Surrogate-based modeling for investigating and controlling the response of an axisymmetric jet to harmonic forcing

We investigate the response of an axisymmetric turbulent jet at Re = 10.000 to a superposition of two azimuthally distributed harmonic forcing signals. This forcing is achieved by means of eight independently controlled loudspeakers at the turbulent jet's exit. The forcing amplitude is limited to 2% of the total mass flow of the main jet and is kept constant for all measurements. The objective is to reduce the centerline velocity of the turbulent jet. A reduction in the centerline velocity implies higher entrainment of the turbulent jet, which is of interest for mixing purposes. We investigate different forcing structures with an axial or helical shape and superpose these signals. In the resulting parameter space, a global minimum is sought. This global optimization is performed by identifying a surrogate model, optimized to reduce the model uncertainty by iteratively measuring the point in parameter space with the highest model uncertainty. A global minimum is then identified from the generated surrogate model. In contrast to other optimization techniques, this approach yields a surrogate model that delivers accurate information not only in the proximity of the minimum but in a much broader parameter range, which aids in understanding the influence of each parameter on the jet response. The results for a superposition of two axisymmetric forcing signals or one axisymmetric and one spinning forcing signals approximately match known results from the literature. In addition, we investigate the superposition of two counter-spinning helical forcings, resulting in a lower centerline velocity than the other measured values. This identified optimal forcing is then validated experimentally, and the jet response is further investigated by visualizing the flow with a laser sheet.