The influence of initial condition on the linear stability of time-dependent circular Couette flow

Chen, J.‐C.; Neitzel, G. Paul; Jankowski, D. F.

doi:10.1063/1.865087

Cited by 22 publications

(13 citation statements)

References 5 publications

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“…Based on the relative condition of Chen et al [28], Kim et al [25] suggested that for the case of n=0.5, the relative instability condition be fullfiled at τ =τ c . If the related process is still diffusion dominant with Ma * =constant at τ =τ c , it is probable that Θ(τ, )=τ 1/2 Θ * (ζ ).…”

Section: Stability Equationsmentioning

confidence: 99%

Onset of marangoni convection in an initially quiescent spherical droplet subjected to the transient heat conduction

Kim

Yoon

Cho³

2009

Korean J. Chem. Eng.

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The onset of Marangoni convection in an initially quiescent spherical droplet subjected to the impulsive change in boundary temperature is analyzed under the linear theory. For this system in which instabilities are driven by interface-tension gradients, a stability analysis on regular cell modes is conducted on the basis of the propagation theory we have developed. The present stability analysis predicts that τ c decreases with increasing Ma. For the limiting case of τ →0, the present study approaches the planar limit as expected.

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Section: Stability Equationsmentioning

confidence: 99%

Onset of marangoni convection in an initially quiescent spherical droplet subjected to the transient heat conduction

Kim

Yoon

Cho³

2009

Korean J. Chem. Eng.

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“…For the case of negative ψ the Soret flux j S has a positive value. The boundary conditions have been obtained by the impermeable conditions for concentration at both boundaries, that is, j=0 at Z=0 and d. The above equations can be solved by using the Laplace transform: (13) where ζ=z/ . For the deep-pool system of small τ (Le≤τ≤0.01) the basic concentration field is approximated by (14) Here −c 0 (τ, 0)=c 0 (τ, 1)= .…”

Section: Governing Equationsmentioning

confidence: 99%

Onset of Soret convection in a nanoparticles-suspension heated from above

Kim

Yoon

2009

Korean J. Chem. Eng.

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The onset of Soret-driven convection in a nanoparticles suspension heated from above is analyzed theoretically based on linear theory and relative instability concept. A new set of stability equations are derived and solved by using the dominant mode method. The dimensionless critical time τ c to mark the onset of instability is presented here as a function of the Rayleigh number, the Lewis number and the separation ratio. Available experimental data indicate that for large Rayleigh number convective motion is detected starting from a certain time τ≈3τ c . This means that the growth period of initiated instabilities is needed for convective motion to be detected experimentally. It seems evident that during τ c ≤τ≤3τ c convective motion is relatively very weak and the primary diffusive transfer is dominant. INTRODUCITONThermal convection in binary mixtures shows quite different characteristics from those in pure fluids [1][2][3][4]. If the suspension of nanoparticles is under consideration, the spatiotemporal properties of convection are much more complex than those of pure fluids or molecular solutions due to the influence of thermal diffusion, i.e., Soretinduced concentration gradients and also the extremely small particle mobility which can be reflected by the Lewis number Le≤10 −4 [5-8]. Here Le(=D C /α) is the Lewis number, D C the diffusion coefficient, α the thermal diffusivity, respectively. The relative importance of the Soret effect with respect to weak solutal diffusion is measured by the separation ratio ψ(=(β C /β T )(D T /D C )), where D T is the Soret diffusion coefficient, and β T (=−ρ −1 (∂ρ/∂T)) and β C (=ρ −1 (∂ρ/∂C)) are the thermal and the solutal expansion coefficient, respectively. For the case of ψ =0 double diffusive convection sets in when Ra+Ra s ≥1708 [9], where Ra(=gβ T ∆Td 3 /αν) is the thermal Rayleigh number and Ra s =(gβ C ∆Cd 3 /Dν) the solutal Rayleigh number, respectively.For non-vanishing ψ, however, the external temperature gradient induces concentration variations and these create the buoyancy force.

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“…This condition is known as the strong stability criterion [2]. Neitzel [4] relaxed this strong stability criterion by considering the growth of the disturbance kinetic energy.…”

Section: -2 Energy Methodsmentioning

confidence: 99%

“…Here, we relax the above stability limits by introducing the relative stability concept: the temporal growth rate of the kinetic energy of the disturbance velocity should exceed that of the base velocity at the onset condition of secondary motion. This stability criterion was proposed by Chen et al [2], and applied into the various problems by Kim et al [6][7][8][9][10]. In the relative stability model the critical time τ r is determined, based on a most dangerous mode of instability:…”

Section: -2 Energy Methodsmentioning

confidence: 99%

“…The analytical difficulties involved in the application of conventional stability theory to this kind of transient flow has been considered [2] and the related instability analysis has been conducted by using the strong and the marginal stability criteria [3][4][5]. The strong stability criterion pursued the stability bounds in terms of time interval where the kinetic energy of disturbances starts to increase.…”

Section: Introductionmentioning

confidence: 99%

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The Onset of Tayler-Görtler Vortices in Impulsively Decelerating Circular Flow

Cho¹,

Kim²

2015

Korean Chemical Engineering Research

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− The onset of instability induced by impulsive spin-down of the rigid-body flow placed in the gap between two coaxial cylinders is analyzed by using the energy method. In the present stability analysis the growth rate of the kinetic energy of the base state and also that of disturbances are taken into consideration. In the present system the primary flow is a transient, laminar one. But for the Reynolds number equal or larger than a certain one, i.e. Re ≥ Re G secondary motion sets in, starting at a certain time. For R e ≥ Re G the dimensionless critical time to mark the onset of vortex instabilities, τ c , is here presented as a function of the Reynolds number Re and the radius ratio η. For the wide gap case of small η, the transient instability is possible in the range of Re G ≤ Re ≤ Re S . It is found that the predicted τ c -value is much smaller than experimental detection time of first observable secondary motion. It seems evident that small disturbances initiated at τ c require some growth period until they are detected experimentally.

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The influence of initial condition on the linear stability of time-dependent circular Couette flow

Cited by 22 publications

References 5 publications

Onset of marangoni convection in an initially quiescent spherical droplet subjected to the transient heat conduction

Onset of marangoni convection in an initially quiescent spherical droplet subjected to the transient heat conduction

Onset of Soret convection in a nanoparticles-suspension heated from above

The Onset of Tayler-Görtler Vortices in Impulsively Decelerating Circular Flow

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