High speed viscous plane couette-poiseuille flow stability

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Tezin Türü: Doktora

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Mühendislik Fakültesi, Makina Mühendisliği Bölümü, Türkiye

Tezin Onay Tarihi: 2004

Tezin Dili: İngilizce

Öğrenci: ALİ ASLAN EBRİNÇ

Asıl Danışman (Eş Danışmanlı Tezler İçin): Zafer Dursunkaya

Eş Danışman: Serkan Özgen

Özet:

The linear stability of high speed-viscous plane Couette and Couette-Poiseuille flows are investigated numerically. The conservation equations along with Sutherland?s viscosity law are studied using a second-order finite difference scheme. The basic velocity and temperature distributions are perturbed by a small-amplitude normalmode disturbance. The small-amplitude disturbance equations are solved numerically using a global method using QZ algorithm to find all the eigenvalues at finite Reynolds numbers, and the incompressible limit of these equations is investigated for Couette-Poiseuille flow. It is found that the instabilities occur, although the corresponding growth rates are often small. Two families of wave modes, Mode I (odd modes) and Mode II (even modes), were found to be unstable at finite Reynolds numbers, where Mode II is the dominant instability among the unstable modes for plane Couette flow. The most unstable mode for plane Couette ? Poiseuille flow is Mode 0, which is not a member of the even modes. Both even and odd modes are acoustic modes created by acoustic reflections between a wIll and a relative sonic line. The necessary condition for the existence of such acoustic wave modes is that there is a region of locally supersonic mean flow relative to the phase speed of the instability wave. The effects of viscosity and compressibility are also investigated and shown to have a stabilizing role in all cases studied. Couette-Poiseuille flow stability is investigated in case of a choked channel flow, where the maximum velocity in the channel corresponds to sonic velocity. Neutral stability contours were obtained for this flow as a function if the wave number,Reynolds number and the upper wall Mach number. The critical Reynolds number is found as 5718.338 for an upper wall Mach number of 0.0001, corresponding to the fully Poiseuille case.