<p>In this paper, we study 2D stationary regimes of mixed convection in a square cavity with a moving lid. All walls of the cavity are considered as solid; the side walls are assumed to be perfectly thermally insulated, while the top and bottom walls are isothermal, the temperature of the bottom wall is higher. The impact of a smooth change in the velocity of the upper wall of on the convective stability of air within a square cavity is investigated both analytically, using low-mode approximation, and numerically, by the finite difference method. Calculations are performed for Grashof numbers up to values thirty times greater than the critical one. It have been shown that for each supercritical Grashof number there is a critical Reynolds number <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12217_2025_10168_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">$Re_c$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <msub> <mi>e</mi> <mi>c</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> such that with a smooth change in the Reynolds number within the interval <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12217_2025_10168_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="136" /> </InlineMediaObject> <EquationSource Format="TEX">$-Re_c< Re < Re_c$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>-</mo> <mi>R</mi> <msub> <mi>e</mi> <mi>c</mi> </msub> <mo><</mo> <mi>R</mi> <mi>e</mi> <mo><</mo> <mi>R</mi> <msub> <mi>e</mi> <mi>c</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> the flow is continuously transformed, changing the structure from normal single-vortex to anomalous double-vortex and vice versa. If, with a change in the Reynolds number, the limits of the specified interval are exceeded, a hysteresis transition from the anomalous flow to the normal one is observed. These findings provide new insights into the complex interplay between thermal and inertial forces in convective flows. Understanding these flow structures and transitions could improve the knowledge of combustion processes.</p>

The Boundaries of the Existence of An Anomalous Convective Air Flow in a Square Cavity with a Moving Lid

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发表日期：

2025年2月12日

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V.A. Sharifulin,
P.S. Beloborodov,
A.N. Sharifulin,
T.P. Lyubimova

摘要

In this paper, we study 2D stationary regimes of mixed convection in a square cavity with a moving lid. All walls of the cavity are considered as solid; the side walls are assumed to be perfectly thermally insulated, while the top and bottom walls are isothermal, the temperature of the bottom wall is higher. The impact of a smooth change in the velocity of the upper wall of on the convective stability of air within a square cavity is investigated both analytically, using low-mode approximation, and numerically, by the finite difference method. Calculations are performed for Grashof numbers up to values thirty times greater than the critical one. It have been shown that for each supercritical Grashof number there is a critical Reynolds number $Re_c$ $R e_{c}$ such that with a smooth change in the Reynolds number within the interval $-Re_c< Re < Re_c$ $- R e_{c} < R e < R e_{c}$ the flow is continuously transformed, changing the structure from normal single-vortex to anomalous double-vortex and vice versa. If, with a change in the Reynolds number, the limits of the specified interval are exceeded, a hysteresis transition from the anomalous flow to the normal one is observed. These findings provide new insights into the complex interplay between thermal and inertial forces in convective flows. Understanding these flow structures and transitions could improve the knowledge of combustion processes.