12 results
Conditional analysis on extreme wall shear stress and heat flux events in compressible turbulent boundary layers
- Peng-Jun-Yi Zhang, Zhen-Hua Wan, Si-Wei Dong, Nan-Sheng Liu, De-Jun Sun, Xi-Yun Lu
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- Journal:
- Journal of Fluid Mechanics / Volume 974 / 10 November 2023
- Published online by Cambridge University Press:
- 03 November 2023, A38
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This study presents a comprehensive analysis on the extreme positive and negative events of wall shear stress and heat flux fluctuations in compressible turbulent boundary layers (TBLs) solved by direct numerical simulations. To examine the compressibility effects, we focus on the extreme events in two representative cases, i.e. a supersonic TBL of Mach number $M=2$ and a hypersonic TBL of $M=8$, by scrutinizing the coherent structures and their correlated dynamics based on conditional analysis. As characterized by the spatial distribution of wall shear stress and heat flux, the extreme events are indicated to be closely related to the structural organization of wall streaks, in addition to the occurrence of the alternating positive and negative structures (APNSs) in the hypersonic TBL. These two types of coherent structures are strikingly different, namely the nature of wall streaks and APNSs are shown to be related to the solenoidal and dilatational fluid motions, respectively. Quantitative analysis using a volumetric conditional average is performed to identify and extract the coherent structures that directly account for the extreme events. It is found that in the supersonic TBL, the essential ingredients of the conditional field are hairpin-like vortices, whose combinations can induce wall streaks, whereas in the hypersonic TBL, the essential ingredients become hairpin-like vortices as well as near-wall APNSs. To quantify the momentum and energy transport mechanisms underlying the extreme events, we proposed a novel decomposition method for extreme skin friction and heat flux, based on the integral identities of conditionally averaged governing equations. Taking advantage of this decomposition method, the dominant transport mechanisms of the hairpin-like vortices and APNSs are revealed. Specifically, the momentum and energy transports undertaken by the hairpin-like vortices are attributed to multiple comparable mechanisms, whereas those by the APNSs are convection dominated. In that, the dominant transport mechanisms in extreme events between the supersonic and hypersonic TBLs are indicated to be totally different.
Wall-cooling effects on pressure fluctuations in compressible turbulent boundary layers from subsonic to hypersonic regimes
- Peng-Jun-Yi Zhang, Zhen-Hua Wan, Nan-Sheng Liu, De-Jun Sun, Xi-Yun Lu
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- Journal:
- Journal of Fluid Mechanics / Volume 946 / 10 September 2022
- Published online by Cambridge University Press:
- 02 August 2022, A14
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Pressure fluctuations play an essential role in the transport of turbulent kinetic energy and vibrational loading. This study focuses on examining the effect of wall cooling on pressure fluctuations in compressible turbulent boundary layers by high-fidelity direct numerical simulations. Pressure fluctuations result from the vorticity mode and the acoustic mode that are both closely dependent on compressibility. To demonstrate the effects of wall cooling at various compressibility intensities, three free-stream Mach numbers are investigated, i.e. $M_\infty =0.5$, 2.0 and 8.0, with real gas effects being absent for $M_\infty =8.0$ due to a low enthalpy inflow. Overall, opposite effects of wall cooling on pressure fluctuations are found between the subsonic/supersonic cases and the hypersonic case. Specifically, the pressure fluctuations normalized by wall shear stress $p^\prime _{rms}/\tau _w$ are suppressed in the subsonic and supersonic cases, while enhanced in the hypersonic case near the wall. Importantly, travelling-wave-like alternating positive and negative structures (APNS), which greatly contribute to pressure fluctuations, are identified within the viscous sublayer and buffer layer in the hypersonic cases. Furthermore, generating mechanisms of pressure fluctuations are explored by extending the decomposition based on the fluctuating pressure equation to compressible turbulent boundary layers. Pressure fluctuations are decomposed into five components, in which rapid pressure, slow pressure and compressible pressure are dominant. The suppression of pressure fluctuations in the subsonic and supersonic cases is due to both rapid pressure and slow pressure being suppressed by wall cooling. In contrast, wall cooling strengthens compressible pressure for all Mach numbers, especially in the hypersonic case, resulting in increased wall pressure fluctuations. Compressible pressure plays a leading role in the hypersonic case, mainly due to the APNS. Essentially, the main effects of wall cooling can be interpreted by the suppression of the vorticity mode and the enhancement of the acoustic mode.
Noise reduction mechanisms for insert-type serrations of the NACA-0012 airfoil
- Ya-Sen Hu, Zhen-Hua Wan, Chuang-Chao Ye, De-Jun Sun, Xi-Yun Lu
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- Journal:
- Journal of Fluid Mechanics / Volume 941 / 25 June 2022
- Published online by Cambridge University Press:
- 09 May 2022, A57
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Trailing-edge serrations inspired by owls are capable of reducing broadband noise. In this study, the wall-resolved large-eddy simulations (LES) are carried out on the flow over NACA-0012 airfoil with additional serrated trailing edges. The computations are conducted with the high-order flux reconstruction method on unstructured meshes. Three kinds of serrations with different lengths are studied and compared with the straight trailing-edge case, and all three types of serration achieved a certain degree of noise reduction. Presently, the medium-length serration achieves the best noise reduction effect. The maximum decrease of overall sound pressure level is approximately 2.4 dB, implying that the length of serration has a substantial impact on the noise reduction effect. The serration has no significant effect on the upstream turbulence statistics, but it changes the flow structure near the serration, such as inducing side vortex pairs attached to the serration edges. Moreover, dynamic mode decomposition shows that the pressure structures vary with the serration length. For the most unstable hydrodynamic wave, the spanwise coherence of the mode structure of pressure in the upstream boundary layer is weakened. In addition, serrations can redistribute the dipole sources on the surfaces of airfoil and serrations. The destructive interference is enhanced to some extent, which is favourable for noise reduction. In contrast with LES simulations, the pure dipole analysis shows that the longest serration case seems to be the best. Furthermore, a recently developed noise theory is used to evaluate the influence of serrations on the flow noise sources qualitatively and quantitatively. It is found that the serrations can mitigate noise source intensity near the serration edges but increase the source intensity in the near wake. The combined effect of serration on the dipole source and flow noise source determines the overall noise reduction effect. To conclude, destructive interference plays a primary role in suppressing noise radiation by serrated trailing edges, and the dual effect of flow noise sources should be considered in future serration designs. As the influence of turbulence structure will make it more difficult to find the optimal serration parameters, the position of high-fidelity simulation will become increasingly important.
Radius ratio dependency of the instability of fully compressible convection in rapidly rotating spherical shells
- Ben Wang, Shuang Liu, Zhen-Hua Wan, De-Jun Sun
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- Journal:
- Journal of Fluid Mechanics / Volume 925 / 25 October 2021
- Published online by Cambridge University Press:
- 02 September 2021, A40
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Based on the fully compressible Navier–Stokes equations, the linear stability of thermal convection in rapidly rotating spherical shells of various radius ratios $\eta$ is studied for a wide range of Taylor number $Ta$, Prandtl number $Pr$ and the number of density scale height $N_\rho$. Besides the classical inertial mode and columnar mode, which are widely studied by the Boussinesq approximation and anelastic approximation, the quasi-geostrophic compressible mode is also identified in a wide range of $N_\rho$ and $Pr$ for all $\eta$ considered, and this mode mainly occurs in the convection with relatively small $Pr$ and large $N_\rho$. The instability processes are classified into five categories. In general, for the specified wavenumber $m$, the parameter space ($Pr, N_\rho$) of the fifth category, in which the base state loses stability via the quasi-geostrophic compressible mode and remains unstable, shrinks as $\eta$ increases. The asymptotic scaling behaviours of the critical Rayleigh numbers $Ra_c$ and corresponding wavenumbers $m_c$ to $Ta$ are found at different $\eta$ for the same instability mode. As $\eta$ increases, the flow stability is strengthened. Furthermore, the linearized perturbation equations and Reynolds–Orr equation are employed to quantitatively analyse the mechanical mechanisms and flow instability mechanisms of different modes. In the quasi-geostrophic compressible mode, the time-derivative term of disturbance density in the continuity equation and the diffusion term of disturbance temperature in the energy equation are found to be critical, while in the columnar and inertial modes, they can generally be ignored. Because the time-derivative term of the disturbance density in the continuity equation cannot be ignored, the anelastic approximation fails to capture the instability mode in the small-$Pr$ and large-$N_\rho$ system, where convection onset is dominated by the quasi-geostrophic compressible mode. However, all the modes are primarily governed by the balance between the Coriolis force and the pressure gradient, based on the momentum equation. Physically, the most important difference between the quasi-geostrophic compressible mode and the columnar mode is the role played by the disturbance pressure. The disturbance pressure performs negative work for the former mode, which appears to stabilize the flow, while it destabilizes the flow for the latter mode. As $\eta$ increases, in the former mode the relative work performed by the disturbance pressure increases and in the latter mode decreases.
On non-Oberbeck–Boussinesq effects in Rayleigh–Bénard convection of air for large temperature differences
- Zhen-Hua Wan, Qi Wang, Ben Wang, Shu-Ning Xia, Quan Zhou, De-Jun Sun
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- Journal:
- Journal of Fluid Mechanics / Volume 889 / 25 April 2020
- Published online by Cambridge University Press:
- 21 February 2020, A10
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We present direct numerical simulations of non-Oberbeck–Boussinesq (NOB) Rayleigh–Bénard (RB) convection due to large temperature differences in two-dimensional (2-D) and three-dimensional (3-D) cells. Perfect air is chosen as the operating fluid and the Prandtl number ($Pr$) is fixed to 0.71 for the reference state $\hat{T}_{0}=300~\text{K}$. In the present system, we consider large temperature differences ranging from 60 K to 240 K, and relatively strong NOB effects are induced at moderate Rayleigh numbers ($Ra$) in the range $3\times 10^{6}\leqslant Ra\leqslant 5\times 10^{9}$. The large temperature difference also induces the turbulence system with large density variation. Due to top-down symmetry breaking under NOB conditions, an increase of the centre temperature $T_{c}$ is found compared to the arithmetic mean temperature $T_{m}$ of the top and bottom plates, and the shift of $T_{c}$ is strongly dependent on Rayleigh number $Ra$ and temperature differential $\unicode[STIX]{x1D716}$. The NOB effects on the Nusselt number ($Nu$) are quite small (${\lesssim}2\,\%$). The power-law scalings of $Nu$ versus $Ra$ are robust against NOB effects, even for the extremely large temperature difference 240 K, which has never been reached in previous experiments and simulations. The Reynolds numbers $Re$, as well as the scalings of $Re$ versus $Ra$, are also insensitive to NOB effects. It is noteworthy that the influence of NOB effects on $Nu$ and $Re$ in 3-D RB flow are weaker than its 2-D counterpart. Furthermore, the extended laminar boundary layer (BL) equations are developed based on the low-Mach-number Navier–Stokes equations, which qualitatively predicts the NOB effects on velocity profiles. Direct numerical simulation results indicate that the top and bottom thermal BLs can compensate each other much better than the velocity BLs under NOB conditions, which contribute to the robustness of $Nu$.
Onset of fully compressible convection in a rapidly rotating spherical shell
- Shuang Liu, Zhen-Hua Wan, Rui Yan, Chao Sun, De-Jun Sun
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- Journal:
- Journal of Fluid Mechanics / Volume 873 / 25 August 2019
- Published online by Cambridge University Press:
- 01 July 2019, pp. 1090-1115
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The onset of thermal convection in a rapidly rotating spherical shell is studied by linear stability analysis based on the fully compressible Navier–Stokes equations. Compressibility is quantified by the number of density scale heights $N_{\unicode[STIX]{x1D70C}}$, which measures the intensity of density stratification of the motionless, polytropic base state. The nearly adiabatic flow with polytropic index $n=1.499<n_{a}=1.5$ is considered, where $n_{a}$ is the adiabatic polytropic index. By investigating the stability of the base state with respect to the disturbance of specified wavenumber, the instability process is found to be sensitive to the Prandtl number $Pr$ and to $N_{\unicode[STIX]{x1D70C}}$. For large $Pr$ and small $N_{\unicode[STIX]{x1D70C}}$, the quasi-geostrophic columnar mode loses stability first; while for relatively small $Pr$ a new quasi-geostrophic compressible mode is identified, which becomes unstable first under strong density stratification. The inertial mode can also occur first for relatively small $Pr$ and a certain intensity of density stratification in the parameter range considered. Although the Rayleigh numbers $Ra$ for the onsets of the quasi-geostrophic compressible mode and columnar mode are different by several orders of magnitude, we find that they follow very similar scaling laws with the Taylor number. The critical $Ra$ for convection onset is found to be always positive, in contrast with previous results based on the widely used anelastic model that convection can occur at negative $Ra$. By evaluating the relative magnitude of the time derivative of density perturbation in the continuity equation, we show that the anelastic approximation in the present system cannot be applied in the small-$Ra$ and large-$N_{\unicode[STIX]{x1D70C}}$ regime.
Penetrative turbulent Rayleigh–Bénard convection in two and three dimensions
- Qi Wang, Quan Zhou, Zhen-Hua Wan, De-Jun Sun
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- Journal:
- Journal of Fluid Mechanics / Volume 870 / 10 July 2019
- Published online by Cambridge University Press:
- 14 May 2019, pp. 718-734
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Penetrative turbulent Rayleigh–Bénard convection which depends on the density maximum of water near $4^{\circ }\text{C}$ is studied using two-dimensional and three-dimensional direct numerical simulations. The working fluid is water near $4\,^{\circ }\text{C}$ with Prandtl number $Pr=11.57$. The considered Rayleigh numbers $Ra$ range from $10^{7}$ to $10^{10}$. The density inversion parameter $\unicode[STIX]{x1D703}_{m}$ varies from 0 to 0.9. It is found that the ratio of the top and bottom thermal boundary-layer thicknesses ($F_{\unicode[STIX]{x1D706}}=\unicode[STIX]{x1D706}_{t}^{\unicode[STIX]{x1D703}}/\unicode[STIX]{x1D706}_{b}^{\unicode[STIX]{x1D703}}$) increases with increasing $\unicode[STIX]{x1D703}_{m}$, and the relationship between $F_{\unicode[STIX]{x1D706}}$ and $\unicode[STIX]{x1D703}_{m}$ seems to be independent of $Ra$. The centre temperature $\unicode[STIX]{x1D703}_{c}$ is enhanced compared to that of Oberbeck–Boussinesq cases, as $\unicode[STIX]{x1D703}_{c}$ is related to $F_{\unicode[STIX]{x1D706}}$ with $1/\unicode[STIX]{x1D703}_{c}=1/F_{\unicode[STIX]{x1D706}}+1$, $\unicode[STIX]{x1D703}_{c}$ is also found to have a universal relationship with $\unicode[STIX]{x1D703}_{m}$ which is independent of $Ra$. Both the Nusselt number $Nu$ and the Reynolds number $Re$ decrease with increasing $\unicode[STIX]{x1D703}_{m}$, the normalized Nusselt number $Nu(\unicode[STIX]{x1D703}_{m})/Nu(0)$ and Reynolds number $Re(\unicode[STIX]{x1D703}_{m})/Re(0)$ also have universal relationships with $\unicode[STIX]{x1D703}_{m}$ which seem to be independent of both $Ra$ and the aspect ratio $\unicode[STIX]{x1D6E4}$. The scaling exponents of $Nu\sim Ra^{\unicode[STIX]{x1D6FC}}$ and $Re\sim Ra^{\unicode[STIX]{x1D6FD}}$ are found to be insensitive to $\unicode[STIX]{x1D703}_{m}$ despite of the remarkable change of the flow organizations.
Flow reversals in two-dimensional thermal convection in tilted cells
- Qi Wang, Shu-Ning Xia, Bo-Fu Wang, De-Jun Sun, Quan Zhou, Zhen-Hua Wan
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- Journal:
- Journal of Fluid Mechanics / Volume 849 / 25 August 2018
- Published online by Cambridge University Press:
- 18 June 2018, pp. 355-372
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The influence of tilt on flow reversals in two-dimensional thermal convection in rectangular cells with two typical aspect ratios, $\unicode[STIX]{x1D6E4}=\text{width/height}=1$ and 2, are investigated by means of direct numerical simulations. For $\unicode[STIX]{x1D6E4}=1$, tilt tends to suppress flow reversals. However, it is found that flow reversals characterized by two main rolls are promoted by tilt for $\unicode[STIX]{x1D6E4}=2$, which are even observed for some cases of small Prandtl numbers ($Pr$) and large tilt angles ($\unicode[STIX]{x1D6FD}$). Different from level cases where the four corner rolls all have opportunities to grow and trigger a flow reversal, the reversals in an anticlockwise tilted cell with $\unicode[STIX]{x1D6E4}=2$ are always led by the growth of the bottom-right or the top-left corner roll. Tilt is favourable for the growth of the bottom-right or the top-left corner roll and thus for breaking the balance between the two main rolls and triggering a flow reversal. The mode decomposition analysis shows that the appearance of the intermediate single-roll mode is crucial for reversals, and flow reversals in a tilted cell with $\unicode[STIX]{x1D6E4}=2$ can be viewed as a mode competition process between single-roll mode and horizontally adjacent double-roll mode. They can only occur in a limited range of $\unicode[STIX]{x1D6FD}$ where the two modes have comparable strength. Furthermore, the Nusselt numbers at the hot plate $Nu_{h}$ and at the cold plate $Nu_{c}$ behave differently during a flow reversal for $\unicode[STIX]{x1D6E4}=2$ due to the preference of single corner roll growth.
Linear and weakly nonlinear analysis of Rayleigh–Bénard convection of perfect gas with non-Oberbeck–Boussinesq effects
- Shuang Liu, Shu-Ning Xia, Rui Yan, Zhen-Hua Wan, De-Jun Sun
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- Journal:
- Journal of Fluid Mechanics / Volume 845 / 25 June 2018
- Published online by Cambridge University Press:
- 20 April 2018, pp. 141-169
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The influences of non-Oberbeck–Boussinesq (NOB) effects on flow instabilities and bifurcation characteristics of Rayleigh–Bénard convection are examined. The working fluid is air with reference Prandtl number $Pr=0.71$ and contained in two-dimensional rigid cavities of finite aspect ratios. The fluid flow is governed by the low-Mach-number equations, accounting for the NOB effects due to large temperature difference involving flow compressibility and variations of fluid viscosity and thermal conductivity with temperature. The intensity of NOB effects is measured by the dimensionless temperature differential $\unicode[STIX]{x1D716}$. Linear stability analysis of the thermal conduction state is performed. An $\unicode[STIX]{x1D716}^{2}$ scaling of the leading-order corrections of critical Rayleigh number $Ra_{cr}$ and disturbance growth rate $\unicode[STIX]{x1D70E}$ due to NOB effects is identified, which is a consequence of an intrinsic symmetry of the system. The influences of weak NOB effects on flow instabilities are further studied by perturbation expansion of linear stability equations with regard to $\unicode[STIX]{x1D716}$, and then the influence of aspect ratio $A$ is investigated in detail. NOB effects are found to enhance (weaken) flow stability in large (narrow) cavities. Detailed contributions of compressibility, viscosity and buoyancy actions on disturbance kinetic energy growth are identified quantitatively by energy analysis. Besides, a weakly nonlinear theory is developed based on centre-manifold reduction to investigate the NOB influences on bifurcation characteristics near convection onset, and amplitude equations are constructed for both codimension-one and -two cases. Rich bifurcation regimes are observed based on amplitude equations and also confirmed by direct numerical simulation. Weakly nonlinear analysis is useful for organizing and understanding these simulation results.
Flow reversals in Rayleigh–Bénard convection with non-Oberbeck–Boussinesq effects
- Shu-Ning Xia, Zhen-Hua Wan, Shuang Liu, Qi Wang, De-Jun Sun
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- Journal:
- Journal of Fluid Mechanics / Volume 798 / 10 July 2016
- Published online by Cambridge University Press:
- 08 June 2016, pp. 628-642
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Flow reversals in two-dimensional Rayleigh–Bénard convection led by non-Oberbeck–Boussinesq (NOB) effects due to large temperature differences are studied by direct numerical simulation. Perfect gas is chosen as the working fluid and the Prandtl number is 0.71 for the reference state. If NOB effects are included, the flow pattern $P_{11}$ with only one dominant roll often becomes unstable by the growth of the cold corner roll, which sometimes results in cession-led flow reversals. By exploiting the vorticity transport equation, it is found that the asymmetries of buoyancy and viscous forces are responsible for the growth of the cold corner roll because both such asymmetries cause an imbalance between the corner rolls and the large-scale circulation (LSC). The buoyancy force near the cold wall increases and decreases near the hot wall originating from the temperature-dependent isobaric thermal expansion coefficient ${\it\alpha}=1/T$ if NOB effects are included. Moreover, the decreased dissipation due to lower viscosity is favourable for the growth of the cold corner roll, while the increased viscosity further suppresses the growth of the hot corner roll. Finally, it is found that the boundary layer near the cold wall plays an important role in the mass transport from LSC to corner rolls subject to mass conservation.
Linear instability analysis of convection in a laterally heated cylinder
- Bo-Fu Wang, Zhen-Hua Wan, Zhi-Wei Guo, Dong-Jun Ma, De-Jun Sun
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- Journal:
- Journal of Fluid Mechanics / Volume 747 / 25 May 2014
- Published online by Cambridge University Press:
- 17 April 2014, pp. 447-459
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The three-dimensional instabilities of axisymmetric flow are investigated in a laterally heated vertical cylinder by linear stability analysis. Heating is confined to a central zone on the sidewall of the cylinder, while other parts of the sidewall are insulated and both ends of the cylinder are cooled. The length of the heated zone equals the radius of the cylinder. For three different aspect ratios, $A= 1.92 $, 2, 2.1 ($A=\mathrm{height}$/radius), the dependence of the critical Rayleigh number on the Prandtl number (from 0.02 to 6.7) has been studied in detail. For such a kind of laterally heated convection, some interesting stability results are obtained. A monotonous instability curve is obtained for $A= 1.92 $, while the instability curves for $A= 2 $ and $A= 2.1 $ are non-monotonous and multivalued. In particular, an instability island has been found for $A=2$. Moreover, mechanisms corresponding to different instability results are obtained when the Prandtl number changes. At small Prandtl number, the flow is oscillatory unstable, which is dominated by hydrodynamic instability. At intermediate Prandtl number, the interaction between buoyancy and shear in the base flow plays a more important role than pure hydrodynamic instability. At even higher Prandtl number, Rayleigh–Bénard instability becomes the dominant process and the flow loses stability through steady bifurcation.
Linear stability analysis of cylindrical Rayleigh–Bénard convection
- Bo-Fu Wang, Dong-Jun Ma, Cheng Chen, De-Jun Sun
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- Journal:
- Journal of Fluid Mechanics / Volume 711 / 25 November 2012
- Published online by Cambridge University Press:
- 13 September 2012, pp. 27-39
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The instabilities and transitions of flow in a vertical cylindrical cavity with heated bottom, cooled top and insulated sidewall are investigated by linear stability analysis. The stability boundaries for the axisymmetric flow are derived for Prandtl numbers from 0.02 to 1, for aspect ratio () equal to 1, 0.9, 0.8, 0.7, respectively. We found that there still exists stable non-trivial axisymmetric flow beyond the second bifurcation in certain ranges of Prandtl number for , and 0.8, excluding the case. The finding for is that very frequent changes of critical mode (azimuthal Fourier mode) of the second bifurcation occur when the Prandtl number is changed, where five kinds of steady modes and three kinds of oscillatory modes are presented. These multiple modes indicate different flow structures triggered at the transitions. The instability mechanism of the flow is explained by kinetic energy transfer analysis, which shows that the radial or axial shear of base flow combined with buoyancy mechanism leads to the instability results.