Fluid flow past bluff bodies (such as circle or square cylinder) is of great concern in previously published literature because of its in engineering applications. TPL (tension leg platform), wires, towers, suspension bridges off-shore structures, tall buildings, piers all of these are constantly subjected to variable fluid flow load. When fluid flow across these objects/structures flow is separated from the main flow direction and creates a large low pressure zone (wake) downstream of these objects. Vortices are shed in the wake region thus causing velocity fluctuations in the low pressure zone and give rise to unsteady drag and lift forces. Now if the vortex shedding frequency matches the natural frequency of the object the phenomenon of resonance will occur that will cause vibration in the structure or ultimately it will come to failure. Heat transfer across bluff bodies which are subjected to vortex shedding has many applications including, electronic cooling components and heat exchanger.

Trend Surface Analysis (TSA), which is a spatial interpolation method, is one of the essential instruments used by natural and environmental scientists to produce a prediction value for an unmeasured location. TSA explores the optimal polynomial surface that passes through sampled data. Data have become the most valuable asset of institutions. As a result of technological developments, the privacy of data has become more important. TSA was applied to so many problems without considering confidentiality of data in the literature. In traditional TSA scheme, there are two parties; client and server. The client requests a prediction value for a specific coordinate where it will spend its money and time for future investment. The server is the data owner which spent a significant amount of money and time to obtain such valuable asset. We propose a privacy-preserving solution to provide TSA-based spatial analysis without violating the confidentiality of both parties’ data. We analyse our scheme in terms of privacy and performance to show that our solution provides accurate prediction model without violating privacy.