Title:

An experimental test for the existence of the Euler wake velocity, validating Eulerlet theory by using a bluff body in a lowspeed wind tunnel

The application of manoeuvrability problems in aerodynamics mainly works for Reynolds average NavierStokes equations particularly for a uniform, steady flow past a fixed body. Further, consider large Reynolds number such that the flow is not turbulent, and the boundary layer is negligibly small and the impermeability boundary condition holds. Instead of using standard techniques and theory for describing the problem, a new method is employed based upon the concept of matching two different Green’s integral representations over a common boundary, one given by approximations valid in the nearfield and the other by approximations in the farfield such that, a nearfield Euler flow is matched to a farfield Oseen flow. Far from the body, linearise the velocity to the uniform stream yielding Oseen flow to leading order and match the nearfield Euler and farfield Oseen flow on a common matching boundary. In particular, match the Green’s integral representations that use Green’s functions which are point force solutions. This gives new Green’s functions which we call Eulerlets and are obtained by collapsing the diffuse wake of the corresponding Oseenlets onto a wake line represented by Heaviside and delta functions. The matching equates terms on the common boundary yielding the Bernoulli equation. One important consequence of the model is the presence of a new Euler wake velocity which is not captured in standard models. This has a constant unchanging downstream profile and arises from the matching to the farfield Oseen wake velocity. The drag calculation is shown to originate solely from a new wake inflow term comprising of layers of different velocities slipping past each other meaning that drag is possible in Euler flow from the momentum loss. So, the model includes a new drag Euler slip wake countering D’Alembert’s paradox. The theory is tested against a wake inflow problem, as this is where it differs from standard Euler representations. In particular, we consider uniform flow past a circular cylinder which is the classic textbook problem demonstrating D’Alembert’s paradox. An experiment is devised to test Eulerlet theory for steady, incompressible, uniform Euler flow past a fixed, closed body. This theory predicts the existence of an Euler wake that has a constant unchanged profile at any downstream station. To experimentally test the theory, a circular cylinder with an axis perpendicular to the flow direction is placed in a closed lowspeed wind tunnel. The velocity profile is obtained by a hotwire anemometer attached to a novel design purposebuilt probe arm moved by an external traverse mechanism and determined at three downstream stations. The Euler wake velocity is then calculated by taking away the potential velocity from the experimentally evaluated fluid velocity. The potential velocity in the wake region itself is estimated by extrapolation from its value outside the wake. The same underlying Euler wake velocity profile is found at two of the three stations, as predicted by the theory. For the third downstream station furthest away, diffusive turbulent effects occur, increasing energy in the wake well and so contaminating the results.
