Global stability of swept flow around a parabolic body: the neutral curve

The onset of transition in the leading-edge region of a swept blunt body depends crucially on the stability characteristics of the flow. Modelling this flow configuration by swept compressible flow around a parabolic body, a global approach is taken to extract pertinent stability information via a DNS-based iterative eigenvalue solver. Global modes combining features from boundary-layer and acoustic instabilities are presented. A parameter study, varying the spanwise disturbance wavenumber and the sweep Reynolds number, showed the existence of unstable boundary-layer and acoustic modes. The corresponding neutral curve displays two overlapping regions of exponential growth and two critical Reynolds numbers, one for boundary-layer instabilities and one for acoustic instabilities. The employed global approach establishes a first neutral curve, delineating stable from unstable parameter configurations, for the complex flow about a swept parabolic body with corresponding implications for swept leading-edge flow.

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Global stability of swept flow around a parabolic body: features of the global spectrum

Journal of Fluid Mechanics ◽

10.1017/s0022112010005252 ◽

2011 ◽

Vol 669 ◽

pp. 375-396 ◽

Cited By ~ 10

Author(s):

CHRISTOPH J. MACK ◽

PETER J. SCHMID

Keyword(s):

Boundary Layer ◽

Reynolds Number ◽

Temporal Stability ◽

Three Dimensional ◽

Leading Edge ◽

Parameter Study ◽

Acoustic Modes ◽

Stabilizing Effect ◽

Unstable Boundary Layer ◽

Temporal Perturbation

The global temporal stability of three-dimensional compressible flow about a yawed parabolic body of infinite span is investigated using an iterative eigenvalue technique in combination with direct numerical simulations. The computed global spectrum provides a comprehensive picture of the temporal perturbation dynamics of the flow, and a wide and rich variety of modes has been uncovered for the investigated parameter choices: stable and unstable boundary-layer modes, different types of stable and unstable acoustic modes, and stable wavepacket modes have been found. A parameter study varying the spanwise perturbation wavenumber and the sweep Reynolds number reproduced a preferred spanwise length scale and a critical Reynolds number for a boundary-layer or acoustic instability. Convex leading-edge curvature has been found to have a strongly stabilizing effect on boundary-layer modes but only a weakly stabilizing effect on acoustic modes. Furthermore, for certain parameter choices, the acoustic modes have been found to dominate the boundary-layer modes.

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Experimental and Theoretical Investigation of the Supersonic Boundary Layer Stability on the Swept Wing

Siberian Journal of Physics ◽

10.54362/1818-7919-2008-3-3-34-38 ◽

2008 ◽

Vol 3 (3) ◽

pp. 34-38

Author(s):

Sergey A. Gaponov ◽

Yuri G. Yermolaev ◽

Aleksandr D. Kosinov ◽

Nikolay V. Semionov ◽

Boris V. Smorodsky

Keyword(s):

Boundary Layer ◽

Three Dimensional ◽

Leading Edge ◽

Supersonic Boundary Layer ◽

Mean Flow ◽

Swept Wing ◽

Wing Model ◽

Dimensional Boundary ◽

The Stability ◽

Good Agreement

Theoretical and an experimental research results of the disturbances development in a swept wing boundary layer are presented at Mach number М = 2. In experiments development of natural and small amplitude controllable disturbances downstream was studied. Experiments were carried out on a swept wing model with a lenticular profile at a zero attack angle. The swept angle of a leading edge was 40°. Wave parameters of moving disturbances were determined. In frames of the linear theory and an approach of the local self-similar mean flow the stability of a compressible three-dimensional boundary layer is studied. Good agreement of the theory with experimental results for transversal scales of unstable vertices of the secondary flow was obtained. However the calculated amplification rates differ from measured values considerably. This disagreement is explained by the nonlinear processes observed in experiment

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Experimental study of weak shock waves influence on the supersonic boundary layer of the flat plate model

EPJ Web of Conferences ◽

10.1051/epjconf/201919600018 ◽

2019 ◽

Vol 196 ◽

pp. 00018 ◽

Cited By ~ 2

Author(s):

Vasiliy Kocharin ◽

Aleksandr Kosinov ◽

Yuriy Yermolayev ◽

Nikolay Semionov

Keyword(s):

Boundary Layer ◽

Experimental Study ◽

Shock Waves ◽

Flat Plate ◽

Leading Edge ◽

Weak Shock ◽

Supersonic Boundary Layer ◽

Complex Flow ◽

Complex Flow Structure ◽

Constant Temperature Anemometer

The experimental study of the effect of weak shock waves on the supersonic boundary layer of the flat plate with a blunt leading edge (the radius of bluntness was r = 2.5 mm) with Mach number M = 2.5 and zero angle of attack was carried out. The measurements were carried out using the constant temperature anemometer. The paper presents a complex flow structure on the surface of the model. High-intensity peaks were found in the regions of the disturbed flow. Also the spectral analysis of perturbations was performed. It is found that the supersonic boundary layer on a flat plate is very sensitive to the effect of weak shock waves.

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Spatio–temporal instability in mixed convection boundary layers

Journal of Fluid Mechanics ◽

10.1017/s002211209900676x ◽

2000 ◽

Vol 402 ◽

pp. 89-107 ◽

Cited By ~ 10

Author(s):

P. MORESCO ◽

J. J. HEALEY

Keyword(s):

Boundary Layer ◽

Reverse Flow ◽

Temporal Stability ◽

Leading Edge ◽

Boundary Layer Separation ◽

Absolute Instability ◽

Limiting Similarity ◽

Buoyancy Forces ◽

Spatio Temporal ◽

The Stability

In this work we analyse the stability properties of the flow over an isothermal, semi-infinite vertical plate, placed at zero incidence to an otherwise uniform stream at a different temperature. Near the leading edge the boundary layer resembles Blasius flow, but further downstream it approaches that of pure buoyancy-driven flow. A coordinate transformation that describes in a smooth way the evolution between these two limiting similarity states, where the viscous and buoyancy forces are respectively dominant, is used to calculate the basic flow. The stability of this flow has been investigated by making the parallel flow approximation, and using an accurate spectral method on the resulting stability equations. We show how the stability modes discussed by other authors can be followed continuously between the forced and free convection limits; in addition, new instability modes not previously reported in the literature have been found. A spatio–temporal stability analysis of these modes has been carried out to distinguish between absolute and convective instabilities. It seems that absolute instability can only occur when buoyancy forces are opposed to the free stream and when there is a region of reverse flow. Model profiles have been used in this latter case beyond the point of boundary layer separation to estimate the range of reverse flows that support absolute instability. Analysis of the Rayleigh equations for this problem suggests that the absolute instability has an inviscid origin.

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An Experimental Study of Vigorous Transient Natural Convection

Journal of Heat Transfer ◽

10.1115/1.3449733 ◽

1970 ◽

Vol 92 (4) ◽

pp. 628-634 ◽

Cited By ~ 21

Author(s):

J. C. Mollendorf ◽

B. Gebhart

Keyword(s):

Boundary Layer ◽

Natural Convection ◽

Moving Boundary ◽

Leading Edge ◽

Linear Stability Theory ◽

Extreme Condition ◽

Transient Effects ◽

Theory Analysis ◽

Main Observation ◽

The Stability

External natural convection transient response leading to transition and established turbulent flow is determined experimentally and compared with the laminar double-integral theory predictions for processes wherein all transient effects are important. The theory is shown to give very accurate predictions during the laminar portion of the transient, and temperature overshool is not observed experimentally. In addition, several unexpected and very interesting observations were made concerning the stability of the flow as it proceeds to turbulence. The first main observation is that the propagating leading edge effect serves as a very effective moving boundary layer trip and triggers the resulting turbulence. Also for the less extreme condition (less vigorous transient) there is a relaminarization of the boundary layer. Explanations of these observations are proposed in the light of recently acquired results of linear stability theory analysis for small disturbances.

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On the long-wave instability of natural-convection boundary layers

Journal of Fluid Mechanics ◽

10.1017/s0022112096004521 ◽

1997 ◽

Vol 335 ◽

pp. 57-73 ◽

Cited By ~ 5

Author(s):

P. G. DANIELS ◽

JOHN C. PATTERSON

Keyword(s):

Boundary Layer ◽

Travelling Waves ◽

Vertical Wall ◽

Phase Speed ◽

Neutral Curve ◽

Neutral Stability ◽

Layer Width ◽

Dimensional Boundary ◽

Prandtl Numbers ◽

The Stability

This paper considers the stability of the one-dimensional boundary layer generated by sudden heating of an infinite vertical wall. A quasi-steady approximation is used to analyse the asymptotic form of the lower branch of the neutral curve, corresponding to disturbances of wavelength much greater than the boundary-layer width. This leads to predictions of the critical wavenumber for neutral stability and the maximum phase speed of the travelling waves. Results are obtained for a range of Prandtl numbers and are compared with solutions of the full stability equations and with numerical simulations and experimental observations of cavity flows driven by sudden heating of the sidewalls.

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Linear and nonlinear receptivity of the boundary layer in transonic flows

Journal of Fluid Mechanics ◽

10.1017/jfm.2015.587 ◽

2015 ◽

Vol 786 ◽

pp. 154-189 ◽

Cited By ~ 9

Author(s):

A. I. Ruban ◽

T. Bernots ◽

M. A. Kravtsova

Keyword(s):

Boundary Layer ◽

Acoustic Noise ◽

Neutral Curve ◽

Wing Surface ◽

Roughness Height ◽

Stokes Layer ◽

Instability Modes ◽

Direct Numerical Method ◽

Tollmien Schlichting ◽

The Stability

In this paper we analyse the process of the generation of Tollmien–Schlichting waves in a laminar boundary layer on an aircraft wing in the transonic flow regime. We assume that the boundary layer is exposed to a weak acoustic noise. As it penetrates the boundary layer, the Stokes layer forms on the wing surface. We further assume that the boundary layer encounters a local roughness on the wing surface in the form of a gap, step or hump. The interaction of the unsteady perturbations in the Stokes layer with steady perturbations produced by the wall roughness is shown to lead to the formation of the Tollmien–Schlichting wave behind the roughness. The ability of the flow in the boundary layer to convert ‘external perturbations’ into instability modes is termed the receptivity of the boundary layer. In this paper we first develop the linear receptivity theory. Assuming the Reynolds number to be large, we use the transonic version of the viscous–inviscid interaction theory that is known to describe the stability of the boundary layer on the lower branch of the neutral curve. The linear receptivity theory holds when the acoustic noise level is weak, and the roughness height is small. In this case we were able to deduce an analytic formula for the amplitude of the generated Tollmien–Schlichting wave. In the second part of the paper we lift the restriction on the roughness height, which allows us to study the flows with local separation regions. A new ‘direct’ numerical method has been developed for this purpose. We performed the calculations for different values of the Kármán–Guderley parameter, and found that the flow separation leads to a significant enhancement of the receptivity process.

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Simplified Analysis of Boundary-Layer Oscillations

Journal of Ship Research ◽

10.5957/jsr.1960.4.3.37 ◽

1960 ◽

Vol 4 (03) ◽

pp. 37-54

Author(s):

Robert Betchov

Keyword(s):

Boundary Layer ◽

Boundary Layers ◽

Nonlinear Effects ◽

Adverse Pressure Gradient ◽

Neutral Curves ◽

Elastic Wall ◽

Unstable Boundary Layer ◽

Incompressible Boundary ◽

Negative Damping ◽

The Stability

The stability of an incompressible boundary layer is analyzed in terms of three basic processes. These are (a) the oscillations of a boundary layer when friction is disregarded, (b) the effects of friction at the wall, and (c) the effects of friction at the critical layer. These processes are separately discussed and evaluated. Simple models are presented. A general equation leads to the eigenvalues. The neutral curves corresponding to five typical cases are determined—parabolic and Blasius boundary layers, boundary layers with suction and with adverse pressure gradient, two-dimensional Poiseuille flow. The unstable boundary layer is discussed briefly. The nonlinear effects of the oscillation on the velocity profile are evaluated. Finally, the case of a boundary layer along an elastic wall is considered, and it is found that the wall may have a significant effect on the layer. In particular, a wall with negative damping could completely stabilize the boundary layer.

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