On the stability of a convective motion generated by a chemically reacting fluid in a pipe

Koliskina, Valentina; Kolyshkin, Andrei A.; Volodko, Inta; Kalis, Harijs

doi:10.1063/1.4952264

Cited by 3 publications

(1 citation statement)

References 5 publications

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“…The role of the Prandtl number of the stability characteristics of the flow is analysed. Later a similar problem is solved for the case, where the heat sources are distributed within the fluid in accordance with the Arrhenius' law (see the solution for the circular pipe in [7] and for the annulus in [8]).…”

Section: Introductionmentioning

confidence: 99%

Linear stability analysis of convective flow in pipe due to radially distributed heat sources

Koliskina

Kolyshkin

2018

Engineering for Rural Development

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A steady convective flow of a viscous incompressible fluid is considered in a tall vertical cylindrical pipe due to internal heat sources of the form Q = A+Br, where A and B are constants and r is the radial coordinate. Models of thermal convection with non-uniform internal heat generation are used in many applications. Examples include absorption of incidental radiation or zeroth-order chemical reactions. The pipe is closed so that the total fluid flux through the cross-section of the pipe is zero. The corresponding system of Navier-Stokes equations under the Boussinesq approximation is solved analytically. Linear stability of the steady convective flow is analyzed using the method of normal modes. The corresponding eigenvalue problem for the system of ordinary differential equations is solved numerically using the collocation method based on the Chebyshev polynomials. In the present paper we restrict ourselves only to asymmetric perturbations for the first azimuthal mode, since experiments for the case of heat sources of constant density have shown that it is the most unstable mode. It is found that even for Prandtl numbers smaller than 0.8 there exist two separate branches of the marginal stability curve. One of the branches is associated with the hydrodynamical mechanism due to the presence of an inflection point in the base flow velocity profile, while the second one is related to the instability in the form of thermal waves that propagate downstream with sufficiently large phase speed. It is found that the Prandtl number and both negative and positive B values have a destabilizing influence on the flow.

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Section: Introductionmentioning

confidence: 99%

Linear stability analysis of convective flow in pipe due to radially distributed heat sources

Koliskina

Kolyshkin

2018

Engineering for Rural Development

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Convective instability of non-isothermal Couette flow between two rotating cylinders caused by internal heat generation in accordance with the Arrhenius law

Kolyshkin¹,

Koliskina²

2017

AIP Conference Proceedings

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Convective Instability of a Steady Flow in an Annulus Caused by Internal Heat Generation

Kolyshkin

Koliskina

Volodko

et al. 2020

Proceedings of the Latvian Academy of Sciences. Section B. Natural, Exact, and Applied Sciences.

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Linear stability of convective motion in a tall vertical annulus was analysed in the paper. The base flow was generated by a non-uniform distribution of heat sources in the radial direction. The base flow velocity and temperature were obtained analytically solving the system of Navier-Stokes equations under the Boussinesq approximation. The linear stability problem was solved for axi-symmetric and asymmetric perturbations by a collocation method based on the Chebyshev polynomials. Numerical results showed that there were three destabilising factors: (1) increase of the gap between the cylinders, (2) increase of the density of internal heat sources towards to the outer boundary of the annulus and (3) increase of the Prandtl number.

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On the stability of a convective motion generated by a chemically reacting fluid in a pipe

Cited by 3 publications

References 5 publications

Linear stability analysis of convective flow in pipe due to radially distributed heat sources

Linear stability analysis of convective flow in pipe due to radially distributed heat sources

Convective instability of non-isothermal Couette flow between two rotating cylinders caused by internal heat generation in accordance with the Arrhenius law

Convective Instability of a Steady Flow in an Annulus Caused by Internal Heat Generation

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