ESTUDO DA APLICAÇÃO DA EQUAÇÃO DE ORR-SOMMERFELDNA ESTABILIDADE HIDRODINÂMICA DA CAMADA LIMITE SOBREPLACAS PLANAS

O estudo sobre os tipos de escoamentos iniciou-se em 1883, através do experimento em tubos, por Osborne Reynolds, no qual, duas regiões foram claramente identificadas: laminar e turbulenta. Entre estas, há uma região conhecida como transição, que é caracterizada pelo surgimento das primeiras perturbações. Algumas destas podem assumir perfis definidos na natureza, por exemplo, a instabilidade de Tollmien-Schlichting, que é o modo mais instável da equação de Orr-Sommerfeld e comumente surge na transição da camada limite em asas de aeronaves. A permanência na região de transição pode trazer benefícios, como redução do arrasto total em superfícies aeronáuticas e aumento da performance de combustão em aeronaves supersônicas. Neste trabalho, apresentar-se-á, a solução numérica da equação de Orr-Sommerfeld aplicada à camada limite de um escoamento sobre placa plana, através de um código desenvolvido em linguagem Python. Como resultados, obteve-se as curvas de estabilidade que permitiram identificar o número de Reynolds em que a transição inicia, bem como, os parâmetros e autovalor da equação de Orr-Sommerfeld que tornam o escoamento estável, instável ou em estabilidade neutra.

Transient linear stability of pulsating Poiseuille flow using optimally time-dependent modes

Time-dependent flows are notoriously challenging for classical linear stability analysis. Most progress in understanding the linear stability of these flows has been made for time-periodic flows via Floquet theory focusing on time-asymptotic stability. However, little attention has been given to the transient intracyclic linear stability of periodic flows since no general tools exist for its analysis. In this work, we explore the potential of using the recent framework of the optimally time-dependent (OTD) modes (Babaee & Sapsis, Proc. R. Soc. Lond. A, vol. 472, 2016, 20150779) to extract information about both the transient and the time-asymptotic linear stability of pulsating Poiseuille flow. The analysis of the instantaneous OTD modes in the limit cycle leads to the identification of the dominant instability mechanism of pulsating Poiseuille flow by comparing them with the spectrum and the eigenmodes of the Orr–Sommerfeld operator. In accordance with evidence from recent direct numerical simulations, it is found that structures akin to Tollmien–Schlichting waves are the dominant feature over a large range of pulsation amplitudes and frequencies but that for low pulsation frequencies these modes disappear during the damping phase of the pulsation cycle as the pulsation amplitude is increased beyond a threshold value. The maximum achievable non-normal growth rate during the limit cycle was found to be nearly identical to that in plane Poiseuille flow. The existence of subharmonic perturbation cycles compared with the base flow pulsation is documented for the first time in pulsating Poiseuille flow.

Blind disturbance separation and identification in a transitional boundary layer using minimal sensing

A novel approach is presented for identifying disturbance sources in wall-bounded shear flows. The underlying approach models the flow state, as measured by sensors embedded in the flow, as a mixture of disturbance sources. The degenerate unmixing estimation technique is adopted as a blind source separation technique to recover the separate sources and their unknown mixing process. The efficiency of this approach stems from its ability to isolate any, a priori unknown, number of sources, using two sensors only. Furthermore, by adding a single additional sensor, the method is expanded to also determine the propagation velocity vector of each of the isolated sources, based on sensor readings from three sensors appropriately located in the flow field. Theoretical guidelines for locating the sensors are provided. The power of the method is demonstrated via computer simulations and wind-tunnel experiments. The numerical study considers disturbances comprising discrete Tollmien–Schlichting waves and wave packets. Linear stability theory is used to model source mixtures acquired by sensors placed in a Blasius boundary layer. The experimental study investigates the flow over a flat plate, with hot wires as sensors, and a loudspeaker and plasma actuators as source generators. Based on numerical and experimental demonstrations, it is believed that the new approach should prove useful in various applications, including active control of boundary layer transition from laminar to turbulent flow.