The two classes of primary modal instability in laminar separation bubbles

Abstract

The self-excited global instability mechanisms existing in flat-plate laminar separation bubbles are studied here, in order to shed light on the causes of unsteadiness and threedimensionality of unforced, nominally two-dimensional separated flows. The presence of two known linear global mechanisms, namely an oscillator behaviour driven by local regions of absolute inflectional instability and a centrifugal instability giving rise to a steady three-dimensionalization of the bubble, is studied in a series of model separation bubbles. These results indicate that absolute instability, and consequently a global oscillator behaviour, does not exist for two-dimensional bubbles with a peak reversed-flow velocity below 12 % of the free-stream velocity. However, the threedimensional instability becomes active for recirculation levels as low as u rev ≈ 7 %. These findings suggest a route to the three-dimensionality and unsteadiness observed in experiments and simulations substantially different from that usually found in the literature of laminar separation bubbles, in which two-dimensional vortex shedding is followed by three-dimensionalization.

Frequency selection mechanisms in the flow of a laminar boundary layer over a shallow cavity

“…The maximum reverse flow in the cavity is only about 8%, and we find, using local stability analysis, that the flow is not locally absolutely unstable anywhere within the domain. This agrees with a trend found in a previous study [17] that suggested that the maximum reverse flow in a laminar separation bubble would need to be larger than 12% for absolute instabilities to arise. The flow is, however, convectively unstable between 0 < x < 6.1.…”

BiGlobal linear stability analysis on low-Re flow past an airfoil at high angle of attack

“…For the LSB on a flat plate, Alam and Sandham 54 concluded, from examining three-dimensional DNS, that a maximum reverse flow velocity u rev /U 0 = 8% leads to the onset of unsteadiness. A similar value of 7% is found by Rodríguez et al 55 where the effect of the Reynolds number is limited. For the present flow configuration, the recirculating wake flow is free of the bounded wall, and the stationary mode stemming from the centrifugal instability is only observed at Re = 800 and 1000 where u rev /U 0 >≈ 20% at the spanwise wavenumber β = 1, as shown in Figure 6.…”

Estudo da instabilidade secundária de uma bolha de separação laminar tridimensional.

“…A figura 1 mostra a evolução da frequência global complexa ω g e a localização do wavemaker X s correspondente ao oscilador global dominante encontrado como função de A, a amplitude da bifurcação. Em linha com as análises para o escoamento base inicial q 0 de [8], Im[ω g ] < 0 para valores pequenos de A, implicando em um decaimento temporal do modo de oscilação global. Os resultados para os escoamentosq 2D eq 3D são muito similares para as amplitudes entre A = 0.006 e A = 0.008.…”

“…Avançando nessas ideias, foi demonstrado em [8] que esta instabilidadeé recuperada como um modo próprio tridimensional das equações de Navier-Stokes linearizada e, as análises da instabilidade primária das bolhas de separação laminar 2D mostraram que não existe uma instabilidade que daria origemàs oscilações autossustentadas nos campos do escoamento, na ausência de forças externas ou fontes de perturbações. Os escoamentos da bolhas de separação bifurcados 2D e 3D, que aparecem como consequência da instabilidade centrífuga, são estáveis.…”