scholarly journals Numerical simulations of thermal convection on a hemisphere

2018 ◽  
Vol 3 (4) ◽  
Author(s):  
C.-H. Bruneau ◽  
P. Fischer ◽  
Y.-L. Xiong ◽  
H. Kellay ◽  
Keyword(s):  
Numerical Simulations ◽  
Thermal Convection

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>

Effect of transverse temperature gradient on the migration of a deformable droplet in a Poiseuille flow

2018 ◽  
Vol 850 ◽  
pp. 1142-1171 ◽  
Author(s):  
Sayan Das ◽  
Shubhadeep Mandal ◽  
Suman Chakraborty
Keyword(s):  
Thermal Conductivity ◽  
Steady State ◽  
Temperature Gradient ◽  
Numerical Simulations ◽  
Thermal Convection ◽  
Shape Deformation ◽  
Droplet Radius ◽  
Channel Height ◽  
State Position ◽  
Transverse Position

Intricate manipulation of droplets in fluidic confinements may turn out to be critically important for achieving their controlled transverse distributions. Here, we study the migration characteristics of a suspended deformable droplet in a parallel plate channel under the combined influence of a constant temperature gradient in the transverse direction and an imposed pressure driven flow. An outstanding question concerning the resultant non-trivial dynamical features that we address here pertains to the nonlinearity that results as a consequence of the shape deformation, which does not permit us to analyse the combined transport as a mere linear superposition of the results for the thermocapillary and imposed flow driven droplet migration in an effort to obtain the final solution. For the analytical solution, an asymptotic approach is used, where we neglect any effect of inertia or thermal convection of the fluid in either of the phases. To obtain a numerical solution, we use the conservative level set method. We perform numerical simulations over a wide range of governing parameters and obtain the dependence of the transverse steady position of the droplet on different parameters. In order to address practical microfluidic set-ups, the influence of a bounding wall as well as the effect of thermal convection and finite shape deformation on the cross-stream migration of the droplet is investigated through numerical simulations. Increase in the thermal Marangoni stress shifts the steady-state transverse position of the droplet further away from the channel centreline, for any particular value of the capillary number (which signifies the ratio of the viscous force to the surface tension force). The confinement ratio, which is the ratio of the droplet radius to the channel height, plays an important role in predicting the transverse position of the droplet and thus has immense consequences for the design of droplet-based microfluidic devices with enhanced functionalities. A large confinement ratio drives the droplet towards the channel centre, whereas a smaller confinement ratio causes the droplet to move towards the wall. Moreover, for a fixed droplet radius and constant imposed temperature gradient, an increase in the channel height results in an increase in the time required for the droplet to reach the steady-state position. However, the final steady-state position of the droplet is independent of its initial position but at the same time dependent on the droplet phase thermal conductivity. A larger droplet thermal conductivity compared with the carrier phase results in a steady-state droplet position closer to the channel centreline. A higher fluid inertia, on the other hand, shifts the steady-state position towards the channel wall.

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.

scholarly journals Poster: Direct numerical simulations of turbulent sheared thermal convection

2018 ◽  
Author(s):  
Alexander Blass ◽  
Xiaojue Zhu ◽  
Jean Favre ◽  
Roberto Verzicco ◽  
Detlef Lohse ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Thermal Convection ◽  
Direct Numerical Simulations

scholarly journals Video: Direct numerical simulations of sheared thermal convection

2017 ◽  
Author(s):  
Alexander Blass ◽  
Xiaojue Zhu ◽  
Jean Favre ◽  
Roberto Verzicco ◽  
Detlef Lohse ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Thermal Convection ◽  
Direct Numerical Simulations

scholarly journals On the sensitivity of 3-D thermal convection codes to numerical discretization: a model intercomparison

2014 ◽  
Vol 7 (5) ◽  
pp. 2065-2076 ◽  
Author(s):  
P.-A Arrial ◽  
N. Flyer ◽  
G. B. Wright ◽  
L. H. Kellogg
Keyword(s):  
Rayleigh Number ◽  
Numerical Simulations ◽  
Spherical Harmonics ◽  
Thermal Convection ◽  
Mantle Convection ◽  
Numerical Study ◽  
Critical Rayleigh Number ◽  
Initial Condition ◽  
Numerical Discretization ◽  
The Impact

Abstract. Fully 3-D numerical simulations of thermal convection in a spherical shell have become a standard for studying the dynamics of pattern formation and its stability under perturbations to various parameter values. The question arises as to how the discretization of the governing equations affects the outcome and thus any physical interpretation. This work demonstrates the impact of numerical discretization on the observed patterns, the value at which symmetry is broken, and how stability and stationary behavior is dependent upon it. Motivated by numerical simulations of convection in the Earth's mantle, we consider isoviscous Rayleigh–Bénard convection at infinite Prandtl number, where the aspect ratio between the inner and outer shell is 0.55. We show that the subtleties involved in developing mantle convection models are considerably more delicate than has been previously appreciated, due to the rich dynamical behavior of the system. Two codes with different numerical discretization schemes – an established, community-developed, and benchmarked finite-element code (CitcomS) and a novel spectral method that combines Chebyshev polynomials with radial basis functions (RBFs) – are compared. A full numerical study is investigated for the following three cases. The first case is based on the cubic (or octahedral) initial condition (spherical harmonics of degree ℓ = 4). How this pattern varies to perturbations in the initial condition and Rayleigh number is studied. The second case investigates the stability of the dodecahedral (or icosahedral) initial condition (spherical harmonics of degree ℓ = 6). Although both methods first converge to the same pattern, this structure is ultimately unstable and systematically degenerates to cubic or tetrahedral symmetries, depending on the code used. Lastly, a new steady-state pattern is presented as a combination of third- and fourth-order spherical harmonics leading to a five-cell or hexahedral pattern and stable up to 70 times the critical Rayleigh number. This pattern can provide the basis for a new accuracy benchmark for 3-D spherical mantle convection codes.

Sign in / Sign up

Export Citation Format

Share Document