Wind turbine wake superposition under pressure gradient

We investigate the effect of pressure gradient on the cumulative wake of multiple turbines in wind tunnel experiments spanning across a range of adverse pressure gradient (APG), zero pressure gradient (ZPG), and favorable pressure gradient (FPG). Compared to the upstream-most turbine, the in-wake turbines exhibit lower (higher) wake velocity in APG (FPG) than in the ZPG. The maximum velocity deficit shows a lesser difference for the in-wake turbine between different cases compared to the upstream-most one. This is linked to the effect of the wake of the upstream turbine. Conversely, the wake width varies more for the in-wake turbines. A new analytical approach to model the cumulative wake velocity deficit is proposed. This approach extends the application of the analytical pressure gradient model to multiple turbine wakes. Specifically, the new approach explicitly accounts for the effect of the pressure gradient induced by the wake of the upstream turbine on the wake of the downstream one. The new method is compared to the linear summation approach and experimental data. It agrees well with the experiments and outperforms the linear summation approach.