Convective Flux Research Articles

The cell-centered positivity-preserving finite volume scheme for 3D convection–diffusion equation on distorted meshes

PurposeThis paper aims to construct positivity-preserving finite volume schemes for the three-dimensional convection–diffusion equation that are applicable to arbitrary polyhedral grids.Design/methodology/approachThe cell vertices are used to define the auxiliary unknowns, and the primary unknowns are defined at cell centers. The diffusion flux is discretized by the classical nonlinear two-point flux approximation. To ensure the fully discrete scheme has positivity-preserving property, an improved discretization method for the convection flux was presented. Besides, a new positivity-preserving vertex interpolation method is derived from the linear reconstruction in the discretization of convection flux. Moreover, the Picard iteration method may have slow convergence in solving the nonlinear system. Thus, the Anderson acceleration of Picard iteration method is used to solve the nonlinear system. A condition number monitor of matrix is employed in the Anderson acceleration method to achieve better robustness.FindingsThe new scheme is applicable to arbitrary polyhedral grids and has a second-order accuracy. The results of numerical experiments also confirm the positivity-preserving of the discretization scheme.Originality/value1. This article presents a new positivity-preserving finite volume scheme for the 3D convection–diffusion equation. 2. The new discretization scheme of convection flux is constructed. 3. A new second-order interpolation algorithm is given to eliminate the auxiliary unknowns in flux expressions. 4. An improved Anderson acceleration method is applied to accelerate the convergence of Picard iterations. 5. This scheme can solve the convection–diffusion equation on the distorted meshes with second-order accuracy.

Computational fluid dynamic model for the prediction of the unsteady operation process of a non-dispersive gold extraction from wastewater

The current study tries to investigate gold extraction in a membrane extractor in unsteady mode. The model was successfully validated using experimental results. The results showed that the diffusive flux on the zone close to the membrane surface is dominant in the first minutes of extraction but later the convective flux is the main flux, particularly at the centre of the shell side. The extraction time of one hour was not ample to extract all gold from the aqueous solution when the volume of solutions was 2000 mL and 3000 mL. Finally, the change in feed flow rate in the range of 30–55 cm3/min did not have a significant influence on the gold extraction time. However, the outlet dimensionless concentration of gold after one hour was increased from 0.24 to 44 with the increase of feed flow rate from 30 cm3/min to 55 cm3/min.

Numerical modeling of heat transfer behavior for two-phase flow in a nozzle considering phase change

The heat transfer and phase change of alumina particles in the gas-particle flow of the nozzle plays an important role in solid rocket motors (SRM) due to the coupling between the heat transfer and two-phase flow. However, it lacks precise modeling of the heat transfer behaviors of condensed particles in the nozzle, especially the phase change effect. In this article, we determine that the Drake model has the highest accuracy in calculating the convective heat flux between two phases, and propose a correlation to obtain radiative heat flux between the particle and walls. Then, a one-dimensional two-phase non-equilibrium model is established to consider the effects of heat transfer and solidification of particles on the two-phase flow in the nozzle. The results show that considering the phase change of particle improves the outlet thrust of the nozzle, but such increment decreases with the gas inlet temperature. When the supercooling phenomenon is considered, the nozzle thrust is reduced by 1.14% compared with that considering no supercooling. As the particle size increases, the outlet temperature of the particle phase rises and can even surpass the solidification temperature of particles and the velocity of the particle phase decreases significantly.

Testing a non-local 1-equation turbulent convection model: A solar model

Turbulent convection models treat stellar convection more physically than standard mixing-length theory by including non-local effects. We recently successfully applied the Kuhfuss version to convective cores in main sequence stars. Its usefulness for convective envelopes remains to be tested. The solar convective envelope constitutes a viable test bed for investigating the usefulness of the 1-equation Kuhfuss turbulent convection model. We used the one-dimensional stellar evolution code GARSTEC to calculate a standard solar model with the 1-equation Kuhfuss turbulent convection model, and compared it to helioseismic measurements and a solar model using standard mixing-length theory. Additionally, we investigated the influence of the additional free parameters of the convection model on the solar structure. The 1-equation Kuhfuss model reproduces the sound-speed profile and the lower boundary of the convective region less well than the mixing-length model, because the inherent non-local effects overestimate the amount of convective penetration below the Schwarzschild boundary. We trace this back to the coupling of the temperature gradient to the convective flux in the 1-equation version of the Kuhfuss theory. The temperature stratification of the solar convective envelope is not well modelled by the 1-equation Kuhfuss turbulent convection model, and the more complex 3-equation version is needed to improve the modelling of convection in the envelopes of 1D stellar evolution models.

Dissolution of Oxide Particles in Multi-component Slags Governed by Diffusive and Convective Fluxes

Dissolution of Oxide Particles in Multi-component Slags Governed by Diffusive and Convective Fluxes

CFD-DEM study of thermal behaviours of chip-like particles flow in a fluidized bed

Chip-like particles are increasingly practised in various thermal applications, yet the unique heat transfer characteristics are not well understood. In this work, a recently developed super-quadric computational fluid dynamics-discrete element method (CFD-DEM) is extended to couple with heat transfer sub-models to study the cooling behaviours of chip-like particles in a three-dimensional (3D) cylindrical fluidized bed. The effect of aspect ratio (AR) on the flow and thermal behaviours of chip-like particles are studied at the particle scale. The results show that the chip-like particles with an AR of 6 show the steepest temperature decrease and thus the fastest cooling process under the given conditions. The unimodal distributions of particle temperature for the small ARs (i.e., 2 and 4) but bimodal distributions for the large AR (i.e., 6) are captured. Further, a large convective heat flux appears in the dilute phase due to vigorous slip velocity and temperature difference while a small convective heat flux occurs in the dense phase where the chip-like particles tend to be in a close-packing status. Finally, the underlying mechanism is explored: the chip-like particles with larger ARs show better heat transfer performance because the AR enhances gas-solid relative movement intensity and the convective heat transfer flux, and the convective heat transfer dominates the whole particle cooling process. The fundamental study sheds light on the design and optimization of fluidized beds of chip-like particles including solar panel recycling and wood chip gasification.

On the study of three-dimensional compressible Navier–Stokes equations

This work is devoted to the study of three-dimensional compressible Navier–Stokes equations on unstructured meshes. The approach used is based on separating the convection and diffusion parts. The convective flux is computed using the Godunov method. For the diffusive part, we present a new finite volume scheme. Numerical results are provided to demonstrate the efficiency of the developed technique.

Assessment of pollution removal mechanisms in steep-asymmetric city-type environments using wind deflectors

Traffic emissions directly impact indoor air quality in near-road buildings. Adjustable wind deflectors on building roofs were previously shown to be effective in mitigating air pollution for ideal city-type environments. This was based on the hypothesis that wind deflectors promoted higher pollutant removal by reducing the dependence on turbulent fluctuations. However, the question of whether such a deflector system would work in a more complex city-type environment such as an asymmetric street canyon remains unanswered. In addition, the fundamental impact a deflector could impart on flow dynamics within street canyons in the context of pollution removal through differing mechanisms also requires further research. The current study seeks to answer both questions by introducing adjustable wind deflectors for step-up and step-down asymmetric canyons with two traffic flow directions. For the step-down canyon, the deflectors promoted CO reduction in building facades by 73.55% and 34.79% from leeward and windward walls under a Cross Road Pollution (CRP) source. A 16.57% reduction was achieved on side walls under a Side Road Pollution (SRP) source. However, apart from the 13.87% CO reduction across windward walls under the CRP source, the wind deflectors predominantly resulted in detrimental results for step-up canyons. The ratio of pollution exchange rate achieved by mean flow-induced fluxes and total pollution exchange rate (θ), Sherwood number is the ratio of convective and diffusive mass transfer (Sh) and average canyon concentration (C‾canyon) were used as indices to investigate pollution removal mechanisms. Although both Shv/sC‾canyon and θv/sC‾canyon relationships exhibited good inverse correlations when the deflector was positioned at different locations, the Shv/sC‾canyon showed superior performance in distinguishing the scenarios where a deflector was involved and when not. This implies that the introduction of wind deflectors impacted more in effecting convective fluxes than fluctuations for pollution removal.

Hybrid compressible lattice Boltzmann method for supersonic flows with strong discontinuities

Within the framework of the hybrid recursive regularized lattice Boltzmann (HRR-LB) model, we propose a novel hybrid compressible LB method to ensure the conservation of total energy in simulating compressible flows with strong discontinuities. This method integrates a LB solver to handle the mass and momentum conservation equations via collision-streaming steps on standard lattices, while a finite volume method (FVM) is employed for the conservation of the total energy equation. The flux reconstruction in the FVM is achieved through a momentum coupled method (MCM). The interface momentum, crucial for reconstructing the convective fluxes and determining the upwind extrapolation of passive scalar quantities in MCM, is derived from the LB method. The validity and accuracy of the proposed method are evaluated through six test cases: (I) isentropic vortex convection in subsonic and supersonic regimes; (II) non-isothermal acoustic pulse; (III) one-dimensional Riemann problems; (IV) two-dimensional Riemann problem; (V) double Mach reflection of a Mach 10 shock wave; and (VI) shock–vortex interaction. Numerical results demonstrate that this method surpasses the previous HRR-LB model by Guo et al. [“Improved standard thermal lattice Boltzmann model with hybrid recursive regularization for compressible laminar and turbulent flows,” Phys. Fluids 32, 126108 (2020)] in terms of accuracy and robustness when dealing with strong shock waves.

Combined radiation and convection in developing flow in a parallel plate channel with real gas behavior: Contrast between gas cooling and heating

Laminar thermally developing gas flow in a two-dimensional parallel plate channel with real gas radiation has been investigated numerically. Real gas spectral radiation effects are accounted for by using the Spectral Line Weighted-sum-of-gray-gases model. Gas mixtures of H2O and CO2, either alone in mixture with N2 or as a mixture of H2O and CO2 are considered. The phenomena are investigated for a range of differences between wall and inlet gas temperature, mole fraction of the radiating species, and total pressure. Predictions for the cases of gas heating and gas cooling are contrasted with results presented by the classical no-radiation case, commonly known as the Graetz solution. The impact of gas radiation on the local mean temperature, convective and radiative wall heat fluxes, and the convective, radiative, and total local Nusselt numbers are studied.The predictions reveal that the inclusion of participating gas radiation results in a much more rapid change in temperature of the gas in the channel than for the convection-only case, for both the gas heating and gas cooling cases. Further, unique differences in the heat transfer behavior for gas cooling (wall temperature below the inlet gas temperature) and gas heating (wall temperature above the inlet gas temperature) scenarios are shown. However, significant differences between the cases of heating and cooling exist. In the classical Graetz solution, for constant thermophysical properties and using appropriately nondimensionalized heat transfer parameters (e.g., Nusselt number, inverse Graetz number) the predictions for fluid heating and cooling are identical. However, the results of this study including the influence of gas radiation demonstrate that the heat transfer behavior depends heavily on whether the gas is heated or cooled. An apparent thermally fully developed condition may exist for the case of gas cooling, whereas the variation in local Nusselt number with dimensionless axial location exhibits a local minimum for the case of gas heating. Further, the case of gas heating results in a more rapid streamwise change in mean temperature in the channel than for the cooling case. The thermal physics of the developing flow for combined convective-radiative transfer with real gas effects are explored for a range of wall and gas inlet temperatures, radiating species mole fractions, and total pressures.

Using Passive Multi-Modal Sensor Data for Thermal Simulation of Urban Surfaces

Abstract. This paper showcases an integrated workflow hinged on passive airborne multi-modal sensor data for the simulation of the thermal behavior of built-up areas with a focus on urban heat islands. The geometry of the underlying parametrized model, or digital twin, is derived from high-resolution nadir and oblique RGB, near-infrared and thermal infrared imagery. The captured bitmaps get photogrammetrically processed into comprehensive surface models, terrain, dense 3D point clouds and true-ortho mosaics. Building geometries are reconstructed from the projected point sets with procedures presupposing outlining, analysis of roof and fac¸ade details, triangulation, and texturing mapping. For thermal simulation, the composition of the ground is determined using supervised machine learning based on a modified multi-modal DeepLab v3+ architecture. Vegetation is retrieved as individual trees and larger tree regions to be added to the meshed terrain. Building materials are assigned from the available visual, infrared and surface planarity information as well as publicly available references. With actual weather data, surface temperatures can be calculated for any period of time by evaluating conductive, convective, radiative and emissive energy fluxes for triangular layers congruent to the faces of the modeled scene. Results on a sample dataset of the Moabit district in Berlin, Germany, showed the ability of the simulator to output surface temperatures of relatively large datasets efficiently. Compared to the thermal infrared images, several insufficiencies in terms of data and model caused occasional deviations between measured and simulated temperatures. For some of these shortcomings, improvement suggestions within future work are presented.

Determination of CO2 convective mixing flux in saline aquifers based on the optimality

Determination of CO2 convective mixing flux in saline aquifers based on the optimality

Numerical analysis of the flow dynamics in Maxwell hybrid nanofluid flow with gyrotactic microorganisms over a permeable stretching surface with convective and zero-mass flux conditions: A comparative analysis

This study observes the 2-D flow of a Maxwell hybrid nanofluid flow on a permeable stretching surface containing Cu and CuO nanoparticles and gyrotactic microorganisms. The thermal convective and zero-mass flux constraints are adopted by incorporating a hot working fluid with a heat transfer coefficient and zero mass flow at the permeable sheet’s surface to investigate the heat transfer rate. This study is designed to present a comparative analysis of the nanofluid (Cu–water) as well as hybrid nanofluid (Cu–CuO/water) flows on a stretching sheet. Examining activation energy in water-based hybrid nanofluid flow offers important insights into the kinetics of chemical reactions, which in turn helps to optimize the features of the nanofluid and build more effective systems that use nanofluids for a variety of applications. The problem formulated initially is converted to dimension-free notation using appropriate variables for finding the numerical solution by incorporating the bvp4c MATLAB function. From the obtained results, it is found that the higher magnetic and porosity factors have declined the velocity profiles. Also, in the absence of porous media and magnetic field effects, the velocity distribution is highly affected when compared with the existence of these effects. It is observed that the velocity profiles of both nanofluids are dominant for Newtonian fluid in comparison to non-Newtonian fluid. Also, the thermal profiles of both nanofluids are dominant for non-Newtonian fluid in comparison to Newtonian fluid. The friction force of hybrid nanofluid is significantly influenced by the magnetic factor, porosity factor, and volume fractions of the solid nanoparticles when compared to nanofluid.

Effects of confined distance and wire spacing on flame spread over double electrical wires for the layout design in buildings

In this study, the flame merging and flame spread behaviors over two identical parallel electrical wires (the ratios of copper core diameter to entire wire diameter are: 6mm/10 mm and 8mm/12 mm for typeⅠand typeⅡ, respectively) were experimentally investigated under different wire spacings (3∼18 mm) and confined distances(10∼30 mm). The results show that the smaller confined distance D will promote the merging, making the wire spacing s increase for the fully merging. With the increase of D, the flame width and flame spread rate Vf will increase.While the flame height will be stretched at smaller D. And Vf is larger than that of single wire at the same D for different wire spacings.The interesting finding is that a pool fire is formed at the middle of the wire spacing when s and D are small, which will enhance the flame spread.The heat flux feedback of components including of the conductive heat flux q˙c″, the first single flame heat flux q˙f1″, the second flame heat flux q˙f2″, the pool fire heat flux q˙pf″ and the gypsum board heat flux q˙g″ are quantitatively analyzed. At the intermittent and non merging stages, the convective and radiative heat fluxes q˙vf2″ and q˙rf2″ will decrease largely due to the interaction weakened greatly. Based on the heat transfer analysis, a flame spread model is established, which can well predict the flame spread rate.These findings can give the useful suggestions on the layout design of electrical wires in confined space in buildings.

The North Atlantic subpolar ocean dynamics during the past 21,000 years

Numerous studies have suggested that the North Atlantic subpolar gyre (SPG), Atlantic Meridional Overturning Circulation (AMOC), and Arctic sea ice impact the polar and global climate. Here, we use a fully linked atmosphere-ocean-sea ice Earth system model to investigate the North Atlantic subpolar ocean dynamics over the last 21 thousand years before the present (ka). We found that the SPG strength, net ocean surface heat flux, and mixed layer depth in the North Atlantic deep convection sites declined during the Heinrich 1 (H1; ∼19–17 ka) and Younger Dryas (YD; ∼12.9–11.3 ka) cold events. Consequently, the deep convection and AMOC strength declined, reducing the northward meridional heat transport and causing the expansion of Atlantic sea ice coverage. We also found that the North Atlantic subpolar net ocean surface heat flux varied coherently with AMOC strength throughout the past 21 ka. Subsequently, we observed a sea ice-capping mechanism wherein an increase (decrease) in Atlantic sea ice coverage during H1/YD (Bølling-Allerød (BA; ∼17–14.35 ka)) reduces (increases) net ocean surface heat flux and deep convection, thereby influencing the AMOC strength. Meanwhile, the SPG and AMOC strengths have been in-phase throughout the past 21 ka, except during the abrupt termination and input of freshwater flux during the BA and Meltwater Pulse 1 A (∼14.4–13.9 ka) events, respectively. In conclusion, our study suggests that a sudden shift in freshwater discharge into the subpolar North Atlantic may disturb the polar ocean dynamics.

Study on the effect of arc chamber structures on the post-arc characteristics of generator circuit breaker

A generator circuit breaker (GCB) is installed at the outlet of generator. However, large-capacity GCBs are highly prone to post-arc thermal breakdown during the breaking process, and the gas flow field largely determines the probability of thermal breakdown occurrence. In this paper, the structure of the arc chamber in the GCB is optimized. From the perspective of accelerating the gas flow field, a “trumpet” shaped arc chamber structure is proposed. Using real SF6 gas physical parameters, a simulation model of the gas flow field is established. By comparing different arc chamber structures, the distributions of temperature and flow velocity varying with time are obtained, the movement of the arc is analyzed. Finally, the arc radius, convection flux density and conduction flux density are quantitatively calculated. Results of the research show that the convection flux density is much greater than the conduction flux density. Compared with the initial and “trumpet” structures, the “trumpet” structure arc radius is reduced by about 19 % and the convection flux density peak is increased by about 118 %. This enhanced the dissipation of post-arc energy, reducing the probability of post-arc thermal breakdown, and provided a reference for the subsequent design of the arc chamber in GCBs.

An Effective Arbitrary Lagrangian-Eulerian-Lattice Boltzmann Flux Solver Integrated with the Mode Superposition Method for Flutter Prediction

An Effective Arbitrary Lagrangian-Eulerian-Lattice Boltzmann Flux Solver Integrated with the Mode Superposition Method for Flutter Prediction

Commissioning of Upgrades to T6 to Study Giant Planet Entry

The scientific potential of a mission to the ice giants is well recognized and has been identified by NASA and ESA as a high priority on several occasions, most recently in the 2023–2032 Decadal Survey. The payload capacity of such a spacecraft is limited by the heat shield thickness, which must be sized conservatively due to a lack of reliable data for convective and radiative heat flux along the proposed entry trajectories. Major upgrades to the Oxford T6 Stalker Tunnel have been commissioned that allow study of giant planet entry trajectories, including a flammable gas handling system, a Mach 10 expansion nozzle, and a steel shock tube with optical access. Initial testing has been completed in shock tube and expansion tunnel modes, with peak shock speeds of 18.9 km/s achieved. Convective heat flux and surface pressure were measured at several locations on a 45° sphere cone model in expansion tunnel mode. Measurements of the radiating shock layer were made in shock tube mode to assess the effect of CH4 concentration. This work establishes the first high-enthalpy giant planet entry test bed in Europe.

Experimental Observations on Film Cooling Effectiveness on Aerodynamic Heating in Hypersonic Flow

An experimental campaign was carried out to examine the effectiveness of film cooling on aerodynamic heating at hypersonic velocities. A flat-faced cylindrical model was tested at flow velocity of 2.5 km/s in a hypersonic shock tunnel. The test model was equipped with temperature sensors for convective heat flux measurement. The coolant gas, nitrogen, was injected through a 2 mm orifice housed at the center of the test model at different pressure ratios. Two different flow regimes were observed, steady and unsteady, with the steady flowfield having overall reduction in heat transfer compared to the unsteady one.

Simulation of temperature field in steel billets moving in the reheating furnace by a meshless method

A simulation of a reheating furnace in a steel production line where the steel billets are heated from room temperature up to 1200 °C is carried out. In this work, governing equations are solved in a strong form by the meshless local radial basis function collocation method (LRBFCM) with explicit time-stepping. The solution of the diffusion equation for the temperature is formulated on a two-dimensional central slice of the billet. The temperature field is solved by considering the positions of multiple billets in the furnace and the radiative and convective heat fluxes on the boundaries of the furnace and the billets. Ray tracing procedure, in which the view factors are computed with a Monte-Carlo method, is employed to determine the radiative heat flux. A sensitivity study is performed on the influence of two different stopping times of the billets in the furnace on the temperature evolution.