Stability Of Convection Research Articles

Impact of temperature-dependent viscosity on linear and weakly nonlinear stability of double-diffusive convection in viscoelastic fluid

The impact of temperature-dependent viscosity on the double-diffusive viscoelastic convective fluids is investigated, with applications in heat transfer, polymer processing, food industry, biomedical engineering, etc. Both linear and weakly nonlinear analyses are carried out to determine the stability of fluids using the Oldroyd-B model. Analytical criteria for the onset of linear stationary and oscillatory convection are derived. The effects of rheological parameters, linearly and exponentially varying viscosity, salinity Rayleigh number and Prandtl number on the system’s stability are investigated. Linear stability analysis reveals that the interaction between thermal and solute diffusions with rheological parameters favours oscillatory convection over stationary convection. In weakly nonlinear theory, a power series expansion derives a Landau amplitude equation, allowing heat and mass transfer analysis in viscoelastic fluids with temperature-dependent viscosity. Numerical results highlight the effects of variable viscosity on heat and mass transfer rates, represented by Nusselt and Sherwood numbers. Further, the weakly non-linear stability analysis evaluates the impact of the Prandtl number, rheological parameters and salinity Rayleigh number on heat and mass transfer rates. These findings are compared with existing results to validate and enhance our understanding of fluid behaviour under different conditions.

Stability of thermal convection in two superimposed miscible viscous fluids under gravitational modulation

Abstract The thermal stability of a system of two superimposed miscible viscous fluid layers, under gravitational modulation, is investigated using linear stability analysis. It is well known in the literature that in the absence of gravitational modulation, there exist two convection regimes depending on the buoyancy number: the single-cell regime, where convection is oscillating and occupies the entire volume of the two fluid layers, and the stratified regime where stationary convection occurs in each fluid layer. Using Chebyshev's spectral collocation method and Floquet's theory, the numerical results show that under gravitational modulation, single-cell convection oscillates at half the frequency of the external oscillation (subharmonic threshold), while the stratified regime oscillates at a frequency equal to that of the forcing (harmonic threshold). The critical buoyancy number corresponding to the transition between the two convection regimes depends, in addition to the viscosity ratio and the depth of the two layers, on certain dimensionless frequencies permeating this transition and also on the amplitude of oscillation via the Froude number. In the plane of the critical Rayleigh number versus dimensionless modulation frequency, the branch associated with stratified convection does not depend on the buoyancy number for equal viscosities whereas this is the case for the whole-convection regime. For different viscosities, both convection regimes depend on the buoyancy number. At last, in the stratified regime (harmonic threshold), the critical value of the viscosity contrast, corresponding to the passage from an active layer to a passive layer and vice versa, increases with the modulation frequency.

Heat transfer research on the cooling process of waxy crude oil storage in the vault tank based on VOF model

This paper focuses on the static cooling process for waxy crude oil stored in dome roof tanks. For the three phases of gas on top, liquid crude oil, and bottom water in storage tank, the VOF method is used to describe the evolution of physical quantities at the “oil–water”/“oil–gas” interface. The porous medium method is used to quantitatively characterize the sol–gel conversion process for waxy crude oil. A physical and mathematical models are established to describe the flow-heat transfer coupling behavior of the three-phase medium of crude oil, gas on top, and water at the bottom of the dome roof tank. In terms of the overall cooling process,The gas at the top of the tank has the simplest and fastest physical field evolution. It has the most uneven distribution (average temperature variance of 4 °C2), the strongest flow (average flow velocity of 0.4 m/s), the highest cooling rate (0.632 °C/h), and the lowest temperature (14.84 °C at the end). Its physical field is influenced by both the atmosphere and crude oil. The evolution of the physical field of crude oil is the most complex. It lags behind the gas at the top of tank and is directly effectted by it. Based on the evolution characteristics of the flow field of crude oil, the cooling process is divided into three stages: Stage I (0–––10 h) is the stage of convection generation and evolution in the crude oil region; Stage II (10 h − 34 h) is the stage of convection stability in the crude oil region; Stage III (after 35 h) is the stage of flow field transformation of crude oil. In stages I and II, the flow and momentum exchange at the oil–gas interface are significant. Crude oil is jointly influenced by the natural convection of the gas at the top of the tank and its own natural convection, forming a counterclockwise large vortex structure. The low-temperature area is near the central axis boundary of storage tank, oil–gas interface, and tank wall. The high-temperature area is within a range of 0.1 m − 3.3 m from the tank wall. After entering stage III, the flow and momentum exchange at the oil–gas interface weaken. The flow field of crude oil is only controlled by its own natural convection and transforms into a clockwise large vortex dominated. The low-temperature area is concentrated in the enclosed area of “oil–gas interface − tank wall” and “oil–water interface − tank wall”. The temperature field changes accordingly. Eventually, the high-temperature area is concentrated in the area slightly above the center of the tank. The physical field evolution of bottom water lags behind crude oil and is most unstable. Its cooling rate is 0.164 °C/h, slightly higher than crude oil’s 0.157 °C/h. The temperature is always slightly lower (33.47 °C at the end), and the physical field is the most uniform (average temperature variance of 0.0003 °C2), affected by the tank bottom environment and liquid crude oil.

Thermal and magnetic evolution of an Earth-like planet with a basal magma ocean

Earth's geodynamo has operated for over 3.5 billion years. The magnetic field is currently powered by thermocompositional convection in the outer core, which involves the release of light elements and latent heat as the inner core solidifies. However, since the inner core nucleated no more than 1.5 billion years ago, the early dynamo could not rely on these buoyancy sources. Given recent estimates of the thermal conductivity of the outer core, an alternative mechanism may be required to sustain the geodynamo prior to nucleation of the inner core. One possibility is a silicate dynamo operating in a long-lived basal magma ocean. Here, we investigate the structural, thermal, buoyancy, and magnetic evolution of an Earth-like terrestrial planet. Using modern equations of state and melting curves, we include a time-dependent parameterization of the compositional evolution of an iron-rich basal magma ocean. We combine an internal structure integration of the planet with energy budgets in a coupled core, basal magma ocean, and mantle system. We determine the thermocompositional convective stability of the core and the basal magma ocean, and assess their respective dynamo activity using entropy budgets and magnetic Reynolds numbers. Our conservative nominal model predicts a transient basal magma ocean dynamo followed by a core dynamo after 1 billion years. The model is sensitive to several parameters, including the initial temperature of the core-mantle boundary, the parameterization of mantle convection, the composition of the basal magma ocean, the radiogenic content of the planet, as well as convective velocity and magnetic scaling laws. We use the nominal model to constrain the range of basal magma ocean electrical conductivity and core thermal conductivity that sustain a dynamo. This highlights the importance of constraining the parameters and transport properties that influence planetary evolution using experiments and simulations conducted at pressure, temperature, and composition conditions found in planetary interior, in order to reduce model degeneracies.

Linear and nonlinear stability of double diffusive convection in a micropolar fluid saturated porous layer with magnetic field and throughflow effects

The linear and nonlinear stability of double-diffusive convection in a porous layer saturated with micropolar fluid is examined. A transverse magnetic field is applied to the flow together with vertical throughflow. The normal mode technique is employed for linear stability analysis, whereas the energy method is used for nonlinear stability analysis. The resulting eigenvalue problems corresponding to linear and nonlinear stability theories are solved numerically by employing the bvp4c routine in MATLAB 2022(b). The critical thermal Rayleigh numbers for both linear and nonlinear analyses are computed for the different values of the governing parameters and presented graphically. A comparison is made between linear and nonlinear stability results. It is observed that the flow is more stable whenever a magnetic field is added to the flow, although the subcritical instability region also slightly increases. Increasing the Darcy number, Lewis number, coupling number, and absolute value of the throughflow parameter destabilizes the flow. On the other hand, raising the porosity of the medium and micropolar parameters stabilizes the flow. Furthermore, there is no subcritical gap in the absence of the throughflow effect, which is a good agreement between the linear and nonlinear thresholds.

The role of temperature-dependent solubility in the stability of thermohaline convection within a Voigt-fluid layer

The study focuses on both linear and weakly nonlinear stability analyses of thermohaline convection within a Voigt-fluid layer, considering the effects of temperature-dependent solubility. Analytical methods are employed to derive conditions for the onset of both stationary and oscillatory convection. The linear stability analysis is performed using normal mode analysis to explore how various physical parameters influence the initiation of convection. Notably, unlike Newtonian fluids, the Navier-Stokes-Voigt fluid suppresses the typical quasiperiodic bifurcation from a steady state. To gain deeper insight into the onset of convection, a weakly nonlinear stability analysis is conducted using a modified perturbation method, leading to the Ginzburg-Landau equation. This reveals the potential for subcritical instability, a phenomenon not fully captured by linear analysis alone. Additionally, the study examines how different physical parameters affect convective heat and mass transfer, with findings that align with previous studies in specific limiting cases.

Numerical Approach of the First Instability Appearance in Inclined Taylor–Couette System

The present study numerically investigates the three-dimensional forced and mixed convection heat transfer in an inclined Taylor–Couette system (η=0.5 and Γ=20) submitted to a radial temperature gradient. The main objective of this study is to determine the effect of the angle inclination duct on the thermal and dynamic fields. Several cases have been dealt with depending on the inclination angle to detect the critical Reynolds number in each case. The model of the conservation equations with their boundary conditions is numerically solved by the finite volume method with a second-order spatiotemporal discretization. The results show that, in forced convection, the effect of the inclination angle is inexistent on the velocity field. However, with the presence of buoyancy effects, which impact flow stability and the transition to turbulence, the inclination influences both velocity and temperature fields. It also shows that selecting the vertical position of the annulus is preferable to obtain hydrodynamic stability in mixed convection. At the same time, from the thermal point of view, it is preferable to select the horizontal position to get dynamic and thermal stability.

Impacts of forced and internal climate variability on changes in convective environments over the eastern United States

Hazards from convective weather pose a serious threat to the contiguous United States (CONUS) every year. Previous studies have examined how future projected changes in climate might impact the frequency and intensity of convective weather using simulations with both convection-permitting regional models and coarser-grid climate and Earth system models. We build on this existing literature by utilizing a large-ensemble of historical and future Earth system model simulations to investigate the time evolution of the forced responses in large-scale convective environments and how those responses might be modulated by the rich spectrum of internal climate variability. Specifically, daily data from an ensemble of 50 simulations with the most recent version of the Community Earth System Model was used to examine changes in the convective environment over the eastern CONUS during March-June from 1870 to 2100. Results indicate that anthropogenically forced changes include increases in convective available potential energy and atmospheric stability (convective inhibition) throughout this century, while tropospheric vertical wind shear is projected to decrease across much of the CONUS. Internal climate variability on decadal and longer time scales can either significantly enhance or suppress these forced changes. The time evolution of two-dimensional histograms of convective indices suggests that future springtime convective environments over the eastern CONUS may, on average, be supportive of relatively less frequent and shorter-lived, but deeper and more intense convection.

ANALYTIC STUDY OF THERMOHALINE CONVECTIVE STABILITY IN A COUPLE-STRESS FLUID

This work investigates nonlinear analysis for thermohaline convective stability in a steady, viscous, incompressible couple-stress fluid by performing a generalized energy method. It is observed that the linear and nonlinear threshold that reflects the physics of the onset of convection is the same. The couple stress and solute gradient are seen to have a stabilizing impact on the system.

Temperature Condition Impact on the Onset of Rayleigh-Benard Convection in a Binary Fluid Saturated Anisotropic Porous Layer

Rayleigh-Benard convection in a saturated anisotropic porous media is investigated numerically. The temperature-dependent viscosity effect was applied to the double-diffusive binary fluid, and the Galerkin method was used to determine the critical Rayleigh numbers for the free-free, rigid-free, and rigid-rigid representing the lower-upper boundaries. The lower and upper boundary was set to be either conducting or insulating to temperature. The purpose of this study is to study the stability of Rayleigh-Benard convection with different temperature conditions in a binary fluid saturated by an anisotropic porous layer. The obtained eigenvalue is numerically solved with respect to various temperatures and velocities using the single-term Galerkin technique. The results, presented graphically, indicate that the rigid-rigid boundaries are more stabilize compared to rigid-free and free-free boundaries. It is also shown that an increase of temperature-dependent viscosity tends to destabilize the onset of double-diffusive convection.

Existence and Stability of Nonmonotone Hydraulic Shocks for the Saint Venant Equations of Inclined Thin-Film Flow

Extending the work of Yang–Zumbrun for the hydrodynamically stable case of Froude number F<2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F<2$$\\end{document}, we categorize completely the existence and convective stability of hydraulic shock profiles of the Saint Venant equations of inclined thin film flow. Moreover, we confirm by numerical experiment that asymptotic dynamics for general Riemann data is given in the hydrodynamic instability regime by either stable hydraulic shock waves, or a pattern consisting of an invading roll wave front separated by a finite terminating Lax shock from a constant state at plus infinity. Notably, profiles, and existence and stability diagrams, are all rigorously obtained by mathematical analysis and explicit calculation.

Instability of penetrative convection in a vertical porous layer with non-Dirichlet temperature conditions

The linear stability of penetrative convection in a differentially heated vertical porous layer with non-Dirichlet boundary conditions on the perturbed temperature field is investigated. The penetrative convection is realized through a uniform internal heating in a porous medium. The instability-driving parameters are the Darcy-Rayleigh number, dimensionless internal heat source strength, the Prandtl-Darcy number, and the Biot number. Neutral stability curves and the critical values of the Darcy-Rayleigh number, the wave number, and the wave speed are computed numerically by employing the Chebyshev collocation method. A comprehensive analysis is conducted on the onset of thermal instability, focusing on the effects of transitioning temperature boundary conditions from Dirichlet to Neumann. A novel finding is the emergence of bi-modal or tri-modal neutral stability curves, which unveil distinct onset modes arising from the combined effects of a heat source and the transition of boundary conditions from isothermal to adiabatic. The threshold value of the Biot number, at which the transition to instability occurs, shows a significant dependence on the internal heat source strength and this threshold value diminishes as the Prandtl-Darcy number attains higher values. Moreover, increase in the Biot number advances the onset of convection, while the Prandtl-Darcy number is found to exert both stabilizing and destabilizing influences on the stability of the base flow.

Double diffusion convection of Maxwell–Cattaneo fluids in a vertical slot

Abstract The convection stability of Maxwell–Cattaneo fluids in a vertical double-diffusive layer is investigated. Maxwell–Cattaneo fluids mean that the response of the heat flux with respect to the temperature gradient satisfies a relaxation time law rather than the classical Fourier one. The Chebyshev collocation method is used to resolve the linearized forms of perturbation equations, leading to the formulation of stability eigenvalue problem. By numerically solving the eigenvalue problem, the neutral stability curves in the a–Gr plane for the different values of solute Rayleigh number RaS are obtained. Results show that increasing the double diffusion effect and Louis number Le can suppress the convective instability. Furthermore, compared with Fourier fluid, the Maxwell–Cattaneo fluids in a vertical slot cause an oscillation on the neutral stability curve. The appearance of Maxwell–Cattaneo effect enhances the convection instability. Meanwhile, it is interesting to find that the Maxwell–Cattaneo effect for convective instability becomes stronger as the Prandtl number rises. That means Prandtl number (Pr) also has a significant effect on convective instability. Moreover, the occurrence of two minima on the neutral curve can be found when Pr reaches 12.

Investigation of Convective Heat Transfer and Stability on a Rotating Disk: A Novel Experimental Method and Thermal Modeling

Experimental and numerical investigations are conducted on a rotating disk from the perspective of convective heat transfer to understand the effect of heating on the stability of flow. A non-invasive approach with a thermal camera is employed to determine local Nusselt numbers for different rotational rates and perturbation parameters, i.e., the strength of the heat transfer. A novel transient temperature data extraction over the disk radius and an evaluation method are developed and applied for the first time for the air on a rotating disk. The evaluation method utilizes the lumped capacitance approach with a constant heat flux input. Nusselt number distributions from this experimental study show that there is a good agreement with the previous experimental correlations and linear stability analysis on the subject. A significant result of this approach is that by using the experimental setup and developed approach, it is possible to qualitatively show that instability in the flow starts earlier, i.e., an earlier departure from laminar behavior is observed at lower rotational Reynolds numbers with an increasing perturbation parameter, which is due to the strength of heating. Two experimental setups are modeled and simulated using a validated in-house Python code, featuring a three-dimensional thermal model of the disk. The thermal code was developed for the rotating disks and brake disks with a simplified geometry. Experimentally evaluated heat transfer coefficients are implemented and used as convective boundary conditions in the thermal code. Radial temperature distributions are compared with the experimental data, and there is good agreement between the experiment and the model. The model was used to evaluate the effect of radial conduction, which is neglected when using the lumped capacitance approach to determine heat transfer coefficients. It was observed that the radial conduction has a slight effect. The methodology and approach used in this experimental study, combined with the numerical model, can be used for further investigations on the subject.

Stability of triple-diffusive convection in a vertical porous layer

Stability of triple-diffusive convection in a vertical porous layer

X-band scintillations in Venus radio occultations observed by Akatsuki

Power fluctuations are observed on radio signals propagating through the Venus atmosphere. These scintillations, due to fluctuations in refractive index, are particularly strong between 56 and 72 km altitude where the strong convective stability favors gravity wave propagation. We examine low-latitude X-band radio occultation experiments performed by the Akatsuki spacecraft to assess the statistical variability of these scintillations. The observed root-mean-square scintillation amplitudes at a given altitude vary by a factor of about 3. Part of this range is due to the different geometry of the occultations: the corresponding variations in refractive structure constant at 60-70 km altitude span a factor of ∼2. These propagation characteristics may influence the optimization of the two-way radio link for the DAVINCI mission currently in development.

Imperfectly Impermeable Boundaries and Variable Viscosity Perspectives on the Stability of Natural Convection in a Vertical Porous Layer

Imperfectly Impermeable Boundaries and Variable Viscosity Perspectives on the Stability of Natural Convection in a Vertical Porous Layer

Effects of variable gravity on stability in couple-stress fluids across various conducting boundaries

This work aims to inspect the effect of variable gravity field on the convective stability of couple stress fluid for different combinations of bounding surfaces. Both linear and nonlinear analyses are conducted to obtain eigenvalue problems. For this analysis, three different combinations of bounding surfaces have been considered. Normal mode analysis is used for linear analysis, while the energy method is used for nonlinear analysis. The numerical values of critical Rayleigh numbers are calculated using the single-term Galerkin technique. It is found that the Rayleigh numbers for the two analyses coincide, suggesting global stability. It is found that the increase in the value of couple stresses stabilize the system. The variable gravity can enhance or reduce the stability of the system depending on the direction of gravity variation which can be easily controlled by its parameter values. It is also observed that fluid confined in rigid-rigid bounding surface is more thermally stable, which is suitable for convection in couple stress fluid.

Formation of convective roll patterns over a longitudinal throughflow in an active inhomogeneous porous medium with weak clogging

The convective stability of a plane-parallel longitudinal throughflow in a system consisting of two porous sublayers with distinct permeability is studied taking into account the weak pore clogging effect and given a finite difference in concentration between the upper and lower boundaries of the system. A system of differential equations for convection is derived within the framework of the continuum approach and the nonlinear MIM model. A linear stability analysis of the basic longitudinal flow is carried out. The boundary value problem is solved using the numerical technique for constructing a fundamental system of solutions. The neutral stability curves of the basic flow with respect to the disturbances in the form of rolls with different wavelength are obtained. For the absence of pore clogging, the convective stability maps of the critical solutal Rayleigh-Darcy number versus the permeability ratio for the initial uncontaminated sublayers, as well as the plots of the critical disturbance frequency and wave number versus the permeability ratio for some values of the Peclet number, are constructed. It is shown that these results have symmetry with respect to the solution for equal initial permeability of sublayers. The clogging effect associated with the solute adsorption and desorption in a porous medium is studied in the two-layered systems with the values 0.1 and 10 of the ratio of initial permeabilities of the sublayers; convection localization occurs in distinct sublayers. It was found that clogging increases the stability of the longitudinal basic flow relative to solutal inhomogeneity and breaks the symmetry of solutions with respect to the case when the two-layered system is reduced to a single layer with the same filtration properties of the porous medium throughout its volume. The influence of sorption effects on the critical parameters of oscillatory convection is investigated by plotting the critical solutal Rayleigh-Darcy number, disturbance frequency and wave number against the adsorption coefficient at fixed values of the desorption coefficient. The isolines of the stream function are constructed to analyze convective flow patterns. It was established that there is a weak relationship between the typical size of local convective roll patterns and the clogging parameters. It is shown that the sorption processes, which can lead to clogging, have a significant impact on the velocity of convective rolls moving along the two-layered system at a slight variation in their sizes.

Nonlinear Convective Stability of a Critical Pulled Front Undergoing a Turing Bifurcation at Its Back: A Case Study

Nonlinear Convective Stability of a Critical Pulled Front Undergoing a Turing Bifurcation at Its Back: A Case Study