The onset of Taylor–Görtler vortices during impulsive spin-down to rest

• Published in: Chemical engineering science Vol. 61; no. 19; pp. 6478 - 6485
• Main Authors: Kim, Min Chan, Kyun Choi, Chang
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.10.2006; Elsevier
• Subjects: Applied sciences; Chemical engineering; Exact sciences and technology; Propagation theory; Spin down; Stability condition; Taylor–Görtler instability; Spin down; Taylor–Görtler instability; Propagation theory; Stability condition; Taylor-Görtler instability; Stability; Swirling flow; Reynolds number; Prediction; Instability; Velocity distribution; Newtonian fluid
• ISSN: 0009-2509; 1873-4405
• DOI: 10.1016/j.ces.2006.06.019

The onset of hydrodynamical instability induced by impulsive spin-down to rest in a cylinder containing a Newtonian fluid is analyzed by using the propagation theory. The primary transient swirl flow is laminar but for an initially high rotating speed secondary motion sets in at a certain time. It is found here that the critical Reynolds number Re c = 320 , below which the flow is unconditionally stable. For Re > Re c the dimensionless critical time τ c to mark the onset of a fastest growing instability is presented as a function of the Reynolds number Re. Available experimental data and also predictions show that deviation of the velocity profiles from their primary ones occurs starting from a certain time τ ≈ 4 τ c . This means that secondary motion is detected experimentally at this characteristic time. It seems that during τ c ⩽ τ ⩽ 4 τ c secondary motion is relatively very weak.