Numerical simulation of the absolutely and convectively unstable wake

Hannemann, Klaus; Oertel, Herbert

doi:10.1017/s0022112089000297

Cited by 118 publications

(78 citation statements)

References 32 publications

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“…Examples are given by Huerre & Monkewitz (1990). These include countercurrent mixing layers in circular jets (Strykowski & Niccum 1991), and the wakes behind circular cylinders (Mathis, Provansal & Boyer 1984;Koch 1985;Triantafyllou, Triantafyllou & Chryssostomidis 1986;Monkewitz 1988;Strykowski & Sreenivasan 1990), blunt bodies (Hannemann & Oertel 1989;Oertel 1990) and a floating cylinder (Triantafyllou & Dimas 1989). But reverse flow certainly does not guarantee absolute instability, nor is it always necessary.…”

Section: Referred To As I)mentioning

confidence: 99%

Global behaviour corresponding to the absolute instability of the rotating-disc boundary layer

2003

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A study is carried out of the linear global behaviour corresponding to the absolute instability of the rotating-disc boundary layer. It is based on direct numerical simulations of the complete linearized Navier–Stokes equations obtained with the novel velocity–vorticity method described in Davies & Carpenter (2001). As the equations are linear, they become separable with respect to the azimuthal coordinate, $\theta$. This permits us to simulate a single azimuthal mode. Impulse-like excitation is used throughout. This creates disturbances that take the form of wavepackets, initially containing a wide range of frequencies. When the real spatially inhomogeneous flow is approximated by a spatially homogeneous flow (the so-called parallel-flow approximation) the results ofthe simulations are fully in accordance with the theory of Lingwood (1995). If the flow parameters are such that her theory indicates convective behaviour the simulations clearly exhibit the same behaviour. And behaviour fully consistent with absolute instability is always found when the flow parameters lie within the theoretical absolutely unstable region. The numerical simulations of the actual inhomogeneous flow reproduce the behaviour seen in the experimental study of Lingwood (1996). In particular, there is close agreement between simulation and experiment for the ray paths traced out by the leading and trailing edges of the wavepackets. In absolutely unstable regions the short-term behaviour of the simulated disturbances exhibits strong temporal growth and upstream propagation. This is not sustained for longer times, however. The study suggests that convective behaviour eventually dominates at all the Reynolds numbers investigated, even for strongly absolutely unstable regions. Thus the absolute instability of the rotating-disc boundary layer does not produce a linear amplified global mode as observed in many other flows. Instead the absolute instability seems to be associated with transient temporal growth, much like an algebraically growing disturbance. There is no evidence of the absolute instability giving rise to a global oscillator. The maximum growth rates found for the simulated disturbances in the spatially inhomogeneous flow are determined by the convective components and are little different in the absolutely unstable cases from the purely convectively unstable ones. In addition to the study of the global behaviour for the usual rigid-walled rotating disc, we also investigated the effect of replacing an annular region of the disc surface with a compliant wall. It was found that the compliant annulus had the effect of suppressing the transient temporal growth in the inboard (i.e. upstream) absolutely unstable region. As time progressed the upstream influence of the compliant region became more extensive.

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Section: Referred To As I)mentioning

confidence: 99%

Global behaviour corresponding to the absolute instability of the rotating-disc boundary layer

2003

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“…Being less computationally expensive, linear stability analysis could be performed before fully resolved direct numerical simulations (DNS) were possible. Hammond & Redekopp (1998) performed local analysis of separated boundary layer profiles in order to determine whether absolute instability could be observed, as it had been for separated shear layers (Huerre & Monkewitz 1985) and bluff-body wakes (Hannemann & Oertel 1989). For certain profiles local absolute instability was observed, depending on both the maximum reverse flow and the height of the reverse flow region.…”

Section: Introductionmentioning

confidence: 99%

Direct numerical simulations of forced and unforced separation bubbles on an airfoil at incidence

2008

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Direct numerical simulations (DNS) of laminar separation bubbles on a NACA-0012 airfoil at Re c = 5 × 10 4 and incidence 5• are presented. Initially volume forcing is introduced in order to promote transition to turbulence. After obtaining sufficient data from this forced case, the explicitly added disturbances are removed and the simulation run further. With no forcing the turbulence is observed to self-sustain, with increased turbulence intensity in the reattachment region. A comparison of the forced and unforced cases shows that the forcing improves the aerodynamic performance whilst requiring little energy input. Classical linear stability analysis is performed upon the time-averaged flow field; however no absolute instability is observed that could explain the presence of self-sustaining turbulence. Finally, a series of simplified DNS are presented that illustrate a three-dimensional absolute instability of the twodimensional vortex shedding that occurs naturally. Three-dimensional perturbations are amplified in the braid region of developing vortices, and subsequently convected upstream by local regions of reverse flow, within which the upstream velocity magnitude greatly exceeds that of the time-average. The perturbations are convected into the braid region of the next developing vortex, where they are amplified further, hence the cycle repeats with increasing amplitude. The fact that this transition process is independent of upstream disturbances has implications for modelling separation bubbles.

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“…In the past, growing evidence has been gathered to support the existence of a relationship between the global wake frequency and the B. Pier ω 0 (X) curve derived from measured or model wake profiles, e.g. Betchov & Criminale (1966), Koch (1985), Triantafyllou, Triantafyllou & Chryssostomidis (1986), Monkewitz & Nguyen (1987), Monkewitz (1988), Hannemann & Oertel (1989), Karniadakis & Triantafyllou (1989); for a review see Huerre & Monkewitz (1990) and Huerre & Rossi (1998). Different resonance principles have been conjectured: Koch (1985) proposed a feedback mechanism associated with the real absolute frequency ω ac 0 ≡ ω 0 (X ac ) prevailing at the downstream boundary X ac of the AU region.…”

Section: Introductionmentioning

confidence: 99%

On the frequency selection of finite-amplitude vortex shedding in the cylinder wake

2002

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In this paper it is shown that the two-dimensional time-periodic vortex shedding régime observed in the cylinder wake at moderate Reynolds numbers may be interpreted as a nonlinear global structure and its naturally selected frequency obtained in the framework of hydrodynamic stability theory. The frequency selection criterion is based on the local absolute frequency curve derived from the unperturbed basic flow fields under the assumption of slow streamwise variations. Although the latter assumption is only approximately fulfilled in the vicinity of the obstacle, the theoretically predicted frequency is in good agreement with direct numerical simulations for Reynolds numbers Re > 100.

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Numerical simulation of the absolutely and convectively unstable wake

Cited by 118 publications

References 32 publications

Global behaviour corresponding to the absolute instability of the rotating-disc boundary layer

Global behaviour corresponding to the absolute instability of the rotating-disc boundary layer

Direct numerical simulations of forced and unforced separation bubbles on an airfoil at incidence

On the frequency selection of finite-amplitude vortex shedding in the cylinder wake

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