Boundary layer instability of the natural convection flow on a uniformly heated vertical plate

Aberra, Tilek; Armfield, S.W.; Behnia, Masud; McBain, G. D.

doi:10.1016/j.ijheatmasstransfer.2012.06.023

Cited by 23 publications

(4 citation statements)

References 43 publications

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“…Here, φ denotes the spatial average of flow variable φ over the homogeneous direction. Although it is difficult to make a direct quantitative comparison due to flow differences, a similar velocity perturbation structure has also been observed in earlier OB stability results for spatially developing natural convection in air (Versteegh & Nieuwstadt 1998;Aberra et al 2012) and water (Brooker, Patterson & Armfield 1997;Brooker et al 2000).…”

Section: Energy Budgets For the Buoyancy-driven And Shear-driven Modessupporting

confidence: 65%

Non-Oberbeck–Boussinesq effects on the linear stability of a vertical natural convection boundary layer

Ke,

Armfield,

Williamson

2024

J. Fluid Mech.

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The non-Oberbeck–Boussinesq effects on the stability of a vertical natural convection boundary layer are investigated using the linearised disturbance equations for air flows up to a temperature difference of $\Delta T=100\,{\rm K}$ . Based on the linear stability results, the neutral curve is shown to be sensitive to the choice of reference temperature. When evaluated using the film temperature $T_f$ , a lower film Grashof number is required to trigger the linear instability for larger $\Delta T$ . The relative contributions of shear and buoyant production to the perturbation kinetic energy budget reveals that the marginally unstable modes are amplified based on different mechanisms: for lower wavenumbers at relatively small Grashof number, the instability is driven by buoyancy; whereas for higher wavenumbers and larger Grashof number, the flow becomes unstable due to a shear instability. The use of reference temperature is found to scale the shear- and buoyant-driven instabilities differently so that no single reference temperature definition would collapse the neutral curves. The linear stability result further demonstrates that at a given Grashof number a higher temperature difference would give a larger amplification rate of the perturbation, which then leads to an earlier onset of the nonlinearities when evaluated at $T_f$ . Finally, by comparing the amplification rates obtained from direct numerical simulation and the linear stability results, the extent of the linear regime is determined for $\Delta T = 100\,{\rm K}$ .

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Section: Energy Budgets For the Buoyancy-driven And Shear-driven Modessupporting

confidence: 65%

Non-Oberbeck–Boussinesq effects on the linear stability of a vertical natural convection boundary layer

Ke,

Armfield,

Williamson

2024

J. Fluid Mech.

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“…It was found that the amplification of the infinitesimal disturbances are eventually limited by nonlinear effects. The effects of the perturbation boundary conditions are further investigated by Aberra et al (2012) using direct numerical simulation and eigenvalue calculation for the spatially developing NCBL at Pr = 0.733 and Pr = 6.7. The choice of the temperature boundary condition (Neumann or Dirichlet type) was seen to have minimal effect on the marginal stability results.…”

Section: Introductionmentioning

confidence: 99%

Stability of a temporally evolving natural convection boundary layer on an isothermal wall

Williamson

Armfield

et al. 2019

J. Fluid Mech.

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The stability properties of a natural convection boundary layer adjacent to an isothermally heated vertical wall, with Prandtl number 0.71, are numerically investigated in the configuration of a temporally evolving parallel flow. The instantaneous linear stability of the flow is first investigated by solving the eigenvalue problem with a quasi-steady assumption, whereby the unsteady base flow is frozen in time. Temporal responses of the discrete perturbation modes are numerically obtained by solving the two-dimensional linearized disturbance equations using a ‘frozen’ base flow as an initial-value problem at various $Gr_{\unicode[STIX]{x1D6FF}}$, where $Gr_{\unicode[STIX]{x1D6FF}}$ is the Grashof number based on the velocity integral boundary layer thickness $\unicode[STIX]{x1D6FF}$. The resultant amplification rates of the discrete modes are compared with the quasi-steady eigenvalue analysis, and both two-dimensional and three-dimensional direct numerical simulations (DNS) of the temporally evolving flow. The amplification rate predicted by the linear theory compares well with the result of direct numerical simulation up to a transition point. The extent of the linear regime where the perturbations linearly interact with the base flow is thus identified. The value of the transition $Gr_{\unicode[STIX]{x1D6FF}}$, according to the three-dimensional DNS results, is dependent on the initial perturbation amplitude. Beyond the transition point, the DNS results diverge from the linear stability predictions as nonlinear mechanisms become important.

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“…Die wenigen bislang bekannten direkten numerischen Simulationen zu instationären freien Konvektionsströmungen an der vertikalen Platte konnten die in Kapitel 2.1 beschriebenen instationären Phänomene dessen ungeachtet jedoch mit sehr guter qualitativer und quantitativer Übereinstimmung abbilden (vgl. [Brooker et al 2000], [Lin et al 2008] sowie [Aberra et al 2012]). [Henkes und Hoogendoorn 1990] sowie [Xu et al 1998]) und erfordern zusätzliche Modellanpassungen (vgl.…”

Section: Berechnung Von Instationären Strömungsgrößenunclassified

Experimentelle Betrachtung der Wärmeübertragung durch instationäre freie Konvektion an der vertikalen Platte

Schaub¹

2019

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Kurzinhalt In der vorliegenden Dissertation werden die Auswirkungen von instationären Prozessen in freier Konvektion an der vertikalen Platte auf die Wärmeübertragung an Luft experimentell untersucht. Die dabei erhobenen Messwerte werden auf der Grundlage einer phänomenologischen Betrachtung in ein analytisches Berechnungsverfahren überführt. So legt eine physikalische Interpretation nahe, dass nach einer plötzlichen Veränderung der Wärmestromdichte ein Überschuss an potentieller Energie in der Strömungsgrenzschicht entsteht, der in einem anschließenden Ausgleichsvorgang durch zusätzliche Konvektionsstrukturen (insb. Kelvin-Helmholtz-Wirbel) in kinetische Energie umgewandelt wird. Betrachtet werden zyklische und sprungartige Variationen der Randbedingungen, deren praktische Anwendung erst durch die Etablierung der elektronischen Leistungsregelung relevant wurde. Derartige Betriebsweisen erlauben beispielsweise für die Wärmeübergabe von Raumheizsystemen eine Intensivieru...

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Boundary layer instability of the natural convection flow on a uniformly heated vertical plate

Cited by 23 publications

References 43 publications

Non-Oberbeck–Boussinesq effects on the linear stability of a vertical natural convection boundary layer

Non-Oberbeck–Boussinesq effects on the linear stability of a vertical natural convection boundary layer

Stability of a temporally evolving natural convection boundary layer on an isothermal wall

Experimentelle Betrachtung der Wärmeübertragung durch instationäre freie Konvektion an der vertikalen Platte

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