Effect of Solute Concentration Gradients on the Onset of Convection: Uniform and Nonuniform Initial Gradients

1986 ◽  
Vol 108 (4) ◽  
pp. 776-782 ◽  
Author(s):  
M. Kaviany ◽  
M. Vogel
Keyword(s):  
Temperature Gradient ◽  
Concentration Gradient ◽  
Fluid Layer ◽  
Onset Time ◽  
Solute Concentration ◽  
Concentration Gradients ◽  
Linear Amplification ◽  
Onset Of Convection ◽  
Gradient Layer ◽  
Good Agreement

The time of the onset of convection in a fluid layer, which is initially stably stratified and then heated from below in a transient manner, is determined experimentally and analytically. The initial stratification is due to the presence of a solute concentration gradient. In addition to initial linear solute concentration distributions two other specific initial solute concentration distributions are considered. In Case 1, a zero gradient layer is located underneath a nonzero and uniform gradient layer. In Case 2, the zero gradient layer is on the top. The linear amplification theory is applied to the prediction of the onset time. Interferometry is used as a means of determining the onset time experimentally. It is shown that since the adverse temperature gradient is concentrated near the bottom, any nonuniformity in the solute concentration gradient in this region reduces the effectiveness of the gradient in delaying the onset. Experimental and predicted results are in good agreement.

scholarly journals Effects of Magnetic Field and Non-Uniform Basic Temperature Gradient

2002 ◽  
Vol 1 (1) ◽  
pp. 1-14
Author(s):  
S. Pranesh
Keyword(s):  
Magnetic Field ◽  
Temperature Gradient ◽  
Fluid Layer ◽  
Suspended Particles ◽  
Conducting Fluid ◽  
Wave Number ◽  
Uniform Temperature ◽  
Onset Of Convection ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid

The effects of a non-uniform temperature gradient and magnetic field on the onset of convection in a horizontal layer of Boussinesq fluid with suspended particles confined between an upper free/adiabatic boundary and a lower rigid/isothermal boundary have been considered. A linear stability analysis is performed. The microrotation is assumed to vanish at the boundaries. The Galerkin technique is used to obtain the Eigen values. The influence of various parameters on the onset of convection has been analysed. Six different non-uniform temperature profiles are considered and their comparative influence on onset is discussed. It is observed that the electrically conducting fluid layer with suspended particles heated from below is more stable compared to the classical electrically conducting fluid without Suspended particles. The critical wave number is found to be insensitive to the changes in the parameters but sensitive to the changes in the Chandrasekhar number.

Onset of Thermal Convection in a Fluid Layer Subjected to Transient Heating From Below

1984 ◽  
Vol 106 (4) ◽  
pp. 817-823 ◽  
Author(s):  
M. Kaviany
Keyword(s):  
Fluid Layer ◽  
Sudden Change ◽  
Onset Time ◽  
Lower Surface ◽  
Analytical Prediction ◽  
Rigid Boundary ◽  
Transient Heating ◽  
Onset Of Convection ◽  
Analytical Results ◽  
Heating From Below

The onset of convection in a horizontal layer of fluid subject to time-dependent heating from below is studied both experimentally and analytically. The fluid layer is confined by a rigid boundary at the bottom and a shear-free surface at the top. The fluid, which is initially quiescent, is heated by increasing the temperature of the lower surface at a constant time-rate. The experimental observation of the time of the onset of convection is made through the sudden change in variation of the temperature of the lower surface with respect to time. The onset is also observed through the sudden change in the fringe pattern created by holographic interferometry. Various layer depths are considered in order to observe the influence of this variable on the onset time. The analytical prediction is made by application of the linear amplification theory subject to boundary conditions similar to those of the experiment. Good agreement is found between the experimental and analytical results. Comparisons are also made with the experimental and analytical results available in the literature.

scholarly journals Numerical Simulation of the Deflagration-to-Detonation Transition in Inhomogeneous Mixtures

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Florian Ettner ◽  
Klaus G. Vollmer ◽  
Thomas Sattelmayer
Keyword(s):  
Hydrogen Content ◽  
Concentration Gradient ◽  
Concentration Gradients ◽  
Deflagration To Detonation Transition ◽  
New Findings ◽  
Safety Studies ◽  
Geometric Boundary ◽  
Detonation Transition ◽  
Coarse Grids ◽  
Good Agreement

In this study the hazardous potential of flammable hydrogen-air mixtures with vertical concentration gradients is investigated numerically. The computational model is based on the formulation of a reaction progress variable and accounts for both deflagrative flame propagation and autoignition. The model is able to simulate the deflagration-to-detonation transition (DDT) without resolving all microscopic details of the flow. It works on relatively coarse grids and shows good agreement with experiments. It is found that a mixture with a vertical concentration gradient can have a much higher tendency to undergo DDT than a homogeneous mixture of the same hydrogen content. In addition, the pressure loads occurring can be much higher. However, the opposite effect can also be observed, with the decisive factor being the geometric boundary conditions. The model gives insight into different modes of DDT. Detonations occurring soon after ignition do not necessarily cause the highest pressure loads. In mixtures with concentration gradient, the highest loads can occur in regions of very low hydrogen content. These new findings should be considered in future safety studies.

Onset of convection in a near-critical binary fluid mixture driven by concentration gradient

2018 ◽  
Vol 848 ◽  
pp. 1098-1126 ◽  
Author(s):  
Zhan-Chao Hu ◽  
Xin-Rong Zhang
Keyword(s):  
Boundary Layer ◽  
Rayleigh Number ◽  
Concentration Gradient ◽  
Fluid Layer ◽  
Initial Density ◽  
Onset Of Convection ◽  
Fluid Mixture ◽  
Concentration Boundary ◽  
Binary Fluid ◽  
Theoretical Criterion

A linear stability analysis is conducted for the onset of natural convection driven by a concentration gradient in a horizontal layer of a near-critical binary fluid mixture. The problem is regarded as a limiting case of double-diffusive convection. The governing equations for small perturbations after normal-mode expansion are solved numerically with finite difference discretization to obtain the critical concentration Rayleigh number. It is found that, when the height of the fluid layer is small, the initial density stratification is negligible and the theoretical criterion developed under Boussinesq approximation with the modified Rayleigh number is accurate even extremely close to the critical point. However, for a large height, the initial density stratification makes the fluid layer become more unstable, and deviations from theoretical predictions are observed. We further propose a method to estimate these deviations, which can be used to check the applicability of the theoretical criterion. As the second part of the study, we apply the criterion to interpret the onset of convection for a transient problem: a near-critical binary fluid mixture confined in a two-dimensional cavity submitted to concentration increases at the bottom wall. The numerical results demonstrate four typical behaviours of the concentration boundary layer: onset of convection, collapse of the concentration boundary layer, return to stability, and remaining stable. Comparisons between numerical results and the stability criterion are made, where consistencies are found except for the behaviour of return to stability. We attribute the inconsistency to the existence of lateral walls, whose stabilizing effect is strong when the return to stability happens.

Effect of Phase Thermal Modulation Without Stationary Temperature Gradient on the Threshold of Convection

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
K. Souhar ◽  
S. Aniss
Keyword(s):  
Temperature Gradient ◽  
Convective Instability ◽  
Stable Equilibrium ◽  
Equilibrium Configuration ◽  
Fluid Layer ◽  
Dimensionless Frequency ◽  
Time Varying ◽  
Horizontal Fluid Layer ◽  
Stationary Component ◽  
Good Agreement

The convective instability of a horizontal fluid layer subject to a time varying gradient of temperature is investigated. The stationary component of the temperature gradient is considered equal to zero and the oscillating components imposed on the horizontal boundaries are in phase and with the same amplitude. The aim of the present paper is to examine the effect of this type of modulation on the onset of convective instability. We show that unlike the case where the equilibrium configuration is stable in the absence of modulation, we have instability when the temperature at the horizontal boundaries is modulated in phase. Also, we observe that in the limit of low and high dimensionless frequency of modulation, ω < 0.5 and ω > 140, the basic state tends to a stable equilibrium configuration and for an intermediate dimensionless frequency, the system is potentially unstable. The results obtained from analytical asymptotic study for low and high dimensionless frequency are in good agreement with the numerical ones.

scholarly journals Exact analysis of Effect of Non-uniform Temperature Gradient on Marangoni Convection with Free Slip Condition

2011 ◽  
Vol 10 (2) ◽  
pp. 1-10
Author(s):  
S.P. Suma ◽  
Y.H. Gangadharaiah
Keyword(s):  
Temperature Gradient ◽  
Marangoni Convection ◽  
Horizontal Layer ◽  
Temperature Profiles ◽  
Uniform Temperature ◽  
Onset Of Convection ◽  
Expansion Procedure ◽  
Single Term ◽  
Basic Temperature ◽  
Good Agreement

The effect of non-uniform basic temperature gradient on the onset of Marangoni convection in a horizontal layer with a free-slip bottom heated from below and cooled from above is considered. A linear stability analysis is performed to undertake a detail investigation. The eigenvalues are obtained for lower rigid isothermal and upper free adiabatic boundaries. The resulting eigenvalue problem is solved exactly and single-term Galerkin expansion procedure. The influence of various parameters on the onset of convection has been analyzed. Three non-uniform basic temperature profiles are considered and the results obtained from both the methods are compared and are found to be in good agreement. Some general conclusions about their destabilizing effects are presented.

Effects of Coriolis force and nonuniform temperature gradient on the Rayleigh–Benard convection

1986 ◽  
Vol 64 (1) ◽  
pp. 90-99 ◽  
Author(s):  
N. Rudraiah ◽  
O. P. Chandna
Keyword(s):  
Temperature Gradient ◽  
Coriolis Force ◽  
Fluid Layer ◽  
Nonuniform Temperature ◽  
Bénard Convection ◽  
Benard Convection ◽  
Bounding Surfaces ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Good Agreement

The effects of the Coriolis force and a nonuniform temperature gradient on the onset of the Rayleigh–Benard convection in a thin, horizontal, rotating fluid layer is studied using linear-stability analysis. It is shown analytically that the method and rate of heating, the Coriolis force, and the nature of the bounding surfaces of the fluid layer significantly influence the value of the Rayleigh number at the onset of marginal convection. The mechanism for suppressing or augmenting convection is discussed in detail. The Galerkin technique employed here is much easier to use than that the method of Chandrasekhar (5). The analytical results obtained from using this procedure are compared with the published experimental data and the results obtained from numerical procedures; good agreement is found.

Heat-flow experiments in liquid 4He with a variable cylindrical geometry

1987 ◽  
Vol 174 ◽  
pp. 209-231 ◽  
Author(s):  
H. Gao ◽  
G. Metcalfe ◽  
T. Jung ◽  
R. P. Behringer
Keyword(s):  
Cylindrical Geometry ◽  
Small Scale ◽  
Onset Of Convection ◽  
Aspect Ratios ◽  
A Value ◽  
Prandtl Numbers ◽  
Convection Rolls ◽  
Flow Experiments ◽  
Increasing Function ◽  
Good Agreement

This paper first describes an apparatus for measuring the Nusselt number N versus the Rayleigh number R of convecting normal liquid 4He layers. The most important feature of the apparatus is its ability to provide layers of different heights d, and hence different aspect ratios [Gcy ]. The horizontal cross-section of each layer is circular, and [Gcy ] is defined by [Gcy ] = D/2d where D is the diameter of the layer. We report results for 2.4 [les ] [Gcy ] [les ] 16 and for Prandtl numbers Pr spanning 0.5 [lsim ] Pr [lsim ] 0.9 These results are presented in terms of the slope N1 = RcdN/dR evaluated just above the onset of convection at Rc. We find that N1 is only a slowly increasing function of [Gcy ] in the range 6 [lsim ] [Gcy ] [lsim ] 16, and that it has a value there which is quite close to 0.72. This value of N1 is in good agreement with variational calcuations by Ahlers et al. (1981) pertinent to parallel convection rolls in cylindrical geometry. Particularly for [Gcy ] [lsim ] 6, we find additional small-scale structure in N1 associated with changes in the number of convection rolls with changing [Gcy ]. An additional test of the linearzied hydrodynamics is given by measurements of Rc. We find good agreement between theory and our data for Rc.

Prediction of solute concentration gradients during growth of discontinuous precipitates in a Fe-13.5 at.% Zn alloy

2021 ◽  
pp. 130317
Author(s):  
Mateusz Chronowski ◽  
Jarosław Opara ◽  
Olga A. Kogtenkova ◽  
Alexander V. Druzhinin ◽  
Paweł Zięba
Keyword(s):  
Solute Concentration ◽  
Concentration Gradients ◽  
Zn Alloy
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