Boundary-Layer Instabilities in Supersonic Expansion Corner Flows

AIAA Journal ◽  
2021 ◽  
pp. 1-8
Author(s):  
Pavel V. Chuvakhov ◽  
Ivan V. Egorov ◽  
Ivan M. Ilyukhin ◽  
Anton O. Obraz ◽  
Alexander V. Fedorov ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Supersonic Expansion ◽  
Corner Flows

Flow along streamwise corners revisited

2003 ◽  
Vol 476 ◽  
pp. 223-265 ◽  
Author(s):  
A. RIDHA
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Three Dimensional ◽  
Numerical Results ◽  
Intermediate Layers ◽  
Concave Corner ◽  
Dimensional Boundary ◽  
Streamwise Pressure Gradient ◽  
Corner Flows ◽  
Corner Layer

In this paper we investigate the three-dimensional laminar incompressible steady flow along a corner formed by joining two similar quarter-infinite unswept wedges along a side-edge. We show that a four-region construction of the potential flow arises naturally for this flow problem, the formulation being generally valid for a corner of an arbitrary angle (π−2α), including the limiting cases of semi- and quarter-infinite flat-plate configurations. This construction leads to five distinct three-dimensional boundary-layer regions, whereby both the spanwise length and velocity scales of the blending intermediate layers are O(δ), with Re−1/2 [Lt ] δ [Lt ] 1, Re being a reference Reynolds number supposed to be large. This reveals crucial differences between concave and convex corner flows. For the latter flow regime, the corner-layer motion is shown to be mainly controlled by the secondary flow which effectively reduces to that past sharp wedges with solutions being unique and existing only for favourable streamwise pressure gradients. In this regime, the corner-layer thickness is shown to be O(Re−0.5+α/π/δ2α/π), −½π [les ] α [les ] 0, which is much smaller than O(Re−1/2) for concave corner flows.Crucially, our numerical results show conclusively that, for α ≠ 0, closed streamwise symmetrically disposed vortices are generated inside the intermediate layers, confirming thus the prediction made by Moore (1956) for a rectangular corner, which has so far remained unconfirmed in the literature.For almost planar corners, three-dimensional corner boundary-layer features are shown, as in (Smith 1975), to arise when α ∼ O(1/ln Re). On the other hand, we show that the flow past a quarter-infinite flat plate would be attained when both values of the streamwise pressure gradient and external corner angle (π+2α) become O(1/ln Re) or smaller.Numerical results for all these flow regimes are presented and discussed.

scholarly journals Interaction of Supersonic Expansion Flow with Boundary Layer in Unsymmetrical Duct.

1994 ◽  
Vol 37 (1) ◽  
pp. 77-82
Author(s):  
Fumio Higashino ◽  
Shigeru Matsuo ◽  
Taro Tsuyuki
Keyword(s):  
Boundary Layer ◽  
Supersonic Expansion

scholarly journals Flow organization in two-dimensional non-Oberbeck–Boussinesq Rayleigh–Bénard convection in water

2009 ◽  
Vol 637 ◽  
pp. 105-135 ◽  
Author(s):  
KAZUYASU SUGIYAMA ◽  
ENRICO CALZAVARINI ◽  
SIEGFRIED GROSSMANN ◽  
DETLEF LOHSE
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Thermal Expansion ◽  
Nusselt Number ◽  
Temperature Profiles ◽  
Two Dimensional ◽  
Number Ratio ◽  
Convection Roll ◽  
Corner Flows ◽  
Rayleigh Benard

Non-Oberbeck–Boussinesq (NOB) effects on the flow organization in two-dimensional Rayleigh–Bénard turbulence are numerically analysed. The working fluid is water. We focus on the temperature profiles, the centre temperature, the Nusselt number and on the analysis of the velocity field. Several velocity amplitudes (or Reynolds numbers) and several kinetic profiles are introduced and studied; these together describe the various features of the rather complex flow organization. The results are presented both as functions of the Rayleigh numberRa(withRaup to 108) for fixed temperature difference Δ between top and bottom plates and as functions of Δ (‘non-Oberbeck–Boussinesqness’) for fixedRawith Δ up to 60K. All results are consistent with the available experimental NOB data for the centre temperatureTcand the Nusselt number ratioNuNOB/NuOB(the label OB meaning that the Oberbeck–Boussinesq conditions are valid). For the temperature profiles we find – due to plume emission from the boundary layers – increasing deviations from the extended Prandtl–Blasius boundary layer theory presented in Ahlerset al. (J. Fluid Mech., vol. 569, 2006, p. 409) with increasingRa, while the centre temperature itself is surprisingly well predicted by that theory. For given non-Oberbeck–Boussinesqness Δ, both the centre temperatureTcand the Nusselt number ratioNuNOB/NuOBonly weakly depend onRain theRarange considered here.BeyondRa≈ 106the flow consists of a large diagonal centre convection roll and two smaller rolls in the upper and lower corners, respectively (‘corner flows’). Also in the NOB case the centre convection roll is still characterized by only one velocity scale. In contrast, the top and bottom corner flows are then of different strengths, the bottom one being a factor 1.3 faster (for Δ = 40K) than the top one, due to the lower viscosity in the hotter bottom boundary layer. Under NOB conditions the enhanced lower corner flow as well as the enhanced centre roll lead to an enhancement of the volume averaged energy based Reynolds number$Re^E \,{=}\, \langle\frac{1}{2} \bu^2 \rangle^{1/2} L/\nu$of about 4% to 5% for Δ = 60K. Moreover, we find$Re^E_{\it NOB}/Re^E_{\it OB} \,{\approx}\, (\beta (T_c)/\beta (T_m))^{1/2}$, with β the thermal expansion coefficient andTmthe arithmetic mean temperature between top and bottom plate temperatures. This corresponds to the ratio of the free fall velocities at the respective temperatures. By artificially switching off the temperature dependence of β in the numerics, the NOB modifications ofReEis less than 1% even at Δ = 60K, revealing the temperature dependence of the thermal expansion coefficient as the main origin of the NOB effects on the global Reynolds number in water.

Effects of continental boundary layer evolution, convection, turbulence and entrainment, on aerosol formation

Tellus B ◽  
2001 ◽  
Vol 53 (4) ◽  
pp. 441-461 ◽  
Author(s):  
E. D. NILSSON ◽  
Ü. RANNIK ◽  
M. KULMALA ◽  
G. BUZORIUS ◽  
C. D. O'DOWD
Keyword(s):  
Boundary Layer ◽  
Aerosol Formation
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