Steady Rayleigh–Be´nard Convection in a Two-Layer System of Immiscible Liquids

1996 ◽  
Vol 118 (2) ◽  
pp. 366-373 ◽  
Author(s):  
A. Prakash ◽  
J. N. Koster
Keyword(s):  
Numerical Simulations ◽  
Thermal Convection ◽  
Reasonable Agreement ◽  
Two Dimensional ◽  
Thermal Coupling ◽  
Layer System ◽  
Immiscible Liquids ◽  
Mechanical Coupling ◽  
Buoyancy Forces ◽  
Coupling Mode

Two-dimensional thermal convection in a system of two immiscible liquids heated from below is studied experimentally and numerically. Convection in the two-layer system is characterized by two distinct coupling modes between the layers. They are mechanical coupling and thermal coupling. These two coupling modes are visualized experimentally and found to be in reasonable agreement with numerical simulations. When buoyancy forces in both layers are of similar strength, thermal coupling is preferred. The mechanical coupling mode dominates when the buoyancy forces are very different in both layers.

Application of Thermal Taylor Dispersion to Upscaling of Geothermal Processes in Heterogeneous Formations

2021 ◽  
Author(s):  
Jinyu Tang ◽  
William R. Rossen
Keyword(s):  
Thermal Diffusivity ◽  
Numerical Simulations ◽  
Thermal Convection ◽  
Thermal Conduction ◽  
Numerical Solutions ◽  
Data File ◽  
Taylor Dispersion ◽  
Supplementary Data ◽  
Layer System ◽  
Effective Thermal Diffusivity

<p>Well-logging data show that geothermal formations typically feature layered heterogeneities. This imposes a challenge in numerical simulations, in particular in the upscaling of geothermal processes. The goal of our study is to develop an approach to (1) simplify the description of heterogeneous geothermal formations and (2) provide an accurate representation of convection/dispersion processes for simulating the up-scaled system.</p><p>In geothermal processes, transverse thermal conduction causes extra spreading of the cooling front: thermal Taylor dispersion. We derive a model from an energy balance for effective thermal diffusivity, α<sub>eff</sub>, to represent this phenomenon in layered media. α<sub>eff</sub>, accounting for transverse heat conduction, is much greater than the longitudinal thermal diffusivity, leading to a remarkably larger effective dispersion. A ratio of times is defined for longitudinal thermal convection and transverse thermal conduction, referred to as transverse thermal-conduction number N<sub>TC</sub>. The value of N<sub>TC</sub> is an indicator of thermal equilibrium in the vertical cross-section. Both N<sub>TC</sub> and α<sub>eff</sub> equations are verified by a match with numerical solutions for convection/conduction in a two-layer system. For N<sub>TC</sub> > 5, the system behaves as a single layer with thermal diffusivity α<sub>eff</sub>.</p><p>When N<sub>TC</sub> > 5, a two-layer system can be combined and represented with α<sub>eff</sub> and average properties of the two layers. We illustrate upscaling approach for simulation of geothermal processes in stratified formations, by grouping layers based on the condition of N<sub>TC</sub> > 5 and the α<sub>eff</sub> model. Specifically, N<sub>TC</sub> is calculated for every adjacent two layers, and the paired layers with a maximum value of N<sub>TC</sub> are grouped first. This procedure repeats on the grouped system until no adjacent layers meet the criterion N<sub>TC</sub> > 5. The upscaled layer properties of the grouped system are used as new inputs in the numerical simulations. The effectiveness of the upscaling approach is validated by a good agreement in numerical solutions for thermal convection/dispersion using original and average layer properties, respectively (Figs. 1 and 2 in the Supplementary Data File). The upscaling approach is applied to well-log data of a geothermal reservoir in Copenhagen featuring many interspersed layers. After upscaling, the formation with 93 layers of thickness 1 – 3 meters is upscaled to 12 layers (Fig. 3 in the Supplementary Data File). The effective thermal diffusivity α<sub>eff</sub> in the flow direction is about a factor of 10 times greater than original thermal diffusivity of the rock. Thus, α<sub>eff</sub> should be used as simulation inputs for representing more accurately geothermal processes in the up-scaled system.</p><p> </p><p> </p>

SYMMETRIC LARGE-SCALE VELOCITY FIELDS IN TWO-DIMENSIONAL THERMAL CONVECTION

1994 ◽  
Vol 04 (05) ◽  
pp. 1369-1374 ◽  
Author(s):  
J. PRAT ◽  
I. MERCADER ◽  
J.M. MASSAGUER
Keyword(s):  
Stability Analysis ◽  
Velocity Field ◽  
Velocity Profile ◽  
Numerical Simulations ◽  
Linear Stability Analysis ◽  
Thermal Convection ◽  
Vertical Profile ◽  
Large Scale ◽  
Velocity Fields ◽  
Two Dimensional

Recent experiments on thermal convection in finite containers [Krishnamurti & Howard, 1981; Howard & Krishnamurti, 1986] show the presence of flows spanning the largest dimension of the container. Numerical simulations of 2D thermal convection showing large-scale flows of this kind have been presented elsewhere [Prat et al., 1993a, 1993b]. In every known example the large scale velocity field has been found to display a vertical profile either antisymmetric or showing rather small departures from antisymmetry. In contrast, theoretical group arguments support the existence of symmetric velocity profiles. In the present paper it will be shown that large-scale velocity fields with vertically symmetric velocity profile do exist. In spite of these flows not being dominant in the range of parameters explored, their geometry and dynamics will be discussed on the basis of a linear stability analysis.

Investigation of thermocapillary convection in a three-liquid-layer system

1999 ◽  
Vol 389 ◽  
pp. 209-228 ◽  
Author(s):  
Ph. GÉORIS ◽  
M. HENNENBERG ◽  
G. LEBON ◽  
J. C. LEGROS
Keyword(s):  
Reasonable Agreement ◽  
Thermocapillary Convection ◽  
Microgravity Environment ◽  
Liquid Interfaces ◽  
Layer System ◽  
Onset Of Convection ◽  
System A ◽  
Buoyancy Forces ◽  
Convective Pattern ◽  
Similar Temperature

This paper presents the first experimental results on Marangoni–Bénard instability in a symmetrical three-layer system. A pure thermocapillary phenomenon has been observed by performing the experiment in a microgravity environment where buoyancy forces can be neglected. This configuration enables the hydrodynamic stability of two identical liquid–liquid interfaces subjected to a normal gradient of temperature to be studied. The flow is driven by one interface only and obeys the criterion based on the heat diffusivity ratio proposed by Scriven & Sternling (1959) and Smith (1966). The measured critical temperature difference for the onset of convection is compared to the value obtained from two-dimensional numerical simulations. The results of the simulations are in reasonable agreement with the velocimetry and the thermal experimental data for moderate supercriticality. Numerically and experimentally, the convective pattern exhibits a transition between different convective regimes for similar temperature gradients. Their common detailed features are discussed.

scholarly journals Towards explicit regulating-ion-transport: nanochannels with only function-elements at outer-surface

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Qun Ma ◽  
Yu Li ◽  
Rongsheng Wang ◽  
Hongquan Xu ◽  
Qiujiao Du ◽  
...  
Keyword(s):  
Ion Transport ◽  
Numerical Simulations ◽  
Power Density ◽  
Outer Surface ◽  
Internal Resistance ◽  
Porous Membranes ◽  
Two Dimensional ◽  
Ionic Selectivity ◽  
Key Features ◽  
Energy Conversion Devices

AbstractFunction elements (FE) are vital components of nanochannel-systems for artificially regulating ion transport. Conventionally, the FE at inner wall (FEIW) of nanochannel−systems are of concern owing to their recognized effect on the compression of ionic passageways. However, their properties are inexplicit or generally presumed from the properties of the FE at outer surface (FEOS), which will bring potential errors. Here, we show that the FEOS independently regulate ion transport in a nanochannel−system without FEIW. The numerical simulations, assigned the measured parameters of FEOS to the Poisson and Nernst-Planck (PNP) equations, are well fitted with the experiments, indicating the generally explicit regulating-ion-transport accomplished by FEOS without FEIW. Meanwhile, the FEOS fulfill the key features of the pervious nanochannel systems on regulating-ion-transport in osmotic energy conversion devices and biosensors, and show advantages to (1) promote power density through concentrating FE at outer surface, bringing increase of ionic selectivity but no obvious change in internal resistance; (2) accommodate probes or targets with size beyond the diameter of nanochannels. Nanochannel-systems with only FEOS of explicit properties provide a quantitative platform for studying substrate transport phenomena through nanoconfined space, including nanopores, nanochannels, nanopipettes, porous membranes and two-dimensional channels.

The Best Perturbation Method for the Parameter Inversion of Two-Dimension Convection-Diffusion Equation

2013 ◽  
Vol 380-384 ◽  
pp. 1143-1146
Author(s):  
Xiang Guo Liu
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Perturbation Method ◽  
Numerical Simulations ◽  
Numerical Solution ◽  
Two Dimensional ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Parameter Inversion ◽  
Parametric Inversion

The paper researches the parametric inversion of the two-dimensional convection-diffusion equation by means of best perturbation method, draw a Numerical Solution for such inverse problem. It is shown by numerical simulations that the method is feasible and effective.

Sign in / Sign up

Export Citation Format

Share Document