Instabilities and transition in flows between two porous concentric cylinders with radial flow and a radial temperature gradient

Колесов, В. В.; Shapakidze, L. D.

doi:10.1063/1.3534026

Cited by 7 publications

(6 citation statements)

References 35 publications

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“…The algorithm for calculating the coefficients of the amplitude system is described in [12] and is similar to the algorithm used in studies of the isothermal [4] and non-isothermal [13,14] Couette flow between cylinders.…”

Section: Calculation Of the Coefficients Of The Amplitude Systemmentioning

confidence: 99%

Occurrence of quasiperiodic flows between two rotating permeable cylinders

Колесов

Romanov

2014

J Appl Mech Tech Phy

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This paper considers viscous incompressible fluid flows between two infinite rotating permeable concentric cylinders near the bifurcation point, which result in secondary steady flow and oscillations with azimuthal waves. Steady periodic and quasiperiodic fluid flow regimes with two, three, and four independent frequencies are obtained by methods of the theory of codimension-two bifurcations of hydrodynamic flows having cylindrical symmetry.

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Section: Calculation Of the Coefficients Of The Amplitude Systemmentioning

confidence: 99%

Occurrence of quasiperiodic flows between two rotating permeable cylinders

Колесов

Romanov

2014

J Appl Mech Tech Phy

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“…The calculations for impermeable [9] and permeable heated [16] cylinders showed that the J-bound pairs of nonsymmetric cycles of the motor subsystem undergo bifurcation of period doubling, including unbounded sequences of these bifurcations. Analogous phenomena take place in the case under consideration.…”

Section: Calculation Of the Cycles Of The Motor Subsystemmentioning

confidence: 99%

Chaos generation in the Couette-Taylor problem for permeable cylinders

Колесов¹,

Romanov²

2013

Fluid Dyn

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The methods of the bifurcation theory of codimension two, together with computer calculations, are used to investigate stationary, periodic, and quasiperiodic flows with two and three independent frequencies, as well as chaotic regimes of fluid flow between two infinite rotating permeable concentric cylinders near the intersection of the bifurcations initiating secondary stationary flow and self-oscillations with azimuthal waves.The experimental investigations [1][2][3] have shown that with increase in the Reynolds number the main stationary rotational-symmetric fluid flow between two rotating permeable cylinders changes for a secondary stationary flow or a self-oscillatory regime with waves traveling in the azimuthal direction. The further increase in the Reynolds number leads to complication of the fluid flow structure and gives rise to different complicated regimes and then to turbulence.The calculations of neutral curves made it possible to found that at certain parameter values the curves corresponding to rotational-symmetric and oscillatory three-dimensional instabilities intersect [4][5][6][7][8].In the mid-eighties of the last century V.I. Yudovich in Russia and J. Iooss and P. Chossat in France devised the bifurcation theory of codimension two for hydrodynamic flows with cylindrical symmetries. This made it possible to investigate different fluid flow regimes in the vicinity of the point of intersection of bifurcations of the origin of secondary stationary flow and azimuthal waves for impermeable cylinders [9,10]. In this study, this theory is applied for calculating complicated fluid flows in the Couette-Taylor problem for permeable cylinders. GOVERNING EQUATIONS AND MAIN REGIMELet a gap between two solid infinite permeable concentric cylinders, R 1 and R 2 in radii (R 1 < R 2 ) rotating at angular velocities Ω 1 and Ω 2 be filled with a viscous homogeneous incompressible fluid. We will assume that there are no external body forces. The quantities R 1 , Ω 1 R 1 ,a nd 1/Ω 1 are taken for the length, velocity, and time scales, respectively.In the cylindrical coordinates r, ϕ, z, with the z axis aligned with the cylinder axis, the dimensionless Navier-Stokes and continuity equations take the form:

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“…Cylindrical vortices with radial flow were already studied in Refs. [23,25,26,[30][31][32][33][34][35][36][37], but the problem of finding cooling scenarios with proper boundary conditions was (to our knowledge) not posed. Dornbrand [25] and later on Pengelley [26] studied the problem precisely having the same purpose as we: to get a solvable model for vortex cooling.…”

mentioning

confidence: 97%

“…Refs. [31,33,35,36] focus on a laminar flow in the incompressible limit (but they account for axial motion). As our analysis shows, compressibility does not need to be large, but retaining it-and hence allowing for the proper coupling between thermodynamics and mechanics-is necessary for the proper theoretical description of cooling.…”

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Modeling gasodynamic vortex cooling

Allahverdyan

Fauve

2017

Phys. Rev. Fluids

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We aim at studying gasodynamic vortex cooling in an analytically solvable, thermodynamically consistent model that can explain limitations on the cooling efficiency. To this end, we study a angular plus radial flow between two (co-axial) rotating permeable cylinders. Full account is taken of compressibility, viscosity and heat conductivity. For a weak inward radial flow the model qualitatively describes the vortex cooling effect-both in terms of temperature and of decrease of the stagnation enthalpy-seen in short uniflow vortex (Ranque) tubes. The cooling does not result from external work, and its efficiency is defined as the ratio of the lowest temperature reached adiabatically (for the given pressure gradient) to the actually reached lowest temperature. We show that for the vortex cooling the efficiency is strictly smaller than 1, but in another configuration with an outward radial flow, we found that the efficiency can be larger than 1. This is related to both the geometry and the finite heat conductivity.

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Instabilities and transition in flows between two porous concentric cylinders with radial flow and a radial temperature gradient

Cited by 7 publications

References 35 publications

Occurrence of quasiperiodic flows between two rotating permeable cylinders

Occurrence of quasiperiodic flows between two rotating permeable cylinders

Chaos generation in the Couette-Taylor problem for permeable cylinders

Modeling gasodynamic vortex cooling

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