Dominant Convection Research Articles

Mechanisms of flame spread over convex polymethyl methacrylate building material

Polymethyl methacrylate (PMMA) is a widely used combustible building material in convex structures, such as highway sound barriers and building façades. However, most flame spread studies focus on flat surfaces. This study investigates flame spread along convex surfaces through a series of burning experiments with varying curvatures and widths. The average path flame spread rate increases along with a bigger curvature and width. By introducing a dimensionless average path flame spread rate, an empirical correlation linking the average path flame spread rate with sample width and curvature is proposed. In reality, flame spread over convex surface exhibits a distinct time-varying process. For a large curvature, the transition of the flame shape from a wall-fire regime to a pool-fire regime is observed during the process. Moreover, as curvature and width increase, the flame spread transitions from a two-stage process (regime I) to a three-stage process (regime II). In regime II, the transient flame spread rate initially decreases, then increases, and finally decreases again. This behavior is due to the shift from convection dominance to radiation dominance, although radiant heat transfer significantly influences regime I as well. During this transition, a two-peak phenomenon in radiant heat flux emerges, indicating the onset of regime II. Based on this phenomenon, a power-law correlation between curvature and sample width as the critical criterion for triggering regime II is determined. The results of this study have implications concerning the fire safety design of buildings.

Spatially and temporally high-order dynamic nonlinear variational multiscale methods for generalized Newtonian flows

Non-Newtonian fluids are of interest in industrial sectors, biological problems and other natural phenomena. This work proposes rheologically-dependent, spatially and temporally high-order non-residual stabilized finite element formulations. The accuracy of the methods is assessed by tackling highly-convective time-dependent power-law flows. The spatial approximation uses Lagrangian finite elements up to fourth order. The temporal integration is done via backward differentiation formulas of order one, two and three. A key aspect of our work is using a non-residual orthogonal variational multiscale (VMS) formulation to stabilize dominant convection and to allow equal-order interpolation of velocity and pressure. Our VMS method uses dynamic nonlinear subscales, which have not been tested so far for generalized Newtonian fluids. In this work, the use of high-order temporal discretizations for the subscale components is systematically evaluated. Numerical experiments consider the flow over a confined cylinder for Reynolds numbers between 40 and 400 and power-law indices between 0.4 and 1.8. Numerical testing demonstrates the method to be stable in all combinations of spatial and temporal orders. Our results show that using high-order spatial discretizations more accurately approximates boundary layers and viscosity fields. Moreover, higher temporal orders allow using larger time steps while still capturing highly dynamic behaviors with better resolution in frequency spectra.

Thermal performance of nanofluid natural convection magneto-hydrodynamics within a chamber equipped with a hot block

In this study, flow and free convection thermal performance within a chamber in the presence of a permanent magnetic field are simulated. Boussinesq approximation and the Lorentz force equation are used for the density variation in free convection, and the magnetic field, respectively. The steady-state, two-dimensional, and incompressible governing equations are simulated using the Semi-Implicit Method for Pressure Linked Equations (SIMPLE). The present study is simulated for different Rayleigh numbers (Ra) corresponding to the situation where the conduction mechanism was predominant (Ra = 100) and the convection heat transfer was predominant (Ra = 105). Also, different intensities of the magnetic field (0 ≤ Ha ≤ 40) and different directions of the magnetic field along with the effects of three different nanoparticles Ag, Cu, and Al2O3 are given. The present study showed that in the case of the dominant convection mechanism, the presence of the magnetohydrodynamics (MHD) condition decreases the Nusselt number (Nu). However, if the conduction is predominant, the applied magnetic field improves the average Nu number. The optimum state for the magnetic field strength was found in the low Rayleigh number. The presence of nanoparticles also intensifies the magnetic field effects. In the high Rayleigh number, the heat transfer rate reduces by 13.5% with the increase of the Hartmann number.

Numerical Study on the Impact of the Richardson Number on Convection in an Enclosure, with Moving Sidewalls for Three Aspect Ratios: A = 1, 2 and 0.5

Using mathematical models, this research investigation seeks to explore how varying aspect ratios and the Richardson number impact the mixing effectiveness, fluid flow velocity, and heat transfer characteristics in a rectangle-shaped space where cooling occurs along the sides and warm with a steady temperature exists throughout the 80% of the bottom section's center. Discretizing the governing equations through the finite volume approach, we solved them iteratively using the Tri-diagonal Matrix Algorithm, where pressure-velocity coupling was successfully implemented via the SIMPLER procedure. Innovative approaches for convection and diffusion terms involved employing a power-law difference scheme alongside a central differential scheme. In various simulations with specified parameters (Re = 100, Pr = 0.71), we visualized results in forms like streamlines, isothermal lines, and temperature/velocity profiles, along with local and average Nusselt numbers. We observe five unique structure formations during flow behavior by analyzing how Richardson numbers impact heat transmission within a specific geometric configuration (enclosure size A = 1). A change in aspect ratio leads to improved control over fluid movement while minimizing structural distortion. A subtle rise in heat transmission emerged as the average Nusselt number and Richardson number intersection strengthened force convection's domination while experiencing significant escalation under conditions conductive to natural convection. Decreasing the aspect ratio increased heat transfer efficiency when the Richardson number rose.

Simulation of Corner Solidification in a Cavity Using the Lattice Boltzmann Method

This study investigates corner solidification in a closed cavity in which the left and bottom walls are kept at a temperature lower than its initial temperature. The liquid material in the cavity initially lies at its phase transition temperature and, due to cold boundary conditions at the left–bottom walls, solidification starts. The simulation of corner solidification was performed using a kinetic-based lattice Boltzmann method (LBM), and the tracking of the solid–liquid interface was captured through the evaluation of time. The present investigation addresses the effect of natural convection over conduction across a wide range of higher Rayleigh numbers, from 106 to 108. The total-enthalpy-based lattice Boltzmann method (ELBM) was used to observe the thermal profiles in the entire cavity with a two-phase interface. The isotherms reveal the relative dominance of natural convection over conduction, and the pattern of interface reveals the effective growth of the solidified layer in the cavity. To quantify the uniformity of cooling, a coefficient of variation (COV) for the thermal field was calculated in the effective solidified zone at a wide range of Ra. The results show that the value of COV increases with Ra and reduces with time. The thermal instability in the flow field is also quantified through FFT analyses.

Numerical study on phase change propulsion mechanism of thermal underwater glider based on spectral method

The thermal underwater glider’s propulsion power is provided by the phase change energy storage tube. To improve the propulsion performance of the glider, it is essential to study the phase change heat transfer characteristics. This work proposes a collocation spectral method to handle the spatial derivative term and introduces a fourth-order Runge-Kutta method to handle the time derivative term. The temperature distribution and liquid volume fraction of the phase change material in the energy storage tube were numerically simulated under specific boundary conditions. The simulation results were then compared to the experimental data, and a good agreement was observed.Based on these findings, the impact of incoming free stream velocity and temperature difference intensity on phase change within the vessel was examined. The results underscored the dominance of convection in solid–liquid phase change and identified key factors influencing phase change in scenarios with Stefan numbers below 0.1342. Additionally, the study highlighted the limitations of fixed-value approximations and the nonlinear nature of phase change over time. These insights provide valuable guidance for developing phase change devices that harness volumetric potential energy aboard underwater thermal gliders.

A mixed finite element spatial discretization scheme and a higher‐order accurate temporal discretization scheme for a strongly discontinuous electromagnetic interface condition in ideal sliding electrical contact problems

AbstractSliding electrical contact involves multiple conductors sliding in contact at different speeds, with current flowing through the contact surfaces. The Lagrangian method is commonly used to describe the electromagnetic field in order to overcome the trouble of convective dominance, especially in high‐speed sliding electrical contact problems. However, to maintain correct field continuity, magnetic vector potential and scalar potential taken as variables cannot be continuous simultaneously at the ideal sliding electrical contact interface. This involves a strongly discontinuous condition for variables. Further, commonly used spatial–temporal discretization algorithms are invalid, for example, the classic finite element (CFEM) framework does not allow discontinuous variables, and the backward Euler method in time domain introduces a significant interface error source associated with the velocity of relative motion. To accurately handle strongly discontinuous conditions in numerical calculations, a mixed nodal finite element scheme and a higher‐order accurate temporal discretization scheme are introduced. In this scheme, classical finite element method is performed in each subdomain, and the derivative terms at the boundary are added as new variables. The effectiveness and accuracy of the above methods are verified by comparing them with a standard solution in a two‐dimensional railgun model and analyzing the current density distribution in a three‐dimensional railgun model.

Error Analysis of the Classical Artificial Diffusion Weak Galerkin Finite Element Method for the steady state- convection diffusion-reaction Equation in 2-D

In this study, we modified the error in the weak Galerkin method when solving problems in which diffusion is the dominant convection( h) in two dimensions. This is done by adding the artificial diffusion term (-δΔw, where δ=h-ϵ). The finite element method for discrete functions using a weakly defined gradient operator is presented in this study. The concept of the weak discrete gradient is introduced, which plays an important role when using numerical methods to solve partial differential equations. The goal of this study is to enhance the accuracy and stability of the solutions by studying the ellipticity and stability properties of the method, which works to ensure that the numerical method retains the properties of the original equation while reducing the fluctuations occurring with the weak galerkin finite element method. Specific theories have been used to estimate the error in parameters -norm, and . Practical examples demonstrate how this method improves the handling of partial equations characterized by convection-dominated diffusion, enhancing its potential for advancing numerical simulations in engineering and physics.

SUPG-based stabilized finite element computations of convection-dominated 3D elliptic PDEs using shock-capturing

This study is interested in stabilized finite element computations of advection-dominated convection–diffusion-type partial differential equations. The governing equations are assumed to be defined on the 3D unit cube and stationary. Towards that end, we stabilize the standard (Bubnov–) Galerkin finite element method (GFEM), which typically suffers from yielding numerical approximations polluted with node-to-node nonphysical oscillations in convection dominance, by employing the streamline-upwind/Petrov–Galerkin (SUPG) formulation. In order to achieve better shock representations near sharp layers, the SUPG-stabilized formulation is also enhanced with a simple and residual-based shock-capturing mechanism, the so-called YZβ technique. Several test computations are performed to assess the efficiency and robustness of the proposed formulation. The test problems are examined under more challenging conditions than those previously studied in the literature, i.e., for flows substantially dominated by convection phenomena. The numerical results and comparisons demonstrate that the SUPG-YZβ combination significantly eliminates both globally spread and localized numerical instabilities. Beyond that, the proposed formulation accomplishes that by using only linear elements on relatively coarser meshes and without making use of any adaptive mesh strategies.

An efficient method for modelling thermal energy storage in packed beds of spherically encapsulated phase change material

An approach for modelling melting (and solidification) in packed beds of encapsulated spherical PCM is presented. The approach includes a calibration step based on comparisons of simulations with experimental results of PCM melting in a cylindrical geometry, followed by detailed simulations of melting in an isolated encapsulated PCM sphere and a PCM sphere in a representative elemental volume of packed PCM spheres to study the impact of external flow conditions on PCM heating and melting. The detailed simulations show that the enthalpy-porosity model provides a reasonable estimate of the overall melting time and a good approximation of the evolution of the liquid/solid melt front during the melting process. The simulations also confirm the dominance of convection during most of the melting process. The temporal integral results of overall heat transfer coefficient and overall energy fraction from the detailed simulations are combined to yield a relationship between overall heat transfer coefficient and overall energy fraction such that the process can be modelled in terms of the condition inside the encapsulated PCM sphere, wherein the condition can also be obtained from the fraction of heat absorbed compared to the energy capacity of the PCM sphere. This relationship is then used as an input to a finite-volume model for packed beds which can be used to predict the charging time of entire packed beds of encapsulated spherical PCM. Results from the simple model show correct trends for the temporal evolution of liquid fraction and PCM temperature, and for overall charging times for the cases considered. This simple approach can substantially reduce the simulation time required to model beds of different shaped encapsulated PCMs and different dimensions.

Специальная разностная схема для решения жестких краевых задач конвективно-диффузионного переноса

The convective-diffusion transfer equation is often found in problems of hydromechanics and heat and mass transfer. The dominance of convection over diffusion and the change in sign of the coefficient at the first derivative lead to the formation of boundary and internal layers with high gradients of the function. This creates serious difficulties in numerical analysis of the problem using traditional difference schemes. The traditional method of approximating the first derivative using central differences at high Peclet numbers can lead to oscillations and violate the monotonicity of the numerical solution. To avoid this problem, it is necessary to significantly reduce the size of grid cells in narrow areas with large gradients of the unknown function. The use of one-sided differences significantly smears the desired solution, due to the viscosity of the scheme, and leads to loss of accuracy. The practical need to solve stiff boundary value problems requires the development and use of computational technologies that guarantee monotonicity, accuracy, and cost-effectiveness in numerical analysis. In this paper, a new special difference scheme is proposed for the numerical solution of a stiff equation of convective-diffusion transfer. The dominant convective term is eliminated from explicit consideration by transforming the equation into self-adjoined form, which permits the use of well-known numerical approximation techniques. The control volume method is used to construct a difference analogue of a differential equation on a three-point template. The resulting scheme is monotonic and conservative. The test examples show great possibilities of the proposed difference scheme for large Peclet numbers on coarse grids in solving stiff boundary value problems of convective diffusion transfer.

Vapor Cloud Behavior of Heavier-Than-Air Hydrocarbon Liquid Evaporating From a Microliter Volume Heated Well Cavity

Abstract Detailed characterization of the vapor cloud above a well or reservoir is not available in literature irrespective of its several practical importance. This study aims to understand the vapor cloud characteristics and vapor phase transport of a heavier-than-air vapor cloud evaporating from a heated microliter circular reservoir. Evaporation of a heavy hydrocarbon (cyclohexane) and a comparatively lighter fluid (ethanol) is studied. Digital holographic interferometry has been used for the characterization of vapor cloud. Gravimetric analysis is used for measurement of evaporation rate from the reservoir. A flat disk-shaped vapor cloud is observed in both heated and nonheated reservoir cases. This is attributed to the presence of radial outward natural convection. The evaporation rate is underpredicted by the diffusion model at a higher Grashof number, i.e., for well heating. Solutal convection dominates near the interface region and thermal convection effect increases in the region away from the liquid–vapor interface. The mole fraction profile depends on the relative strength of the thermal and solutal Grashof number. Thermal convection effect is stronger in lighter vapor of ethanol compared to that of cyclohexane. Overall, this study shows dominance of solutal convection on the vapor cloud characteristics above both heated and unheated reservoir.

The moving finite element method with streamline-upwind Petrov–Galerkin for magnetohydrodynamic flows problems at high Hartmann numbers

It is widely acknowledged that both the streamline-upwind Petrov–Galerkin (SUPG) method and moving mesh method can enhance the stability of finite element method in solving convection-dominated convection–diffusion problems. However, in the case of strong convection-dominated conditions, they still exhibit numerical oscillations and the solutions will not even converge. In order to address similar phenomena observed in solving magnetohydrodynamic (MHD) flow problems at high Hartmann numbers with strong convective dominance, the MHD equation was first decoupled into two convection–diffusion equations. Subsequently, a new approach called the moving mesh streamline-upwind Petrov–Galerkin method (MM-SUPG) was proposed by coupling the moving mesh technique with SUPG method. The MM-SUPG method contains two independent part: the finite element method with SUPG for solving the decoupled MHD equation and a mesh-redistribution algorithm. To verify its effectiveness for solving the MHD equation at high Hartmann number, a classical MHD fluid flow problem was numerically tested using both the MM-SUPG method and the moving finite element method (MFEM). Compared to the MFEM, the proposed method not only yields stable numerical solutions under strong convective dominance while reducing unnecessary false oscillations, but also improves calculation accuracy to some extent using the same mesh.

Design and Mixing Analysis of a Passive Micromixer Based on Curly Baffles.

A novel passive micromixer based on curly baffles is proposed and optimized through the signal-to-noise analysis of various design parameters. The mixing performance of the proposed design was evaluated across a wide Reynolds number range, from 0.1 to 80. Through the analysis, the most influential parameter was identified, and its value was found to be constant regardless of the mixing mechanism. The optimized design, refined using the signal-to-noise analysis, demonstrated a significant enhancement of mixing performance, particularly in the low Reynolds number range (Re< 10). The design set obtained at the diffusion dominance range shows the highest degree of mixing (DOM) in the low Reynolds number range of Re< 10, while the design set optimized for the convection dominance range exhibited the least pressure drop across the entire Reynolds number spectrum (Re< 80). The present design approach proved to be a practical tool for identifying the most influential design parameter and achieving excellent mixing and pressure drop characteristics. The enhancement is mainly due to the curvature of the most influential design parameter.

Half boundary method for two-dimensional steady-state nonlinear convection-diffusion equations

In this research, half-boundary method (HBM) is developed for nonlinear convection-diffusion equations (CDEs) which play an important role in applied mathematics and physics. The HBM is based on the variable relationship between the nodes inside the domain and the nodes on half of the boundaries, making it ideal for reducing the maximum order of matrix and calculation memory storage. Besides, the HBM can solve discontinuous problems directly without adding continuity conditions due to the use of the mixed variables. The effectiveness and accuracy of the proposed algorithm are investigated mainly for the two-dimensional(2D) steady-state Burgers’ equation, the material nonlinear 2D CDEs and the system of 2D Burgers’ equations. The results show the excellent performance of the HBM in simulating flow and heat transfer, especially for convection domination.

Experimental investigation of power transient flow boiling

To advance the mechanistic understanding of power transients in flow boiling, experimental investigations are performed to capture the thermal response of four different kinds of cladding materials, including FeCrAls, to Fuchs reactivity initiated accident transients and linear ramp power transients. The transition boiling regime is phenomenologically reflected in power-transient flow boiling, which is different from steady-state boiling. In light of this, the critical heat flux that is usually featured with temperature overshooting does not indicate thermal safety margin of cladding materials as conservatively as the maximum heat flux, which is greater than critical heat flux in the power transient boiling curve. This is physically attributed to the thermal energy deposition on the cladding wall. In addition, the thermal energy released from the cladding wall results in different boiling heat transfer coefficient for the decreasing and increasing power stages respectively during the Fuchs power transient. The maximum heat flux difference gap, which appears due to changes in cladding materials and transient time scales, is appreciable under an intermediate heat convection regime. However, this difference gap is gradually weakened by the progressive increasing of mass flux and/or inlet subcooling due to the enhanced dominance of heat convection over heat conduction. The small difference gap of maximum heat flux is found to be insignificant under the weak heat convection because of power transient induced annular flow instability.

Analysis of continuous data assimilation scheme for the Navier–Stokes equations using variational multiscale method

In this study, we analyse a continuous data assimilation (CDA) scheme which enables us to combine an observable data with a numerical method to obtain better solutions in which these solutions are also closely similar to the current state of the system. The scheme is applied on a Navier–Stokes system which is discretized with two-step Backward Differentiation Formula (BDF2) in time and finite element in space. In order to improve the accuracy and prevent some non-physical oscillations due to the effect of small viscosity and the dominance of convection, a projection based variational multiscale method (VMS) has also been applied to the system. We present the long-time stability and long-time convergence analyses of the scheme in details and several numerical tests in order to support theoretical findings and demonstrate the promise of the method.

Experimental study on interaction mechanism on the mass burning rate in two n-heptane fires with cross airflows

This work aims to interpret the flame interaction mechanisms of the mass burning rates of two pool fires in a cross-airflow. The flame morphology, mass burning rate, and heat feedback components are measured. The results show that the mass burning rates of the two pool fires increase rapidly, then decrease, and finally increase slowly with wind speed. Owing to the blockage and air entrainment restriction effect of the upstream flame on cross airflow, the critical transition (from increasing to decaying) of the mass burning rate of the downstream flame corresponds to a relatively larger cross airflow speed under the same experimental conditions. In general, with increasing fire spacing, the dominant mechanism of flame interaction transitions from interactive blockage and air entrainment restriction to heat feedback enhancement to monopolar blockage and air entrainment restriction. The process of the primary control mechanism from radiation dominance to convection dominance with the increase of airflow speed is revealed. Finally, based on the stagnant layer theory, a model of the mass burning rates is developed for the convection-dominated multiple pool fires in the non-merging stage.

Characterizing burning behavior of biomass fuels with discrete distribution

Discrete distribution of biomass fuels is an important configuration for the implication of wildland fire. In this study, flame spread and burning behaviors were examined by designing 90 groups of birch array geometries. Five inclination angles (denoted by θ, 15°−90°), three spacings (S, 3 mm, 6 mm, and 9 mm), and five column numbers (n, 3–11) were varied. Flame spread behavior is characterized by three regimes, a steady fire (regime Ⅰ), a growing fire (regime Ⅱ), and a fast-developed fire (regime III). Correlations of determining flame spread regime are proposed. Under these regimes, mass loss rate per unit area (ṁ″) has a power-law dependency on porosity (φ), where the power-law index increases from regime Ⅰ, Ⅱ to regime III. In the regime III, ṁ″ is independent of φ when φ > 1.6 mm. The three spread regimes are attributed to the transition of the controlling mechanism from radiation to convection dominance. Moreover, by introducing the total mass transfer number BT, the influence of the controlling mechanism is classified into two regions, radiation dominance (region I) and convective dominance (region II), in which the three flame spread regimes are evaluated.

Error analysis of a SUPG-stabilized POD-ROM method for convection-diffusion-reaction equations

A reduced order model (ROM) method based on proper orthogonal decomposition (POD) is analyzed for convection-diffusion-reaction equations. The streamline-upwind Petrov–Galerkin (SUPG) stabilization is used in the practically interesting case of dominant convection, both for the full order method (FOM) and the ROM simulations. The asymptotic choice of the stabilization parameter for the SUPG-ROM is done as proposed in the literature. This paper presents a finite element convergence analysis of the SUPG-ROM method for errors in different norms. The constants in the error bounds are uniform with respect to small diffusion coefficients. An approach for a posteriori error estimation is discussed. Numerical studies illustrate the performance of the SUPG-ROM method.