Effect of pressure gradient on the stability of compressible boundary layers

Zurigat, Yousef H.; Nayfeh, Ali H.; Masad, Jamal A.

doi:10.2514/3.11206

Cited by 27 publications

(9 citation statements)

References 12 publications

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“…For instance [14], examined the effect of a pressure gradient on the stability of compressible boundary-layer flows. The effect of a pressure gradient on the stability of several base flows with inflection points, has also been investigated.…”

Section: Resultsmentioning

confidence: 99%

The stability of Falkner-Skan flows with several inflection points

Heeg¹,

Dijkstra²,

Zandbergen³

1999

Z. angew. Math. Phys.

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Non-unique solutions to the Falkner-Skan equation with multiple inflection points have been investigated with respect to stability properties. A temporal stability analysis based on the Orr-Sommerfeld equation has been performed. Attention has been paid to the effect of the number of inflection points in these solutions on the stability properties. While the standard Falkner-Skan flow does not have any inflection points in a favourable pressure gradient, the first non-unique solution branch has two such points. The presence of these two inflection points implies a dramatic reduction of the critical Reynolds number by four orders of magnitude. Moreover, in base flows with more than two inflection points additional neutral waves occur with the same Reynolds number but with different wave numbers. Mathematics Subject Classification (1991).Stability of parallel flows, 76E05.

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Section: Resultsmentioning

confidence: 99%

The stability of Falkner-Skan flows with several inflection points

Heeg¹,

Dijkstra²,

Zandbergen³

1999

Z. angew. Math. Phys.

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“…Compared with zero pressure gradient, favorable pressure gradient (hereafter referred to as FPG) significantly stabilizes the boundary layer in both incompressible and compressible flows (the first mode as well as Mack's second mode). This is supported by a number of studies, e.g., with direct numerical simulation [5,10,18], linear stability theory [4,6,7] and very recent experiments [23,25]. Hence, in the review by Reed et al [9], the instability of boundary layer with FPG is described as "very weak, if it exists at all".…”

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confidence: 89%

The New Mode of Instability in Viscous High-Speed Boundary Layer Flows

Ren¹

2018

AAMM

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The new mode of instability found by Tunney et al.,[24] is studied with viscous stability theory in this article. When the high-speed boundary layer is subject to certain values of favorable pressure gradient and wall heating, a new mode becomes unstable due to the appearance of the streamwise velocity overshoot (U(y) > U ∞ ) in the base flow. The present study shows that under practical Reynolds numbers, the new mode can hardly co-exist with conventional first mode and Mack's second mode. Due to the requirement for additional wall heating, the new mode may only lead to laminar-turbulent transition under experimental (artificial) conditions. Compared with zero pressure gradient, favorable pressure gradient (hereafter referred to as FPG) significantly stabilizes the boundary layer in both incompressible and compressible flows (the first mode as well as Mack's second mode). This is supported by a number of studies, e.g., with direct numerical simulation [5,10,18], linear stability theory [4,6,7] and very recent experiments [23,25]. Hence, in the review by Reed et al. [9], the instability of boundary layer with FPG is described as "very weak, if it exists at all". In fact, with FPG, the profile of the base flow U(y) becomes fuller, and the thickness of the boundary layer is decreased, which is mainly responsible for the stabilization of the boundary layer.On the other hand, wall-heating/cooling is one of the common passive flow control methods used on various occasions. Its influence on boundary layer stability has been well documented (see reviews in [3,9]). In contrast to the adiabatic condition, wall heating can destabilize the first mode while stabilizing Mack's second mode. Wall cooling, instead, has opposite effects. One shall distinguish between wall-heating and localized wall-heating. The latter gives rise to wall temperature jump effect and can destabilize Mack's second mode (see recent analysis in [22]).When the flow is subject to the dual effects of FPG and wall-heating, a new mode comes to light. A first analytical study was performed by Tunney et al., [24] under the inviscid assumption. The direct cause of the instability is the appearance of streamwise velocity overshoot (U(y) > U ∞ near the upper edge of the boundary layer). Discussion on the overshoot can be found in Tunney et al., [24] and the references therein. Under inviscid assumption, the new mode was shown to have comparable growth rate as the conventional first mode and Mack's higher mode. However, the possible importance of the new mode is not evaluated. In this paper, we report a viscous stability analysis (with spatial mode) on this new mode which is more relevant for developing boundary layers. The impact and limitations of the new mode will be discussed. In Section 2 the methodology and the base flow are introduced. Modal stability is discussed in Section 3, and the paper is concluded in Section 4.

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“…Equations (25)(26)(27)(28) are solved by backward integration in the streamwise direction with the initial condition given at…”

Section: Adjoint Of Boundary-layer Equationsmentioning

confidence: 99%

“…As mentioned earlier, an approach of optimal NLF design is to formulate an inverse problem in which the target pressure is designed to damp the amplification of disturbances and the parameters of optimization describe the shape, as in Refs. [23][24][25]. Inverse problems of this kind were investigated first by Lighthill 26 and, through an optimal control approach, by Jameson.…”

Section: Introductionmentioning

confidence: 99%