to reconstruct the velocity
field from measurements at a single sensor point in the wake of an aerofoil. In
particular, we consider a NACA0012 airfoil at $Re=600$ and $16^{\deg}$ angle of
attack. Under these conditions, the flow exhibits a vortex shedding limit
cycle. A reduced order model (ROM) of the flow field is extracted using proper
orthogonal decomposition (POD). Subsequently, a subspace system identification
algorithm (N4SID) is applied to extract directly the estimator matrices from
the reduced output of the system (the POD coefficients). We explore
systematically the effect of the number of states of the estimator, the sensor
location, the type of sensor measurements (one or both velocity components),
and the number of POD modes to be recovered. When the signal of a single
velocity component (in the stream wise or cross stream directions) is measured,
the reconstruction of the first two dominant POD modes strongly depends on the
sensor location. We explore this behaviour and provide a physical explanation
based on the non-linear mode interaction and the spatial distribution of the
modes. When however, both components are measured, the performance is very
robust, and is almost independent of the sensor location when the optimal
number of estimator states is used. Reconstruction of the less energetic modes
is more difficult, but still possible.

Fluid Dynamics