scholarly journals Transient Rayleigh–Bénard–Marangoni convection due to evaporation: a linear non-normal stability analysis

2010 ◽  
Vol 648 ◽  
pp. 521-539 ◽  
Author(s):  
F. DOUMENC ◽  
T. BOECK ◽  
B. GUERRIER ◽  
M. ROSSI
Keyword(s):  
Stability Analysis ◽  
Marangoni Convection ◽  
Basic Flow ◽  
Critical Parameters ◽  
Surface Cooling ◽  
Normal Stability ◽  
Rayleigh Benard ◽  
General Method ◽  
Good Agreement ◽  
Critical Wavenumber

The convective instability in a plane liquid layer with time-dependent temperature profile is investigated by means of a general method suitable for linear stability analysis of an unsteady basic flow. The method is based on a non-normal approach, and predicts the onset of instability, critical wavenumber and time. The method is applied to transient Rayleigh–Bénard–Marangoni convection due to cooling by evaporation. Numerical results as well as theoretical scalings for the critical parameters as function of the Biot number are presented for the limiting cases of purely buoyancy-driven and purely surface-tension-driven convection. Critical parameters from calculations are in good agreement with those from experiments on drying polymer solutions, where the surface cooling is induced by solvent evaporation.

scholarly journals Effects of Controller and Nonuniform Temperature Profile on the Onset of Rayleigh-Bénard-Marangoni Electroconvection in a Micropolar Fluid

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
H. M. Azmi ◽  
R. Idris
Keyword(s):  
Stability Analysis ◽  
Linear Stability Analysis ◽  
Micropolar Fluid ◽  
Marangoni Convection ◽  
Temperature Gradients ◽  
Temperature Profiles ◽  
Nonuniform Temperature ◽  
Onset Of Convection ◽  
Basic Temperature ◽  
Rayleigh Benard

Linear stability analysis is performed to study the effects of nonuniform basic temperature gradients on the onset of Rayleigh-Bénard-Marangoni electroconvection in a dielectric Eringen’s micropolar fluid by using the Galerkin technique. In the case of Rayleigh-Bénard-Marangoni convection, the eigenvalues are obtained for an upper free/adiabatic and lower rigid/isothermal boundaries. The influence of various parameters has been analysed. Three nonuniform basic temperature profiles are considered and their comparative influence on onset of convection is discussed. Different values of feedback control and electric number are added up to examine whether their presence will enhance or delay the onset of electroconvection.

Global Stability Analysis of the Wake behind a Circular Cylinder Based on the POD-Chiba Method

2011 ◽  
Vol 137 ◽  
pp. 72-76
Author(s):  
Wei Zhang ◽  
Xian Wen ◽  
Yan Qun Jiang
Keyword(s):  
Stability Analysis ◽  
Circular Cylinder ◽  
Global Stability ◽  
Dimensional Model ◽  
Global Stability Analysis ◽  
The Stability ◽  
Low Dimensional ◽  
Proper Orthogonal ◽  
Calculated Amount ◽  
Good Agreement

A proper orthogonal decomposition (POD) method is applied to study the global stability analysis for flow past a stationary circular cylinder. The flow database at Re=100 is obtained by CFD software, i.e. FLUENT, with which POD bases are constructed by a snapshot method. Based on the POD bases, a low-dimensional model is established for solving the two-dimensional incompressible NS equations. The stability of the flow solution is evaluated by a POD-Chiba method in the way of the eigensystem analysis for the velocity disturbance. The linear stability analysis shows that the first Hopf bifurcation takes place at Re=46.9, which is in good agreement with available results by other high-order accurate stability analysis methods. However, the calculated amount of POD is little, which shows the availability and advantage of the POD method.

scholarly journals Stability and Sensitivity Analysis of Hydrodynamic Instabilities in Industrial Swirled Injection Systems

2017 ◽  
Author(s):  
Thomas L. Kaiser ◽  
Thierry Poinsot ◽  
Kilian Oberleithner
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Vortex Core ◽  
Large Eddy Simulations ◽  
Mode Shapes ◽  
Mean Flow ◽  
Precessing Vortex Core ◽  
Large Eddy ◽  
Good Agreement

The hydrodynamic instability in an industrial, two-staged, counter-rotative, swirled injector of highly complex geometry is under investigation. Large eddy simulations show that the complicated and strongly nonparallel flow field in the injector is superimposed by a strong precessing vortex core. Mean flow fields of large eddy simulations, validated by experimental particle image velocimetry measurements are used as input for both local and global linear stability analysis. It is shown that the origin of the instability is located at the exit plane of the primary injector. Mode shapes of both global and local linear stability analysis are compared to a dynamic mode decomposition based on large eddy simulation snapshots, showing good agreement. The estimated frequencies for the instability are in good agreement with both the experiment and the simulation. Furthermore, the adjoint mode shapes retrieved by the global approach are used to find the best location for periodic forcing in order to control the precessing vortex core.

Effect of Sidewall Conductance on Nusselt Number for Rayleigh-Bénard Convection: A Semi-Analytical and Experimental Correction

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
U. Madanan ◽  
R. J. Goldstein
Keyword(s):  
Thermal Conductivity ◽  
Nusselt Number ◽  
Analytical Model ◽  
Thermal Conductance ◽  
Bénard Convection ◽  
Benard Convection ◽  
Extended Surfaces ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Good Agreement

Abstract The effect of sidewall conductance on Nusselt number for the Rayleigh-Bénard convection is examined by performing nearly identical sets of experiments with sidewalls made of three different materials. These experimental results are utilized to extrapolate and estimate the Nusselt number for an ideal zero-thermal-conductivity sidewall case, which is the case when the sidewalls are perfectly insulating. A semi-analytical model is proposed, based on the concept of extended surfaces, to compute the discrepancy in Nusselt number caused by the presence of finite thermal conductance of the sidewalls. The predictions obtained using this model are found to be in good agreement with the corresponding experimentally determined values.

A theory of the lifted temperature minimum on calm clear nights

1993 ◽  
Vol 344 (1671) ◽  
pp. 183-206 ◽  
Keyword(s):  
Surface Temperature ◽  
Critical Rayleigh Number ◽  
Surface Cooling ◽  
Turbulent Friction ◽  
Temperature Boundary ◽  
Unstable Layer ◽  
Eddy Transport ◽  
Two Parameters ◽  
Rayleigh Benard ◽  
Temperature Boundary Condition

Numerous reports from several parts of the world have confirmed that on calm clear nights a minimum in air temperature can occur just above ground, at heights of the order of 12 m or less. This phenomenon, first observed by Ramdas & Atmanathan (1932), carries the associated paradox of an apparently unstable layer that sustains itself for several hours, and has not so far been satisfactorily explained. We formulate here a theory that considers energy balance between radiation, conduction and free or forced convection in humid air, with surface temperature, humidity and wind incorporated into an appropriate mathematical model as parameters. A complete numerical solution of the coupled air—soil problem is used to validate an approach that specifies the surface temperature boundary condition through a cooling rate parameter. Utilizing a flux-emissivity scheme for computing radiative transfer, the model is numerically solved for various values of turbulent friction velocity. It is shown that a lifted minimum is predicted by the model for values of ground emissivity not too close to unity, and for sufficiently low surface cooling rates and eddy transport. Agreement with observation for reasonable values of the parameters is demonstrated. A heuristic argument is offered to show that radiation substantially increases the critical Rayleigh number for convection, thus circumventing or weakening Rayleigh-Benard instability. The model highlights the key role played by two parameters generally ignored in explanations of the phenomenon, namely surface emissivity and soil thermal conductivity, and shows that it is unnecessary to invoke the presence of such particulate constituents as haze to produce a lifted minimum.

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