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Impinging jets have been widely studied, and the addition of swirl has been found to be beneficial to heat transfer. As there is no literature on Reynolds-averaged Navier Stokes equations (RANS) nor experimental data of swirling jet flows generated by a rotating pipe, the purpose of this study is to fill such gap by providing results on the performance of this type of design.

As the flow has a different behaviour at different parts of the design, the same turbulent model cannot be used for the full domain. To overcome this complexity, the simulation is split into two coupled stages. This is an alternative to use the costly Reynold stress model (RSM) for the rotating pipe simulation and the SST k-ω model for the impingement.

The addition of swirl by means of a rotating pipe with a swirl intensity ranging from 0 up to 0.5 affects the velocity profiles, but has no remarkable effect on the spreading angle. The heat transfer is increased with respect to a non-swirling flow only at short nozzle-to-plate distances H/D < 6, where H is the distance and D is the diameter of the pipe. For the impinging zone, the highest average heat transfer is achieved at H/D = 5 with swirl intensity S = 0.5. This is the highest swirl studied in this work.

High-fidelity simulations or experimental analysis may provide reliable data for higher swirl intensities, which are not covered in this work.

This two-step approach and the data provided is of interest to other related investigations (e.g. using arrays of jets or other surfaces than flat plates).

This paper is the first of its kind RANS simulation of the heat transfer from a flat plate to a swirling impinging jet flow issuing from a rotating pipe. An extensive study of these computational fluid dynamics (CFD) simulations has been carried out with the emphasis of splitting the large domain into two parts to facilitate the use of different turbulent models and periodic boundary conditions for the flow confined in the pipe.

This paper aims to consider the thrust force generated by two plunging and pitching plates in a tandem configuration in forward flight to find out the configuration that maximizes the propulsive efficiency with high-enough time-averaged lift force.

To that end, the Navier–Stokes equations for the incompressible and two-dimensional flow at Reynolds number $500 are solved. As the number of parameters is quite large, the case of constant separation between the plates (half their chord length), varying seven non-dimensional parameters related to the phase shift between the heaving motion of the foils, the phase lag between pitch and heave of each plate independently and the frequency and amplitude of the heaving and pitching motions are considered. This analysis complements some other recent studies where the separation between the foils has been used as one of the main control parameters.

It is found that the propulsive efficiency is maximized for a phase shift of 180° (counterstroking), when the reduced frequency is 2.2 and the Strouhal number based on half the plunging amplitude is 0.17, the pitching amplitude is 25° and when pitch leads heave by 135° in both the fore -plate and the hind plate. The propulsive efficiency is about 20 per cent, just a bit larger than that of an isolate plate with the same motion as the fore-plate, but the corresponding lift force is negligible for a single plate. The paper discusses this vortical flow structure in relation to other less efficient ones. Finally, the effect of the separation between the plates and the Reynolds number is also briefly discussed.

The kinematics of two flapping plates in tandem configuration that maximizes the propulsive efficiency are characterized discussing physically the associated vortical flow structures in comparison with less efficient kinematic configurations. A much larger number of parameters in the optimization procedure than in previous related works is considered.