  The growth of computational resources in the past decades has expanded the
application of Computational Fluid Dynamics (CFD) from the traditional fields
of aerodynamics and hydrodynamics to a number of new areas. Examples range from
the heat and fluid flows in nuclear reactor vessels and in data centers to the
turbulence flows through wind turbine farms and coastal vegetation plants.
However, in these new applications complex structures are often exist (e.g.,
rod bundles in reactor vessels and turbines in wind farms), which makes fully
resolved, first-principle based CFD modeling prohibitively expensive. This
obstacle seriously impairs the predictive capability of CFD models in these
applications. On the other hand, a limited amount of measurement data is often
available in the systems in the above-mentioned applications. In this work we
propose a data-driven, physics-based approach to perform full field inversion
on the effects of the complex structures on the flow. This is achieved by
assimilating observation data and numerical model prediction in an iterative
Ensemble Kalman method. Based on the inversion results, the velocity and
turbulence of the flow field can be obtained. A major novelty of the present
contribution is the non-parametric, full field inversion approach adopted,
which is in contrast to the inference of coefficient in the ad hoc models often
practiced in previous works. The merits of the proposed approach are
demonstrated on the flow past a porous disk by using both synthetic data and
real experimental measurements. The spatially varying drag forces of the porous
disk on the flow are inferred. The proposed approach has the potential to be
used in the monitoring of complex system in the above mentioned applications.
