Replicating impinging synthetic jets as a train of consecutive viscous Lamb-Ossen vortex pairs

In small scale applications, synthetic jets have proven to be an efficient cooling technique when impinged onto heating surfaces. These jets are produced by the quick injection-ejection of fluid from an orifice, which generates a train of counter-rotating vortex pairs that sustain a fluctuating jet flow with positive momentum. Previously, in an effort to understand the fundamental mechanisms that drive this phenomenon, an idealized numerical canonical geometry was created and studied using CFD, which liberated the jet from actuator artifacts. Due to its highly vortical nature, the fluid can penetrate the thermal boundary layer better than a conventional steady jet. In the wall jet region, the passing of the main vortices gives rise to secondary vortices with opposite rotation that cause the entrainment of cold fluid towards the vicinity of the heated surface, thus broadening the effective impinging area and further enhancing the heat transfer. This study intends to advance prior fundamental studies by focusing in the fluid dynamics associated with this type of flow. Counter-rotating viscous Lamb-Ossen vortex pairs were repeatedly placed inside a domain at a given time interval (frequency) with a given intensity. The method of images was used to replicate the presence of the perpendicular static surface that acts as an inviscid wall. A numerical code written in Matlab™ language was developed to calculate the unsteady interaction between the N vortices, and the consequently induced fluid flow. This was used to compare the approach proposed with the canonical CFD data. A method is proposed to predict the vortex intensity evolution, which presented excellent agreement with the numerical data. It was found that the Lamb-Ossen vortex pair translational velocity and trajectory were comparable to the synthetic jet in the free jet region. The canonical vortex slowed when entering the stagnation region due to wall effects and the presence of the secondary vortex that induced a velocity onto the primary vortex opposite to its translation. Four effects were identified, each having different or opposite relationships with the jet parameters and the heat transfer, providing multiple options when it comes to finding optimum operating conditions.