The linear evolution of centrifugal instabilities in curved, compressible mixing layers

Owen, David G.; Seddougui, Sharon O.; Otto, S. R.

doi:10.1063/1.869368

Cited by 6 publications

(13 citation statements)

References 14 publications

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“…The two cases of a zero and a non-zero buoyancy parameter will be considered separately. The former case is relatively well understood, or at least when either curvature or buoyancy is present-the boundary layer experiencing the combined effects of curvature and buoyancy has not been studied in depth (with the exception of the inviscid theory of Stott and Denier [23]) but the effects are easily surmised from knowledge of both the individual problems [9,11,14] and the equivalent mixing layer problem [18][19][20]. The buoyancy-coupled boundary layer has received little attention in the literature and thus will be the main focus of attention here.…”

Section: Linear Resultsmentioning

confidence: 99%

The stability of a curved, heated boundary layer: linear and nonlinear problems

Watson

Otto²

2005

ANZIAM J.

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We consider the stability of high Reynolds number flow past a heated, curved wall. The influence of both buoyancy and curvature, with the appropriate sense, can render a flow unstable to longitudinal vortices. However, conversely each mechanism can make a flow more stable; as with a stable stratification or a convex curvature. This is partially due to their influence on the basic flow and also due to additional terms in the stability equations. In fact the presence of buoyancy in combination with an appropriate local wall gradient can actually increase the wall shear and these effects can lead to supervelocities and the promotion of a wall jet. This leads to the interesting discovery that the flow can be unstable for both concave and convex curvatures. Furthermore, it is possible to observe sustained vortex growth in stably stratified boundary layers over convexly curved walls. The evolution of the modes is considered in both the linear and nonlinear regimes.

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Section: Linear Resultsmentioning

confidence: 99%

The stability of a curved, heated boundary layer: linear and nonlinear problems

Watson

Otto²

2005

ANZIAM J.

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“…A theoretical investigation of the Görtler instability was later conducted by Owen et al ͑henceforth referred to as OSO͒ within a curved laminar compressible mixing-layer system. 5 OSO demonstrated that in a compressible mixing layer the centrifugal instabilities can also be observed for certain parameter regimes within the system for which the faster stream curves into a cooler slower stream. Such modes have no counterpart in the corresponding incompressible curved mixing-layer investigation by Otto et al, 6 and they were labeled as the "thermal modes."…”

Section: Introductionmentioning

confidence: 96%

Centrifugal instabilities in curved compressible wakes

Stephen

2009

Physics of Fluids

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This investigation is concerned with the linear development of Görtler vortices in the high-Reynolds-number laminar compressible wake behind a flat plate which is aligned with the centerline of a curved mixing-layer system. The Görtler modes were previously found to exist within curved compressible mixing layers by Owen et al. ͓Phys. Fluids 8, 2506 ͑1997͔͒. This study extends that investigation and demonstrates the effect a wake has on the growth rate and location of such modes. The investigations were made by examining the growth rate and the location of the Görtler modes in the limit of large Görtler number and high wave number within the wake-dominated curved compressible mixing-layer systems based on three wake flow models. An analytic Gaussian wake profile is first used to model the behavior of the basic flow within the mixing layer at the trailing edge of the splitter plate. It is found that the wake has an amplification effect on the growth of the Görtler instability within the concavely curved or "unstably" curved compressible mixing layers. It is also found that within the convexly curved or "stably" curved compressible mixing layers wake modes can occur that behave differently to the "thermal modes," which were previously found within the plain curved compressible system by Owen et al. Another analytic composite model which has some practical applications is then used to predict the behavior of the modes within the systems. Solutions from a numerical wake flow model have been compared with the predictions based on the analytic wake flow models.

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“…It was also seen that a change in the initial perturbation only served to alter the base of the neutral curves and not the ultimate downstream behaviour. Owen, Seddougui & Otto (1997) completed a similar study to Hall (1982) (and also to the analytical part of Otto et al 1996) for a compressible mixing layer. As well as finding modes that have counterparts in the incompressible problem herein referred to as 'conventional modes', Owen et al (1997) found a new class of modes which do not exist in the incompressible problem; these 'thermal modes' arise when a significantly cooler and slower stream curves away from a faster stream (which is analogous to convex curvature).…”

Section: Introductionmentioning

confidence: 99%

“…Owen, Seddougui & Otto (1997) completed a similar study to Hall (1982) (and also to the analytical part of Otto et al 1996) for a compressible mixing layer. As well as finding modes that have counterparts in the incompressible problem herein referred to as 'conventional modes', Owen et al (1997) found a new class of modes which do not exist in the incompressible problem; these 'thermal modes' arise when a significantly cooler and slower stream curves away from a faster stream (which is analogous to convex curvature). It is worth noting that both of these classes of modes owe their existence to the presence of centrifugal force, the main difference being that the 'conventional modes' are driven by velocity shear, whereas the 'thermal modes' are sustained by thermal gradients.…”

Section: Introductionmentioning

confidence: 99%

“…We exploit the high-wavenumber limit of the inviscid problem to gain some very useful information pertaining to the ranges of free-stream temperature and velocity ratios for which these modes persist. It happens that the ratio of stream speeds used in most of Owen et al (1997) was fortuitous. Far downstream, the modes become localized within a certain region, and Owen et al (1997) determined where within the mixing layer this was located.…”

Section: Introductionmentioning

confidence: 99%

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Görtler vortices in compressible mixing layers

Sarkies

Otto

2001

J. Fluid Mech.

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In experiments, Plesniak, Mehta & Johnson (1994) have noted that curved two-stream mixing layers are susceptible to centrifugal instabilities under the condition that the slower of the streams curves towards the faster one; this condition is analogous to the concave curvature condition for the stability of the flow over a plate. The modes which arise manifest themselves as vortices aligned with the dominant flow direction. Previous numerical and analytical work has elucidated the structure of these vortices within incompressible mixing layers; Otto, Jackson & Hu (1996). In this paper we go on to investigate the rôles of compressibility and heating in determining the streamwise fate of Görtler vortices within these situations.The development of the disturbances is monitored downstream and curves of neutral stability are plotted. The effect of changing the Mach number and free-stream temperatures is studied in detail. It is found that for certain parameter régimes modes can occur within convexly curved, or ‘stable’ mixing layers; these ‘thermal modes’ have no counterpart within incompressible mixing layers. By making use of a large Görtler number analysis we are able to verify our numerical results, and derive a very simple condition which yields information about the parameter ranges for which certain modes are likely to occur. As an aside this method can be used to show that no degree of wall cooling will allow sustained growth of Görtler vortices within boundary layers over convex plates.

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The linear evolution of centrifugal instabilities in curved, compressible mixing layers

Cited by 6 publications

References 14 publications

The stability of a curved, heated boundary layer: linear and nonlinear problems

The stability of a curved, heated boundary layer: linear and nonlinear problems

Centrifugal instabilities in curved compressible wakes

Görtler vortices in compressible mixing layers

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