Computation Of Convection Research Articles

Utilizing Euler poles for the evaluation of plate rigidity in numerical mantle convection models

SUMMARY Evidence that the Earth’s surface is divided into a tessellation of piece-wise rigidly translating plates is the primary observation supporting the solid-state creep-enabled convection paradigm, utilized to investigate evolution of the Earth’s mantle. Accordingly, identifying the system properties that allow for obtaining dynamically generated plates remains a primary objective in numerical global mantle convection simulations. The first challenge for analysing fluid dynamic model output for the generation of rigid plates is to identify candidate plate boundaries. Here, we utilize a previously introduced numerical tool for plate boundary detection which uses a user specified threshold (tolerance) to automatically detect candidate plate boundaries. The numerical tool is applied with different sensitivities, to investigate the nature of the surface velocity fields generated in three calculations described in earlier work. The cases examined differ by the values that they specify for the model yield stress, a parameter that can allow the formation of tightly focussed bands of surface deformation. The three calculations we examine include zones comprising possible plate boundaries that are characterized by convergence, divergence and strike-slip behaviour. Importance of the potential plate boundaries is assessed by examining the rigidity of the inferred model generated plates. The rigidity is measured by comparing the model velocities to the rigid rotation velocities implied by the statistically determined Euler poles for each candidate plate. We quantify a lack in rigidity by calculating a deformity field based on disagreement of actual surface velocity with rotation about the Euler pole. For intermediate yield stress and boundary detection threshold value, we find that the majority of the model surface can translate almost rigidly about distinct plate Euler poles. Regions that conform poorly to large-scale region rigid translation are also obtained but we find that generally these regions can be decomposed into subsets of smaller plates with a lower tolerance value. Alternatively, these regions may represent diffuse boundary zones. To clarify the degree to which the mantle convection model behaviour shows analogues with Earth’s current-day surface motion, we apply the plate boundary detection and Euler pole calculation methods to previously published terrestrial strain-rate data. Strong parallels are found in the response of the terrestrial data and mantle convection calculations to the threshold value, such that appropriate choice of that parameter results in very good agreement between observations and convection model character. We conclude that plates generated by fluid dynamic convection models can exhibit motion that is markedly rigid, and define statistics (plateness) and fields (deformity) by which the generation of self-consistently determined plate rigidity can be quantified, as well as describing how plate recognition might be optimized. We also note that in agreement with the Earth’s current state, we obtain a dozen dominant plates in the case exhibiting the most plate-like (rigid) surface, suggesting that this approximate number of plates is perhaps intrinsic to the geometry, surface area and physical properties of Earth’s mantle.

Study on Temperature Distribution Law of Tunnel Portal Section in Cold Region Considering Fluid–Structure Interaction

The design of tunnels in cold regions contributes greatly to the feasibility and sustainability of highways. Based on the heat transfer mechanism of the tunnel surrounding rock–lining–air, this paper uses FEPG software to carry out secondary excavation and development, then the air heat convection calculation model is established by using a three-dimensional extension of the characteristic-based operator-splitting (CBOS) finite-element method and the explicit characteristic–Galerkin method. By coupling with the heat conduction model of the tunnel lining and surrounding rock, the heat conduction-thermal convection fluid–structure interaction finite-element calculation model of tunnels in cold regions is established. Relying on the Qinghai Hekashan tunnel project, the temperature field of the tunnel portal section is calculated and studied by employing the fluid–structure interaction finite-element model and then compared with the field monitoring results. It is found that the calculated values are basically consistent with the measured values over time, which proves the reliability of the model. The calculation results are threefold: (1) The temperature of the air, lining, and surrounding rock in the tunnel changes sinusoidally with the ambient temperature. (2) The temperature of each layer gradually lags behind, and the temperature variation amplitude of the extreme value of the layer temperature gradually decreases with the increase in the radial distance of the lining. (3) In the vicinity of the tunnel entrance, the lining temperature of each layer remains unchanged, and the temperature gradually decreases or increases with the increase in the depth. The model can be used to study and analyze the temperature field distribution law of the lining and surrounding rock under different boundary conditions, and then provide a calculation model with both research and practical value for the study of the temperature distribution law of tunnels in cold regions in the future.

Rainbow Schlieren Deflectometry for spherical fields: A new algorithm and numerical validation approach

The authors present a new algorithm for analyzing ray deflection within spherical refractive index fields. The algorithm emanates from the well-known deconvolution algorithm for axisymmetric refractive index fields using the inverse Abel transformation and can be used for experimental Rainbow Schlieren Deflectometry (RSD) data. It was numerically validated by Computational Fluid Dynamics (CFD) calculations of free convection around an isothermal sphere and successive ray tracing through the determined temperature field. The algorithm determined radial temperature profiles and local Nusselt numbers from resulting deflection angles of the ray tracing simulations. An excellent agreement between original and reconstructed temperature field within the limits of assumptions was reached. This proves the usability of the algorithm for the experimental determination of spherical refractive index fields from future heat or mass transfer experiments.

Simulation Calculation and Analysis of Connate Water Convection on Steam Chamber Expansion in Steam-Assisted Gravity-Drainage Process

Steam-assisted-gravity-drainage (SAGD) is a widely employed method to enhance heavy oil production and efficiency, and the key to ensuring its steady operation is the maintenance of a steam chamber. Heat conduction and convection of steam to connate water are essential factors in the heat transfer process. In this paper, we developed a novel analytical model to investigate the heat transfer process on the boundary of the steam chamber, driven by the pressure difference between the injected steam and the original reservoir. Both conduction and convection are considered in this new model, and the calculated results are in good agreement with the simulated data by using CMG-STARS. After model validation, the effects of physical properties and operating conditions (relative permeability, initial water saturation, and steam temperature) on the heat transfer process are investigated. The results reveal that connate water saturation plays a large role than the steam temperature in conductive heat flux; low saturation leads to more efficient crude oil exploitation. This work provides new insights into the recovery mechanisms of a SAGD process.

Simplified Model for Heat Transport for Cables in Pipes

This paper addresses challenges with modeling of heat transfer phenomenon for cables in duct or pipes when applying a numerical solution. Heat transport mechanisms between the cable and pipe surfaces are conduction, convection and radiation. Numerical calculation of convection when applying a finite element analysis (FEA), or other numerical tools requires heavy computation power and great skills of the program operator. In general, this is the most difficult part when modeling the heat transfer between the cable and the pipe surfaces and practitioners are often forced to use simplifications or approximate models. This paper introduces a simplified model where the contribution from convection is replaced by a heat source at the pipe wall and a corresponding heat sink at the cable. The phenomenon of air rising vertically in the tube resulting in the upper half of the pipe being heated more by convection than the lower half is also modelled. The simplified model is compared to both known models from thermodynamics, FEA including convection and laboratory as well as the full-scale field measurements. The simplified model shows good correspondence to both simulations and measurements, with the temperatures deviating by less than 1 °C.

Experience of using semiempirical differential models of turbulence for calculation of liquid-metal convection in a bottom heated cylinder

Experience of using semiempirical differential models of turbulence for calculation of liquid-metal convection in a bottom heated cylinder

Geodynamic Characteristics in the Southwest Margin of South China Sea

The strike-slip fault system in the southwestern margin of South China Sea (SCS) lies on the transition zone between the continental shelf and slope of SCS, which is an important ocean–continent boundary. By using submarine heat flow data, a seismic shear wave tomography model, and gravity potential field data, this paper investigates the distribution of submarine heat flow in the southwestern margin of SCS, the thermal–rheological structure of the crust and mantle, the temperature–viscosity characteristics of the upper mantle Vs low-velocity layer, the tangential stress field of the rheological boundary layer at the lithosphere base, and the convective velocity structure of the mantle asthenosphere. Our new results show that the deep geothermal activity in the southwestern margin of SCS is intense, and the high heat flow area of the mantle with Qm/Qs >70% is distributed along an NNE-trending strip. Moreover, both the east and west sides of the strike–slip fault zone correspond to two low-value areas with a viscosity coefficient of 1021–1022 Pa⋅s at Moho depth, and beneath the Nansha Block are strong and cold blocks with a viscosity coefficient of 1024–1025 Pa⋅s. The northward and eastward shear stress components τN and τE of the rheological boundary layer at the base of the lithosphere mantle decrease with depth. At 65-km depth, both τN and τE are greater than 5.5 × 108 N/m2. At 100-km depth, both τN and τE are less than 1 × 108 N/m2. The calculation results based on the seismic shear wave model of the upper mantle and the gravimetric geoid model indicate that the depth of 120–250 km is the low-velocity layer, and the average temperature of the mantle at 180-km depth can be up to 1,300°C. Moreover, the average effective viscosity coefficient is close to 1018 Pa⋅s, which satisfies the temperature and viscosity conditions for partial melting or convective migration of mantle material. The mantle convection calculation results show that the average flow rate is 8.5 cm/a at 200-km depth and 2.2 cm/a at 400-km depth.

2D/3D RANS and LES Calculations of Natural Convection in a Laterally-Heated Cylindrical Enclosure Using Boussinesq and Temperature-Dependent Formulations

This article presents an investigation of fluid flow and natural convection heat transfer in a cylindrical enclosure heated laterally. Two-dimensional (2D) Reynolds-averaged Navier–Stokes (RANS) equations and three-dimensional (3D) Large Eddy Simulation (LES) calculations are conducted using commercial computational fluid dynamics (CFD) software, ANSYS FLUENT. The Rayleigh number (Ra) = 2E+7 is constant in all of the simulations and is based on a length scale that is equal to the ratio of volume to the lateral area of the reactor, i.e., R/2, where R is the radius of the reactor. The validity of the Boussinesq approximation is analyzed by comparing calculations using both the Boussinesq approximation and temperature-dependent properties (non-Boussinesq approach) using 2D RANS and 3D LES (Dynamic Smagorinsky) formulations. Moreover, 2D axisymmetric k-ω SST RANS model will be implemented to investigate whether the 2D axisymmetric model can give results that are comparable to those of the 3D LES (Dynamic Smagorinsky) model when the corresponding longitudinal or azimuthal cross section are compared. In other words, the validity of using a 2D model instead of a 3D model for the current geometry, flow regime and thermal boundary conditions will be discussed. The flow and temperature contours of these two types of simulations are analyzed, compared to determine the various aspects of each case and discussed for deeper physical insight.

Global mantle convection models produce transform offsets along divergent plate boundaries

The presence of offsets, appearing at intervals ranging from 10s to 100s of kilometres, is a distinct characteristic of constructive tectonic plate margins. By comparison, boundaries associated with subduction exhibit uninterrupted continuity. Here, we present global mantle convection calculations that result in a mobile lithosphere featuring dynamically derived plate boundaries exhibiting a contrasting superficial structure which distinguishes convergence and divergence. Implementing a yield-stress that governs the viscosity in the lithosphere, spreading boundaries at the top of a vigorously convecting mantle form as divergent linear segments regularly offset by similar length zones that correlate with a large degree of shear but comparatively minimal divergence. Analogous offset segments do not emerge in the boundaries associated with surface convergence. Comparing the similarity in the morphologies of the model plate margins to the Earth’s plate boundaries demonstrates that transform-like offsets are a result of stress induced weakness in the lithosphere owing to passive rupturing.

Analytical Simulation for Transient Natural Convection in a Horizontal Cylindrical Concentric Annulus

In this study, a new scheme is suggested to find the analytical approximating solutions for a two-dimensional transient natural convection in a horizontal cylindrical concentric annulus bounded by two isothermal surfaces. The new methodology depends on combining the algorithms of Yang transform and the homotopy perturbation methods. Analytical solutions for the core, the outer layer and the inner layer at small times are found by a new method. Also, the effect of Grashof number, Prandtl number and radius proportion on the heat transfer and the flow of fluid (air) at different values was studied. Moreover, the study calculates the mean of the Nusselt number along with the effect of the Grashof number and radius proportion on it as parameters which acts as clues for heat transfer calculations of the natural convection for the annulus. The results, obtained by using the new method, prove that it is efficient and has high exactness compared to the other methods, used to find the analytical approximate solution for the transient natural convection in a horizontal cylindrical concentric annulus. The convergence of the new method was also discussed theoretically by referring to some theorems, and experientially by a verification of the solutions resulting from the simulations of the convergent condition. Furthermore, the graphs of the new solutions show the veracity, utility and exigency of the new method, and come in line with solutions offered by previous studies.

Characterization of size effect of natural convection in melting process of phase change material in square cavity* *Project supported by the National Natural Science Foundation of China (Grant Nos. 51908197 and 12072107), the Tackle Key Problems in Science and Technology Project of Henan Province, China (Grant No. 202102310262), the Program for Innovative Research Team of Science & Technology of Henan

The accelerating effect of natural convection on the melting of phase change material (PCM) has been extensively demonstrated. However, such an influence is directly dependent on the size and shape of domain in which phase change happens, and how to quantitatively describe such an influence is still challenging. On the other hand, the simulation of natural convection process is considerably difficult, involving complex fluid flow in a region changing with time, and is typically not operable in practice. To overcome these obstacles, the present study aims to quantitatively investigate the size effect of natural convection in the melting process of PCM paraffin filled in a square latent heat storage system through experiment and simulation, and ultimately a correlation equation to represent its contribution is proposed. Firstly, the paraffin melting experiment is conducted to validate the two-dimensional finite element model based on the enthalpy method. Subsequently, a comprehensive investigation is performed numerically for various domain sizes. The results show that the melting behavior of paraffin is dominated by the thermal convection. When the melting time exceeds 50 s, a whirlpoor flow caused by natural convection appears in the upper liquid phase region close to the heating wall, and then its influencing range gradually increases to accelerate the melting of paraffin. However, its intensity gradually decreases as the distance between the melting front and the heating wall increases. Besides, it is found that the correlation between the total melting time and the domain size approximately exhibits a power law. When the domain size is less than 2 mm, the accelerating effect of natural convection becomes very weak and can be ignored in practice. Moreover, in order to simplify the complex calculation of natural convection, the equivalent thermal conductivity concept is proposed to include the contribution of natural convection to the total melting time, and an empirical correlation is given for engineering applications.

Моделирование теплообмена и трения в тонком воздушном ламинарном пограничном слое над боковой поверхностью затупленного конуса малого удлинения

It is not possible to obtain a high-quality solution to a convective heat transfer problem without numerically integrating the differential equations describing the boundary layer, which involves a whole range of computational issues. Developing relatively simple yet adequately accurate computation methods becomes crucial. Using the effective length method may be considered to be the first step towards solving this problem. This method boasts an accuracy of convective heat transfer calculation that is acceptable in practice, due to which it became prevalent in aircraft design. However, this method is also relatively labour-intensive, although significantly less so than numerical integration of the boundary layer differential equations. The most efficient approach to solving heat transfer and friction problems in engineering practice would be using simple algebraic equations based on fitting the results of rigorous numerical computations or experimental investigations. Regrettably, there is no information published regarding how accurate these equations are for various operation conditions. The paper presents a solution to this problem based on deriving systematic numerical solutions to the boundary layer equations in the most rigorous analytical statement, along with conducting a thorough analysis of the equation accuracy for both the equations derived and previously published

Numerical analysis of dopant concentration in 200 mm (8 inch) floating zone silicon

In this paper, the calculation of dopant concentration for 200 mm floating zone silicon was carried out. The numerical model includes natural convection, thermocapillary convection, electromagnetic force, and rotation of the melt. The dopant concentration was obtained using steady-state calculation of dopant convection and diffusion. Through the comparison between the melt flow and normalized resistivity distribution, we investigated that, besides the well-known separation point, there was a secondary minimum resistivity near external triple point. This phenomenon was also indicated in previous experimental result, and thus was confirmed that the phenomenon was caused by strong electromagnetic force at external triple point.

A Lagrangian Perspective on Parameterizing Deep Convection

Abstract The parameterization of deep moist convection as a subgrid-scale process in numerical models of the atmosphere is required at resolutions that extend well into the convective “gray zone,” the range of grid spacings over which such convection is partially resolved. However, as model resolution approaches the gray zone, the assumptions upon which most existing convective parameterizations are based begin to break down. We focus here on one aspect of this problem that emerges as the temporal and spatial scales of the model become similar to those of deep convection itself. The common practice of static tendency application over a prescribed adjustment period leads to logical inconsistencies at resolutions approaching the gray zone, while more frequent refreshment of the convective calculations can lead to undesirable intermittent behavior. A proposed parcel-based treatment of convective initiation introduces memory into the system in a manner that is consistent with the underlying physical principles of convective triggering, thus reducing the prevalence of unrealistic gradients in convective activity in an operational model running with a 10 km grid spacing. The subsequent introduction of a framework that considers convective clouds as persistent objects, each possessing unique attributes that describe physically relevant cloud properties, appears to improve convective precipitation patterns by depicting realistic cloud memory, movement, and decay. Combined, this Lagrangian view of convection addresses one aspect of the convective gray zone problem and lays a foundation for more realistic treatments of the convective life cycle in parameterization schemes.

Numerical simulations of solidification structures and macrosegregation by a cellular automaton model coupled with flow calculations

In this study, a numerical model was developed, and direct simulations were performed to predict solidification grain structures and macrosegregation based on a three-dimensional cellular automaton finite difference (CAFD) method coupled with flow calculation of natural convection and shrinkage flow. First, to evaluate the model coupled with natural convention, simulations of unidirectional solidification for Al-10wt% Mg alloy were performed. Mg-rich plumes rising in the melt were seen due to subsequent upward flow, and Mg-rich channels forming in the mushy zone were observed. Columnar grains were then formed, and they became coarse afterwards. Next, to evaluate the model coupled with shrinkage flow, simulations of casting Al-10wt% Cu alloy in a unique mold, which can form macrosegregation in the central region of the small ingot, were performed. The bridging of columnar grains formed during solidification, and the positive segregation was generated in the region below the bridging. Thus, the main factor for this macrosegregation is the shrinkage flow with bridging. From the comparison of simulation results with and without the chill for the unique mold, it was established that the shrinkage flow and the bridging of solidification structures play an important role in macrosegregation.

Role of Atmospheric Convection in Global Warming

Aims: Geophysical convection calculations can potentially obscure details necessary to understand convective-heat-transfer changes caused by changes in the adverse temperature gradient. The objective is to ascertain the functional relationship between adverse temperature gradient and convection efficiency.
 Methodology: A classroom-demonstration experiment was conducted to illustrate the principle that convection efficiency is a direct function of the adverse temperature gradient.
 Results: Application of this principle to climate science has profound implications for global warming. A brief period of global warming during World War ll followed by rapid global cooling afterward is attributable, not to carbon dioxide, but to particulate pollution and its generalization to post-1950 global warming. Rather than simply blocking sunlight and causing global cooling, aerosol particles are radiation absorbers that rapidly transfer heat to the surrounding atmosphere, raising its temperature relative to atmospheric temperature at Earth’s surface. Thus the reduction of the adverse temperature gradient between the upper troposphere and the surface reduces atmospheric convection and concomitantly reduces convection-driven surface heat loss, causing global warming, heating the oceans, and reducing CO2 solubility and releasing dissolved CO2 to the atmosphere.
 Conclusions: Increasing levels of atmospheric CO2, rather than causing global warming, are symptomatic of particulate-pollution-caused global warming. The Anthropocene idea cannot be justified by anthropogenic CO2. Instead the Anthropocene is better characterized by anthropogenic particulate pollution. A drastic reduction in particulate-pollutant emissions will be followed by a rapid and drastic reduction in global warming, as tropospheric pollution-particulates fall to ground in days to weeks, thus increasing atmospheric convection efficiency and potentially providing a radical solution to the global climate crisis. Moreover, reduction of particulate-pollution, the greatest environmental health-threat, will potentially save millions of lives and reduce the suffering of many more.

Effect of plume motion path on heat transfer characteristics in two-dimensional turbulent thermal convection

The Grossman and Lohse (GL) theory is an important theory for studying the heat transfer characteristics of the turbulent convection. Previous computational studies have found that when the Ra number is higher than a certain value, the change of the heat transfer Nu number with Ra number in two-dimensional turbulent thermal convection is different from that in the three-dimensional thermal convection, deviating from the multiples line of the GL theory prediction. Therefore, the value of studying the two-dimensional numerical calculation of turbulent thermal convection with high Ra number is questioned. The numerical calculations of a series of two-dimensional turbulent thermal convection events with high and very high Ra number(specifically, maximum Ra = 10<sup>13</sup> with Pr = 0.7 and 4.3) are carried out in this paper. The results show that there exists a good correlation between the heat transfer Nu number and the variation of large scale circulation path length(that reflects the plume motion) with Ra number in the two-dimensional turbulent convection, and they have two Ra number transition points. The first transition point appears in the large scale circulation from the ellipse to the circle, when its circumference C<sub>LSC</sub> of the large scale circulation suddenly decreases with Ra number increasing. The second transition point appears at the minimum circumference C<sub>LSC</sub>, and then the plume rheology becomes vortex group and the circumference C<sub>LSC</sub> increases with Ra number increasing. The Ra number at transition point for a smaller Pr number is lower. The variation of the heat transfer Nu number after Ra<sup>0.3</sup> compensation shows that the local scale law of Nu number decreases as the circumference C<sub>LSC</sub> of the large scale circulation becomes small, and a phenomenon of deviating from the multiples line of GL theory prediction appears. When Ra number is higher than the second transition point, the local scale law of the Nu number varying with Ra number is in good agreement with the multiples line of GL theory prediction again in 2D turbulent thermal convection. It means that the numerical results of two-dimensional turbulent thermal convection can correctly reflect the heat transfer characteristics of turbulent thermal convection under the condition of very high Ra number.

Multi-step Simulation of Vacuum-carburizing Reactor based on Kinetics Approach

A novel and efficient simulation technique for the purpose of optimization of vacuum-carburizing process was proposed. This method consists of three steps: calculation of gas convection and diffusion, calculation of only gas diffusion, and calculation of carbon diffusion in steel. The first step provides the gas convection velocity that is employed in the second step. Adsorption rate of carbon on the steel surface is obtained in the second step, and carbon concentration in the steel is calculated in the third step based on the adsorption rate of carbon. Experiments were conducted to verify the proposed method in both laboratory- and industrial-scale reactors. Comparison of the computational predictions to the experimental data revealed that the proposed technique enabled accurate prediction of the adsorption rate of carbon on the steel surface at various temperature conditions, the amount of carburized carbon at each operating time, and the profile of carbon concentration in the steel; in other words, the carburized depth. In addition, the calculation of the industrial-scale reactor, whose simulation model consisted of approximately seven million computational meshes, was completed within about two days. Therefore, the proposed simulation technique could be used to control and optimize the process in industrial vacuum-carburizing reactors.

Numerical appraisal of three low Mach number algorithms for radiative–convective flows in enclosures

The present study investigates three different algorithms for the numerical simulation of non-Boussinesq convection with thermal radiative heat transfer based on a low-Mach number formulation. The solution methodology employs a fractional step approach based on the finite-volume method on arbitrary polyhedral meshes. The three algorithms compute the coupled governing equations in a segregated manner using the conservative form of momentum equations in conjunction with a variable coefficient pressure Poisson equation. The first algorithm (Algorithm A) uses conservation of mass and energy equation to compute density and temperature. The other two algorithms (Algorithm B) and (Algorithm C) calculates temperature and density from the equation of state respectively and solves a conservative form of the continuity and energy equation to obtain density and temperature respectively. The energy and mass conservation errors arising due to the use of Algorithms B and C are derived concerning various non-dimensional parameters governing the flow and heat transfer. The significance of these errors is highlighted by performing investigations over a range of Rayleigh, Prandtl, and Planck numbers for various two and three-dimensional natural convection problems with radiative heat transfer. Finally, the role of balancing of the pressure and buoyancy terms is emphasized for robust calculations of large temperature difference thermo-buoyant convection with radiative heat transfer.

New geophysical complex-field approach to modelling dynamics of heat-mass-transfer and ventilation in atmosphere of the industrial region

New generalized approach, including an improved theory of atmospheric circulation in combination with the hydrodynamic model (with correct account of turbulence in atmosphere of the urban area) and the Arakawa-Schubert method of calculation of cloud convection and theory of complex geophysical field is applied to the simulation of heat and air transfer in atmosphere of industrial region. The modelling ventilation data (mesocirculation) parameters over territory of Odessa, as well as the area of the Fukushima power plant after 2011 accident are presented.