scholarly journals On Moderate-Rayleigh-Number Convection in an Inclined Porous Layer

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 101
Author(s):  
Baole Wen ◽  
Gregory P. Chini
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Numerical Simulations ◽  
Porous Layer ◽  
Large Scale ◽  
Single Species ◽  
Roll Motion ◽  
Boundary Layer Instability ◽  
Inclination Angles ◽  
Porous Medium Convection

We investigate the flow structure and dynamics of moderate-Rayleigh-number ( R a ) thermal convection in a two-dimensional inclined porous layer. High-resolution numerical simulations confirm the emergence of O ( 1 ) aspect-ratio large-scale convective rolls, with one ‘natural’ roll rotating in the counterclockwise direction and one ‘antinatural’ roll rotating in the clockwise direction. As the inclination angle ϕ is increased, the background mean shear flow intensifies the natural-roll motion, while suppressing the antinatural-roll motion. Our numerical simulations also reveal—for the first time in single-species porous medium convection—the existence of spatially-localized convective states at large ϕ , which we suggest are enabled by subcritical instability of the base state at sufficiently large inclination angles. To better understand the physics of inclined porous medium convection at different ϕ , we numerically compute steady convective solutions using Newton iteration and then perform secondary stability analysis of these nonlinear states using Floquet theory. Our analysis indicates that the inclination of the porous layer stabilizes the boundary layers of the natural roll, but intensifies the boundary-layer instability of the antinatural roll. These results facilitate physical understanding of the large-scale cellular flows observed in the numerical simulations at different values of ϕ .

scholarly journals On Moderate-Rayleigh-Number Convection in an Inclined Porous Layer

2019 ◽  
Author(s):  
Baole Wen ◽  
Gregory P. Chini
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Porous Layer ◽  
Large Scale ◽  
Single Species ◽  
Roll Motion ◽  
Boundary Layer Instability ◽  
Inclination Angles ◽  
Porous Medium Convection ◽  
First Time

We investigate the flow structure and dynamics of moderate-Rayleigh-number ($Ra$) thermal convection in a two-dimensional inclined porous layer. Direct numerical simulations (DNS) confirm the emergence of $\mathit{O}(1)$ aspect-ratio large-scale convective rolls, with one `natural' roll rotating in the counterclockwise direction and one `antinatural' roll rotating in the clockwise direction. As the inclination angle $\phi$ is increased, the background mean shear flow intensifies the natural-roll motion, while suppressing the antinatural-roll motion. Moreover, our DNS reveal---for the first time in single-species porous medium convection---the existence of \emph{spatially-localized} convective states at large $\phi$, which we suggest are enabled by subcritical instability of the base state at sufficiently large inclination angles. To better understand the physics of inclined porous medium convection at different $\phi$, we numerically compute steady convective solutions using Newton iteration and then perform secondary stability analysis of these nonlinear states using Floquet theory. Our analysis indicates that the inclination of the porous layer stabilizes the boundary layers of the natural roll, but intensifies the boundary-layer instability of the antinatural roll. These results facilitate physical understanding of the large-scale cellular flows observed in the DNS at different values of $\phi$.

Inclined porous medium convection at large Rayleigh number

2018 ◽  
Vol 837 ◽  
pp. 670-702 ◽  
Author(s):  
Baole Wen ◽  
Gregory P. Chini
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Heat Transport ◽  
Porous Layer ◽  
Upper Bound ◽  
Large Scale ◽  
Travelling Wave ◽  
Mode Instability ◽  
Bulk Mode ◽  
Porous Medium Convection

High-Rayleigh-number ($Ra$) convection in an inclined two-dimensional porous layer is investigated using direct numerical simulations (DNS) and stability and variational upper-bound analyses. When the inclination angle $\unicode[STIX]{x1D719}$ of the layer satisfies $0^{\circ }<\unicode[STIX]{x1D719}\lesssim 25^{\circ }$, DNS confirm that the flow exhibits a three-region wall-normal asymptotic structure in accord with the strictly horizontal ($\unicode[STIX]{x1D719}=0^{\circ }$) case, except that as $\unicode[STIX]{x1D719}$ is increased the time-mean spacing between neighbouring interior plumes also increases substantially. Both DNS and upper-bound analysis indicate that the heat transport enhancement factor (i.e. the Nusselt number) $Nu\sim CRa$ with a $\unicode[STIX]{x1D719}$-dependent prefactor $C$. When $\unicode[STIX]{x1D719}>\unicode[STIX]{x1D719}_{t}$, however, where $30^{\circ }<\unicode[STIX]{x1D719}_{t}<32^{\circ }$ independently of $Ra$, the columnar flow structure is completely broken down: the flow transitions to a large-scale travelling-wave convective roll state, and the heat transport is significantly reduced. To better understand the physics of inclined porous medium convection at large $Ra$ and modest inclination angles, a spatial Floquet analysis is performed, yielding predictions of the linear stability of numerically computed, fully nonlinear steady convective states. The results show that there exist two types of instability when $\unicode[STIX]{x1D719}\neq 0^{\circ }$: a bulk-mode instability and a wall-mode instability, consistent with previous findings for $\unicode[STIX]{x1D719}=0^{\circ }$ (Wen et al., J. Fluid Mech., vol. 772, 2015, pp. 197–224). The background flow induced by the inclination of the layer intensifies the bulk-mode instability during its subsequent nonlinear evolution, thereby favouring increased spacing between the interior plumes relative to that observed in convection in a horizontal porous layer.

Stability of Gravity Driven Convection in a Cylindrical Porous Layer Subjected to Vibration

2006 ◽  
Author(s):  
Saneshan Govender
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Linear Stability ◽  
Density Gradient ◽  
Porous Layer ◽  
Binary Alloy ◽  
Critical Rayleigh Number ◽  
Linear Stability Theory ◽  
Direct Result ◽  
Porous Cylinder

In both pure fluids and porous media, the density gradient becomes unstable and fluid motion (convection) occurs when the critical Rayleigh number is exceeded. The classical stability analysis no longer applies if the Rayleigh number is time dependant, as found in systems where the density gradient is subjected to vibration. The influence of vibrations on thermal convection depends on the orientation of the time dependant acceleration with respect to the thermal stratification. The problem of a vibrating porous cylinder has numerous important engineering applications, the most important one being in the field of binary alloy solidification. In particular we may extend the above results to understanding the dynamics in the mushy layer (essentially a reactive porous medium) that is sandwiched between the underlying solid and overlying melt regions. Alloyed components are widely used in demanding and critical applications, such as turbine blades, and a consistent internal structure is paramount to the performance and integrity of the component. Alloys are susceptible to the formation of vertical channels which are a direct result of the presence convection, so any technique that suppresses convection/the formation of channels would be welcomed by the plant metallurgical engineer. In the current study, the linear stability theory is used to investigate analytically the effects of gravity modulation on convection in a homogeneous cylindrical porous layer heated from below. The linear stability results show that increasing the frequency of vibration stabilizes the convection. In addition the aspect ratio of the porous cylinder is shown to influence the stability of convection for all frequencies analysed. It was also observed that only synchronous solutions are possible in cylindrical porous layers, with no transition to sub harmonic solutions as was the case in Govender (2005a) for rectangular layers or cavities. The results of the current analysis will be used in the formulation of a model for binary alloy systems that includes the reactive porous medium model.

Numerical Study of Transient High Rayleigh Number Convection in an Attic-Shaped Porous Layer

1983 ◽  
Vol 105 (3) ◽  
pp. 476-484 ◽  
Author(s):  
D. Poulikakos ◽  
A. Bejan
Keyword(s):  
Rayleigh Number ◽  
Numerical Simulations ◽  
Porous Layer ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Critical Rayleigh Number ◽  
Scale Analysis ◽  
Geometric Ratio ◽  
Rayleigh Numbers ◽  
Transient And Steady State

Scaling arguments and numerical analysis are used to document the transient and steady-state regimes of natural convection in a triangular porous layer cooled from above (along the sloping wall). The numerical simulations are conducted in the high Rayleigh number domain, Ra = 100, 1000, where Ra is the Darcy-modified Rayleigh number based on height, H. The scale analysis predicts the existence of distinct thermal boundary layers if Ra1/2 (H/L) > 1, where H/L is the height/length geometric ratio of the attic-shaped porous layer. The numerical simulations confirm the scaling results, as well as the prediction that the flow consists primarily of an elongated horizontal counterflow driven by the cold wall. In addition, the numerical solutions show the presence of a Be´nard-type instability at high enough Rayleigh numbers. For example, if H/L = 0.2, the instability is present when Ra > 620; this critical Rayleigh number is found to increase as H/L increases.

scholarly journals Bidispersive vertical convection

2017 ◽  
Vol 473 (2207) ◽  
pp. 20170481 ◽  
Author(s):  
M. Gentile ◽  
B. Straughan
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Temperature Gradient ◽  
Porous Material ◽  
Global Stability ◽  
Porous Layer ◽  
Initial Temperature ◽  
Vertical Layer ◽  
Stability Threshold ◽  
Rayleigh Numbers

A bidispersive porous material is one which has usual pores but additionally contains a system of micro pores. We consider a fluid-saturated bidispersive porous medium in the vertical layer x ∈(−1/2,1/2) with gravity in the − z (downward) direction. The walls of the layer are maintained at different constant temperatures. A suitable Rayleigh number is defined and we derive a global stability threshold below which no instability may arise. We additionally show that the porous layer is stable for all Rayleigh numbers provided the initial temperature gradient is bounded in a precise sense.

Convective shutdown in a porous medium at high Rayleigh number

2013 ◽  
Vol 719 ◽  
pp. 551-586 ◽  
Author(s):  
Duncan R. Hewitt ◽  
Jerome A. Neufeld ◽  
John R. Lister
Keyword(s):  
Porous Medium ◽  
Equation Of State ◽  
Rayleigh Number ◽  
Numerical Simulations ◽  
Numerical Models ◽  
Closed Domain ◽  
Dynamical Structure ◽  
Two Fluids ◽  
Flat Interface ◽  
Box Models

AbstractConvection in a closed domain driven by a dense buoyancy source along the upper boundary soon starts to wane owing to the increase of the average interior density. In this paper, theoretical and numerical models are developed of the subsequent long period of shutdown of convection in a two-dimensional porous medium at high Rayleigh number $\mathit{Ra}$. The aims of this paper are twofold. Firstly, the relationship between this slowly evolving ‘one-sided’ shutdown system and the statistically steady ‘two-sided’ Rayleigh–Bénard (RB) cell is investigated. Numerical measurements of the Nusselt number $\mathit{Nu}$ from an RB cell (Hewitt et al., Phys. Rev. Lett., vol. 108, 2012, 224503) are very well described by the simple parametrization $\mathit{Nu}= 2. 75+ 0. 0069\mathit{Ra}$. This parametrization is used in theoretical box models of the one-sided shutdown system and found to give excellent agreement with high-resolution numerical simulations of this system. The dynamical structure of shutdown can also be accurately predicted by measurements from an RB cell. Results are presented for a general power-law equation of state. Secondly, these ideas are extended to model more complex physical systems, which comprise two fluid layers with an equation of state such that the solution that forms at the (moving) interface is more dense than either layer. The two fluids are either immiscible or miscible. Theoretical box models compare well with numerical simulations in the case of a flat interface between the fluids. Experimental results from a Hele-Shaw cell and numerical simulations both show that interfacial deformation can dramatically enhance the convective flux. The applicability of these results to the convective dissolution of geologically sequestered ${\mathrm{CO} }_{2} $ in a saline aquifer is discussed.

Interaction of temperature- and salinity-driven natural convection in homogeneous porous media

2020 ◽  
Author(s):  
Márk Szijártó ◽  
Attila Galsa
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Numerical Simulations ◽  
Theoretical Models ◽  
Time Dependent ◽  
Two Dimensional ◽  
Thermohaline Convection ◽  
Rayleigh Numbers

&lt;p&gt;Onset of thermal and haline convection was studied separately by Lapwood (1948) and Wooding (1956) in theoretical models using analytical methods. They established that the buoyancy force caused by difference in temperature (&amp;#916;&lt;em&gt;T&lt;/em&gt;) or concentration (&amp;#916;&lt;em&gt;c&lt;/em&gt;) can induce natural convection depending on the model properties (e.g. geometry, permeability, etc.). In the course of further numerical simulations, the thermal (&lt;em&gt;Ra&lt;sub&gt;T&lt;/sub&gt;&lt;/em&gt;) and the haline Rayleigh number (&lt;em&gt;Ra&lt;sub&gt;H&lt;/sub&gt;&lt;/em&gt;) proved itself useful to characterise the type, the intensity and the form of the natural convection (e.g. Diersch and Kolditz, 2002). The main purpose of our study was to examine numerically the combined effect of temperature- and salinity-driven natural convection in a two-dimensional homogeneous porous medium.&lt;/p&gt;&lt;p&gt;Two-dimensional finite element base model was set up in agreement with the Elder problem (Wooding, 1956) in order to verify the numerical calculation. First, it was established that (1) the critical Rayleigh numbers are mathematically equivalent in the two separated cases (&lt;em&gt;Ra&lt;/em&gt;&lt;sub&gt;&lt;em&gt;Tcr&lt;/em&gt;&lt;/sub&gt;=&lt;em&gt;Ra&lt;sub&gt;Hcr&lt;/sub&gt;&lt;/em&gt;=4&amp;#960;&lt;sup&gt;2&lt;/sup&gt;), and (2) time-dependent thermal or haline natural convections evolve, when the Rayleigh number lies within the range of 300&amp;#8211;600. Numerical simulations were accomplished to investigate the interaction of the temperature- and salinity-driven natural convection. Non-dimensional thermal expansion and haline concentration were increased from &amp;#945;&amp;#916;&lt;em&gt;T&lt;/em&gt;=0.01 to 1 and from &amp;#946;&amp;#916;&lt;em&gt;c&lt;/em&gt;=10&lt;sup&gt;-5&lt;/sup&gt; to 10&lt;sup&gt;-3&lt;/sup&gt;, respectively, while the variation of the Darcy flux, the temperature, the concentration, the Nusselt and the Sherwood numbers was computed. The main points of this study were that (1) how the onset of the thermohaline convection is facilitated by the positive interaction of the thermal and haline effects (&lt;em&gt;Ra&lt;sub&gt;THcr&lt;/sub&gt;&lt;/em&gt;); (2) under what conditions time-dependent flow evolves in the theoretical models; (3) whether a new non-dimensional number can be defined instead of the two separated Rayleigh numbers in order to characterise the behaviour of the thermonaline convection. These simulations draw attention to the importance of understanding the physical background of thermohaline convection, for instance, at the margin of confined and unconfined carbonate systems (e.g. Buda Thermal Karst), or in the case of groundwater flow induced by water pumping/injection of deep geothermal power plants.&lt;/p&gt;&lt;p&gt;The project was supported by the &amp;#218;NKP-19-3 and &amp;#218;NKP-19-4 New National Excellence Program of the Ministry for Innovation and Technology, the Hungarian Research Fund (K 129279) and the J&amp;#225;nos Bolyai Scholarship of the Hungarian Academy of Science. This research is a part of a project that has received funding from the European Union&amp;#8217;s Horizon 2020 research and innovation program under grant agreement No 810980.&lt;/p&gt;&lt;p&gt;References:&lt;/p&gt;&lt;p&gt;Diersch, H.-J.G., Kolditz, O. (2002), Variable-density flow and transport in porous media: approaches and challenges. Advances in Water Resources, 25, 899-944.&lt;/p&gt;&lt;p&gt;Lapwood, E.R. (1948), Convection of a fluid in a porous medium. Mathematical Proceedings of the Cambridge Philosophical Society, 44, 508-521.&lt;/p&gt;&lt;p&gt;Wooding, R.A. (1956), Steady state free thermal convection of liquid in a saturated permeable medium. Journal of Fluid Mechanics, 2, 273-285.&lt;/p&gt;

scholarly journals Structure and stability of steady porous medium convection at large Rayleigh number

2015 ◽  
Vol 772 ◽  
pp. 197-224 ◽  
Author(s):  
Baole Wen ◽  
Lindsey T. Corson ◽  
Gregory P. Chini
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Boussinesq Equations ◽  
Systematic Investigation ◽  
Maximum Heat ◽  
Fully Nonlinear ◽  
Instability Modes ◽  
Steady Solutions ◽  
Porous Medium Convection

A systematic investigation of unstable steady-state solutions of the Darcy–Oberbeck–Boussinesq equations at large values of the Rayleigh number $\mathit{Ra}$ is performed to gain insight into two-dimensional porous medium convection in domains of varying aspect ratio $L$. The steady convective states are shown to transport less heat than the statistically steady ‘turbulent’ flow realised at the same parameter values: the Nusselt number $\mathit{Nu}\sim \mathit{Ra}$ for turbulent porous medium convection, while $\mathit{Nu}\sim \mathit{Ra}^{0.6}$ for the maximum heat-transporting steady solutions. A key finding is that the lateral scale of the heat-flux-maximising solutions shrinks roughly as $L\sim \mathit{Ra}^{-0.5}$, reminiscent of the decrease of the mean inter-plume spacing observed in turbulent porous medium convection as the thermal forcing is increased. A spatial Floquet analysis is performed to investigate the linear stability of the fully nonlinear steady convective states, extending a recent study by Hewitt et al. (J. Fluid Mech., vol. 737, 2013, pp. 205–231) by treating a base convective state, and secondary stability modes, that satisfy appropriate boundary conditions along plane parallel walls. As in that study, a bulk instability mode is found for sufficiently small-aspect-ratio base states. However, the growth rate of this bulk mode is shown to be significantly reduced by the presence of the walls. Beyond a certain critical $\mathit{Ra}$-dependent aspect ratio, the base state is most strongly unstable to a secondary mode that is localised near the heated and cooled walls. Direct numerical simulations, strategically initialised to investigate the fully nonlinear evolution of the most dangerous secondary instability modes, suggest that the (long time) mean inter-plume spacing in statistically steady porous medium convection results from a balance between the competing effects of these two types of instability.

Relationship between total plasma homocysteine and the risk of aneurysms – a meta-analysis

VASA ◽  
2020 ◽  
pp. 1-6
Author(s):  
Hanji Zhang ◽  
Dexin Yin ◽  
Yue Zhao ◽  
Yezhou Li ◽  
Dejiang Yao ◽  
...  
Keyword(s):  
Large Scale ◽  
Meta Analysis ◽  
Single Species ◽  
Total Plasma ◽  
Control Groups ◽  
Randomized Controlled ◽  
Randomized Controlled Studies ◽  
The Difference ◽  
The Relationship ◽  
Healthy Participants

Summary: Our meta-analysis focused on the relationship between homocysteine (Hcy) level and the incidence of aneurysms and looked at the relationship between smoking, hypertension and aneurysms. A systematic literature search of Pubmed, Web of Science, and Embase databases (up to March 31, 2020) resulted in the identification of 19 studies, including 2,629 aneurysm patients and 6,497 healthy participants. Combined analysis of the included studies showed that number of smoking, hypertension and hyperhomocysteinemia (HHcy) in aneurysm patients was higher than that in the control groups, and the total plasma Hcy level in aneurysm patients was also higher. These findings suggest that smoking, hypertension and HHcy may be risk factors for the development and progression of aneurysms. Although the heterogeneity of meta-analysis was significant, it was found that the heterogeneity might come from the difference between race and disease species through subgroup analysis. Large-scale randomized controlled studies of single species and single disease species are needed in the future to supplement the accuracy of the results.

Sign in / Sign up

Export Citation Format

Share Document