Three-dimensional Direct Numerical Simulations Research Articles

Wall-bounded thermal turbulent convection driven by heat-releasing point particles

In this work we investigate the thermal convection driven by heat-releasing point particles. Three-dimensional direct numerical simulations are conducted for$1\times 10^7\le {\textit {Ra}} \le 1\times 10^{10}$and$0.01\le {\textit {St}} \le 10$, where the Rayleigh number${\textit {Ra}}$and Stokes number${\textit {St}}$measure the strengths of the heat releasing rate and the Stokes drag, respectively. A regime at intermediate Stokes numbers is identified with most particles accumulating into the top boundary layer region, while for other cases particles are constantly advected over the entire domain. For the latter state, the flow motions are stronger at the upper part of the domain. The thicknesses of both momentum and thermal boundary layers at the top plate follow the same scaling law with${\textit {Ra}}$and show minor dependences on${\textit {St}}$. The volume-averaged temperature and convective flux exhibit non-monotonic variations as${\textit {St}}$increases and reach their minimums at intermediate${\textit {St}}$. The fraction coefficient of heat flux, i.e. the ratio between the heat flux through the bottom plate and the total flux through both plates, shares the similar dependence on${\textit {St}}$as the convective flux. The relation between these scaling laws can be explained by using the global balance between the dissipation and convective flux. The scaling laws for the transition between different flow regimes are also proposed and agree with the numerical results. The preferential concentration of particles is observed for all cases and is strongest at intermediate Stokes numbers, for which multiscale clustering emerges with small clusters forming larger ones.

Oblique-mode breakdown of the vertical buoyancy layer

The O-type transition caused by a pair of small-amplitude oblique waves in a vertical buoyancy layer of a fluid with Prandtl number $0.71$ at a Reynolds number of $200$ is investigated using linear stability analysis and three-dimensional direct numerical simulation. The small-amplitude oblique waves experience linear growth and undergo nonlinear interactions to generate streamwise vortices/streaks, two-dimensional streamwise waves and harmonic oblique waves. The streamwise vortices/streaks and two-dimensional streamwise waves have twice the spanwise or streamwise wavenumber of the original perturbation, respectively. Unlike the O-type transition in isothermal flat-plate incompressible and compressible boundary layers where streaks dominate the transition, in the vertical buoyancy layer, either streaks or two-dimensional streamwise waves can dominate the flow field during the early stages of oblique transition. The growth rates of streaks and two-dimensional waves are dependent on the wavenumber of the initial oblique waves. Streaks dominate the flow for high streamwise wavenumbers, while two-dimensional streamwise waves dominate the flow for low streamwise wavenumbers. Analysis of the turbulent kinetic energy production and the Reynolds stresses reveals that the early stages of the transition differ depending on the wavenumber of the oblique waves. An increase in the initial amplitude of the oblique waves causes a faster transition from laminar flow; however, the growth rates of the streaks and two-dimensional streamwise waves are independent of the initial amplitude. Even though different modes are dominant during the early stages of the O-type transition, the onset of chaotic flow is caused by the breakdown of streak modes.

A Comparison between Statistical Behaviours of Scalar Dissipation Rate between Homogeneous MILD Combustion and Premixed Turbulent Flames

Three-dimensional Direct Numerical Simulations (DNS) data has been utilised to analyse statistical behaviours of the scalar dissipation rate (SDR) and its transport for homogeneous methane-air mixture turbulent Moderate or Intense Low oxygen Dilution (MILD) combustion for different O2 dilution levels and turbulence intensities for different reaction progress variable definitions. Additional DNS has been conducted for turbulent premixed flames and passive scalar mixing for the purpose of comparison with the SDR statistics of the homogeneous mixture MILD combustion with that in conventional premixed combustion and passive scalar mixing. It has been found that the peak mean value of the scalar dissipation rate decreases with decreasing O2 concentration for MILD combustion cases. Moreover, SDR magnitudes increase with increasing turbulence intensity for both MILD and conventional premixed combustion cases. The profiles and mean values of the scalar dissipation rate conditioned upon the reaction progress variable are found to be sensitive to the choice of the reaction progress variable definition. This behaviour arises due to the differences in the distributions of the species mass fractions within the flame. The strain rate contribution and the molecular dissipation term are found to be the leading order contributors in the scalar dissipation rate transport for MILD combustion; whereas, in conventional premixed flames, the terms rising from density variation and reaction rate gradient also play leading roles in addition to the strain rate and molecular dissipation contributions. By contrast, the terms due to density gradient and reaction rate gradient remain negligible in comparison to the leading order contributors in MILD combustion cases due to small density variation because of moderate temperature rise and small reaction rate gradient magnitudes. Furthermore, the qualitative behaviour of the strain rate contribution to the SDR transport in premixed flames is significantly different to that in the case of MILD combustion and passive scalar mixing. The findings of the current analysis indicate that the scalar dissipation rate statistics in MILD combustion show several qualitative similarities to the passive scalar mixing despite major differences with the SDR transport in conventional turbulent premixed flames. This further suggests that the scalar dissipation rate models, which were originally proposed in the context of passive scalar mixing, have the potential to be applicable for MILD combustion but the models for the premixed turbulent combustion may not be applicable for MILD combustion of homogeneous mixtures.

Analysis of the Evolution of the Surface Density Function During Premixed V-Shaped Flame–Wall Interaction in a Turbulent Channel Flow at Reτ = 395

ABSTRACT The flame–turbulence interaction and statistical behavior of the surface density function (SDF; i.e. magnitude of the reaction progress variable gradient) in the vicinity of the wall for a stoichiometric methane-air flame are investigated using a three-dimensional direct numerical simulation of a turbulent premixed V-flame interacting with an isothermal inert wall in a fully developed turbulent channel flow at a friction Reynolds number . The results show that the mean SDF significantly decreases in the viscous sublayer in comparison to the corresponding values for the same reaction progress variable in the unstretched laminar flame. Moreover, the mean values of SDF for a given value of reaction progress variable decrease in the downstream direction with the progress of flame quenching in all zones of turbulent boundary layer. The effective normal strain rate (), which acts to reduce the SDF as it increases, is much higher in the viscous sublayer than in the other layers. In the viscous sublayer, the contribution of the gradient of displacement speed in the flame-normal direction () to has been shown to dominate the fluid-dynamic normal strain rate (). This tendency is qualitatively similar to the previous findings for a V-flame interacting with an isothermal inert wall at . However, the maximum mean value of at is approximately twice of that at , which causes a sharper drop in the SDF in the viscous sublayer at higher .

Experimental and numerical investigation of bistability in rotating permanent magnet-generated electrolyte flow in a ring-shaped container

Here, the stability of a transversely magnetized rotating permanent magnet-generated flow in a concentric cylindrical ring channel is studied. Numerical calculations show that the steady-state solution becomes asymmetric through a pitchfork bifurcation at a Reynolds number (Re) of 60. The two new antisymmetric steady-state solutions become cyclic at Re = 90. Nonlinearities develop at larger Re values and the limit cycle solutions are destabilized at Re = 250, enabling random transition events between the two pitchfork branches. Such transitions have been observed in all kinds of natural phenomena, spanning from neuroscientific to astrophysical systems, which are often too complex to be directly computed. Our presented system is physical yet simple enough to be used to conduct a parametric study with full three-dimensional direct numerical simulations. It raises the possibility of numerically and experimentally analyzing transitions in more detail. Experimental measurements indicated the existence of long-lived states and suitability for the proposed system for future studies of such phenomenon. However, the experimental results did not conclusively observe bistability.

The lift force on deformable and freely moving bubbles in linear shear flows

This paper provides a comprehensive explanation for the lift force acting on a freely deformable bubble rising in a linear shear flow and examines how the lift force scales with the undisturbed shear rate in cases governed by different lift force mechanisms. Four distinct flow mechanisms are identified from previous studies, and the associated bubble-induced vorticity dynamics are outlined. We provide a theoretical framework to qualitatively explain the lift force acting on a bubble in terms of moments of the bubble-induced vorticity. We support our theoretical framework with three-dimensional multiphase direct numerical simulations to illustrate how the vorticity dynamics associated with the four mechanisms generate the lift force. These findings provide a comprehensive explanation for the behaviour of the lift force in a wide range of relevant governing parameters. Additionally, our simulation results show how differently the lift force scales with the shear rate, depending on the dominating lift force mechanism. These results indicate that the shear rate should, in general, be accounted for in highly viscous flows (low Galilei numbers) or at significant bubble deformations (moderate-to-high Eötvös numbers) when modelling the lift force coefficient.

Flow rate–pressure drop relations for new configurations of slender compliant tubes arising in microfluidics experiments

We investigate the steady-state fluid–structure interaction between a Newtonian fluid flow and a deformable microtube in two novel geometric configurations arising in recent microfluidics experiments. The first configuration is a cylindrical fluidic channel surrounded by an annulus of soft material with a rigid outer wall, while the second one is a cylindrical fluidic channel extruded from a soft rectangular slab of material. In each configuration, we derive a mathematical theory for the nonlinear flow rate–pressure drop relation by coupling lubrication theory for the flow with linear elasticity for the inner tube wall’s deformation. Using the flow conduit’s axial slenderness and its axisymmetry, we obtain an analytical expression for the radial displacement in each configuration from a plane-strain configuration. The predicted displacement field, and the resulting closed-form flow rate–pressure drop relation, are each validated against three-dimensional direct numerical simulations via SimVascular’s two-way-coupled fluid–structure interaction solver, svFSI, showing good agreement. We also show that weak flow inertia can be easily incorporated in the derivation, further improving the agreement between theory and simulations for larger imposed flow rates.

Influence of equivalence ratio on turbulent burning velocity and extreme fuel consumption rate in lean hydrogen-air turbulent flames

• The extreme fuel consumption rate (FCR) exhibits a high degree of universality. • The time-averaged extreme values are very close to the peak critically strained laminar flames. • This work supports a corner-stone hypothesis of the leading point concept of premixed turbulent burning. Unsteady three-dimensional Direct Numerical Simulations of seven statistically one-dimensional, planar, highly turbulent, complex-chemistry, lean H 2 -air flames are performed using either mixture averaged or equidiffusive model of molecular transport. The equivalence ratio is varied from 0.35 to 0.70 and the Karlovitz number Ka is varied from 3 to 565. Normalized turbulent burning velocities U T /S L are strongly increased when using the mixture-averaged model, with an increase by a factor of 4.1 being documented even at Ka as high as 565. Here, S L is the laminar flame speed. Moreover, the increase in U T /S L is significantly more pronounced in leaner flames, which are characterized by a thinner reaction zone and a larger Zel’dovich number. Furthermore, U T /S L is increased by the turbulence length scale. The extreme (maximum over the computational domain at a single instant) local values of fuel consumption rate (FCR) exhibit a high degree of universality, i.e., in all studied cases and at all instants, these rates are close to the peak values of FCR obtained from the counterpart critically strained, twin, counter-flow laminar premixed flames. This finding appears to directly support a corner-stone hypothesis of the leading point concept of premixed turbulent burning, thus, suggesting the use of characteristics of the critically strained laminar premixed flames as input parameters for models of turbulent combustion of lean H 2 /air mixtures.

Multiple Mapping Conditioning Mixing Time Scales for Turbulent Premixed Flames

A novel multiple mapping conditioning (MMC) mixing time scale model for turbulent premixed combustion has been developed. It combines time scales for the flamelet and distributed flame regimes with the aid of a blending function. The blending function serves two purposes. Firstly, it helps to identify zones where the premixed flame resides and where the time scale associated with the premixed flame shall be used. Secondly, it uses the Karlovitz number to identify the turbulent premixed combustion regime and to reduce the weighting of the premixed flame time scale if Karlovitz numbers are high and deviations from the flamelet regime are expected. A series of three-dimensional direct numerical simulations (DNS) of statistically one dimensional, freely propagating turbulent methane-air flames provides a wide range of turbulent combustion regimes for the mixing model validation. The new mixing time scale provides correct predictions of the flame speed of freely propagating turbulent flames which could not be matched by most recognized mixing models. The turbulent flame structure predicted by the new model is in good agreement with DNS for all combustion regimes from flamelet to the thickened reaction zone.

Effects of molecular diffusion modeling on turbulent premixed NH[formula omitted]/H[formula omitted]/air flames

Ammonia (NH3) is a promising carbon-free energy carrier and can be used as a fuel in gas turbines for power generation. Using a blend of NH3 and hydrogen (H2) has the potential to address the poor combustion properties of NH3/air mixtures. Predictive modeling of the NH3/H2 combustion process requires a clear understanding of molecular diffusion due to the high diffusivity of H2. While the effects of molecular diffusion modeling (MDM) have been extensively investigated in laminar/turbulent hydrocarbon and pure H2 flames, comparatively less investigations have been made to explore the impact of MDM on turbulent premixed NH3/H2/air combustion characteristics as well as NO emission. To this end, four three-dimensional direct numerical simulations of temporally evolving turbulent premixed NH3/H2/air jet flames are performed in this work considering MDM methods of increased complexity: 1) unity Lewis number (UL); 2) unity Lewis number with Soret effect (UL+S); 3) mixture-averaged diffusion with Soret effect (MA+S); and 4) full multicomponent diffusion with Soret effect (MC+S), respectively. The emphasis is placed on assessing MDM effects on flame structure, NO production, and combined role of MDM and stretch rate. Comparing MA+S with UL+S under both laminar and turbulent conditions indicates that the differential diffusion effect is significantly suppressed in the turbulent NH3/H2/air flames considered here. While MDM can affect the local equivalence ratio, it is found that the choice of the MDM method has a negligible impact on the major species and NO distribution conditioned on progress variable, as well as on critical reactions. However, MDM still shows a notable impact on NO production and turbulent flame speed. Specifically, from the most detailed model (MC+S) to the most simplified model (UL), the NO production speed decreases by 30% for the fuel pathway but increases by 338% for the thermal pathway; simultaneously, the global turbulent flame speed decreases by 18%. Furthermore, it is found that both NO mass fraction and local displacement speed are very sensitive to flame curvature and strain, while MDM has a negligible impact on the responses of normalized NO mass fraction and local displacement speed to the change in flame curvature or strain. This suggests that the effects of curvature and strain should be included in flamelet-based models to accurately predict NO emission and NH3/H2/air flame propagation, even when using the assumption of unity Lewis number.

The effects of turbulence on the flame structure and NO formation of ammonia turbulent premixed combustion at various equivalence ratios

Ammonia is carbon-free and is regarded as a potential fuel to address global warming issues. In this work, three-dimensional direct numerical simulations (DNS) of ammonia/air turbulent premixed flames were performed to explore the influence of turbulence and equivalence ratio on the flame structure and NO formation characteristics. Two equivalence ratios were considered, i.e.ϕ = 0.9 and ϕ = 1.1. The general flame structures were presented and species distributions were examined. The NO mass fraction was found to be the highest in the product for the lean case and in the reaction zone for the rich case. The conditional mean values of species mass fractions and reaction rates were compared with those of the unstrained and strained laminar premixed flames to explore how well the laminar flame structures can approach those of the turbulent flame. The budget analysis of the species transport equations showed that turbulent diffusion plays an important role in species transport. The turbulent diffusivity DT was estimated using the gradient hypothesis based on the DNS data. Various laminar flame simulations with different diffusivities were carried out. It was shown that the conditional means of the DNS agree well with those of the laminar flames including DT in the transport property calculation. The global and local NO formation characteristics were investigated. It was found that the mean NO production conditioned on the progress variable is lower compared with the corresponding laminar flame in the rich case. However, the relative contributions from various NO pathways are rarely affected by turbulence. The NO mass fraction is higher in negative curvature regions compared with positive curvature regions of the flame surface for the rich case, which is due to the preferential diffusion of H2 and other radicals and the enhanced NO pathways in negatively curved regions.

DNS Of the ignition process of n-heptane/air premixed combustion with low-temperature chemistry in turbulent boundary layer

In the present work, three-dimensional direct numerical simulation (DNS) of n-heptane/air premixed combustion in turbulent boundary layer was performed to explore the near-wall ignition process with low-temperature chemistry. A reduced chemical mechanism with 58 species and 387 elementary reactions for n-heptane combustion was used in the DNS. The general characteristics of the ignition process near the wall were examined. It was found that low-temperature ignition (LTI) dominates the upstream region, and high-temperature ignition (HTI) appears in the downstream region. The ignition process and the low-temperature chemistry pathways of the DNS are compared with those of a corresponding laminar case. It was found that the ignition process was affected by turbulence, which results in thickened reaction zones. However, the carbon flow analysis of low-temperature chemistry showed that turbulence rarely affects the low-temperature chemistry pathway. The combustion modes of various regions were scrutinized based on the budget terms of species transport equations and the chemical explosion mode analysis (CEMA). It was shown that the reaction term of RO2 is significant during the LTI process of the upstream region, and the reaction terms of CH2O and CO2 are evident in the downstream region, indicating the occurrence of HTI. It was also shown that auto-ignition is dominant in the upstream region. With increasing streamwise distance, the contribution of flame propagation increases, which takes over that of auto-ignition in the near-wall region.

Plasma breakdown in bubbles passing between two pin electrodes

The ignition of plasmas in liquids has applications from medical instrumentation to manipulation of liquid chemistry. Formation of plasmas directly in a liquid often requires prohibitively large voltages to initiate breakdown. Producing plasma streamers in bubbles submerged in a liquid with higher permittivity can significantly lower the voltage needed to initiate a discharge by reducing the electric field required to produce breakdown. The proximity of the bubble to the electrodes and the shape of the bubbles play critical roles in the manner in which the plasma is produced in, and propagates through, the bubble. In this paper, we discuss results from a three-dimensional direct numerical simulation (DNS) used to investigate the shapes of bubbles formed by injection of air into water. Comparisons are made to results from a companion experiment. A two-dimensional plasma hydrodynamics model was then used to capture the plasma streamer propagation in the bubble using a static bubble geometry generated by the DNS The simulations showed two different modes for streamer formation depending on the bubble shape. In an elliptical bubble, a short electron avalanche triggered a surface ionization wave (SIWs) resulting in plasma propagating along the surface of the bubble. In a circular bubble, an electron avalanche first traveled through the middle of the bubble before two SIWs began to propagate from the point closest to the grounded electrode where a volumetric streamer intersected the surface. In an elliptical bubble approaching a powered electrode in a pin-to-pin configuration, we experimentally observed streamer behavior that qualitatively corresponds with computational results. Optical emission captured over the lifetime of the streamer curve along the path of deformed bubbles, suggesting propagation of the streamer along the liquid/gas boundary interface. Plasma generation supported by the local field enhancement of the deformed bubble surface boundaries is a mechanism that is likely responsible for initiating streamer formation.

Quantification of the Cross-helicity Turbulent Cascade in Compressible MHD Simulations

In plasma turbulence, energy and cross helicity are transferred across scales at a constant rate as a consequence of nonlinear interactions. In incompressible magnetohydrodynamics (MHD), the energy cascade rate of both quantities can be computed by means of the temporal evolution of second-order structure functions, known as Karman–Howarth–Monin (KHM) equations. In the present work, we derive the KHM equation to compute the energy cascade rate of cross helicity in compressible MHD. Using three-dimensional direct numerical simulations, we validate the equation and use it to measure the cross-helicity turbulence properties. Our results show a slower development of the cross-helicity cascade with respect to the energy one and the presence of inverse cascades of energy and cross helicity at large scales when in the presence of a strong mean field. We propose the relation of these phenomena with the longer duration of geomagnetic storms after the arrival of solar winds with large cross helicity and the observation of patchy inertial ranges displaying positive and negative cascade rates for certain solar wind intervals.

Large eddy simulation of a turbulent supercritical hydrothermal flame with a novel direct moment closure model

A novel direct moment closure (DMC) model has been developed in the context of large eddy simulation (LES) and applied to simulate a supercritical flame. To evaluate the performance of the model, three-dimensional direct numerical simulation (DNS) of a supercritical hydrothermal non-premixed jet flame is conducted. The characteristics of the ignition and propagation of the supercritical hydrothermal flame are analyzed, and then the a-priori analysis of the DMC model is carried out based on the DNS model data. It is found that the prediction of reaction rate can be remarkably improved by the DMC model compared with the laminar chemistry closure (LCC) model. In the a-posteriori study, LES of the turbulent supercritical hydrothermal flame with the DMC and LCC models have been performed and compared with the DNS data respectively. It turns out that the LES-DMC model can successfully reproduce the complex behaviors of the turbulent supercritical hydrothermal flame, and the predicted mean and rms values of velocities, temperature, and species are more accurate than those of the LES-LCC model.

Effects of water droplet injection on turbulent premixed flame propagation: a direct numerical simulation investigation

The influence of water droplet injection on the propagation rate of statistically planar stoichiometric n-heptane-air flames has been analysed based on three-dimensional carrier phase Direct Numerical Simulations for different turbulence intensities and different initially mono-sized droplets. It has been found that most water droplets do not completely evaporate within the flame due to their large latent heat of evaporation for the conditions considered here. Thus, the cooling effect due to the extraction of latent heat during the evaporation of water droplets dominates over the dilution of the concentration of reactants and gives rise to smaller reaction rate of reaction progress variable and thicker flame front than in the corresponding premixed turbulent flame without droplets. These effects (a) strengthen with decreasing droplet size due to higher rate of evaporation for smaller droplets, but (b) weaken with an increase in turbulence intensity. The interaction of water droplets with the flame affects the density-weighted displacement speed through its reaction and molecular diffusion components and the magnitudes of these components remain much greater than the components due to cross-scalar dissipation rate and two-phase coupling. The flame-water droplet interaction for the parameter range considered here acts to reduce the mean density-weighted displacement speed, consumption speed and turbulent flame speed, and this reduction becomes increasingly prominent with decreasing droplet diameter. However, it has been found that the presence of water droplets does not alter the qualitative nature of the strain rate and curvature dependences of both density-weighted displacement speed and consumption speed for the range of parameters considered here, but the correlation strength is altered by the presence of water droplets.

Vertical and torsional vibrations before the collapse of the Tacoma Narrows Bridge in 1940

We perform a three-dimensional direct numerical simulation of flow over the Tacoma Narrows Bridge to understand the vertical and torsional vibrations that occurred before its collapse in 1940. Real-scale structural parameters of the bridge are used for the simulation. The Reynolds number based on the free-stream velocity and height of the deck fence is lower ( ${Re}=10\ 000$ ) than the actual one on the day of its collapse ( ${Re}=3.06 \times 10^{6}$ ), but the magnitude of a fluid property is modified to provide the real-scale aerodynamic force and moment on the deck. The vertical and torsional vibrations are simulated through two-way coupling of the fluid flow and structural motion. The vertical vibration occurs from the frequency lock-in with the vortex shedding, and its wavelength and frequency agree well with the recorded data in 1940. After saturation of the vertical vibration, a torsional vibration resulting from the aeroelastic fluttering grows exponentially in time, with its wavelength and frequency in excellent agreement with the recorded data of the incident. The critical flutter wind speed for the growth of torsional vibration is obtained as $3.56 < U_c / (f_{nat} B) \le 4$ , where $U_{c}$ is the critical flutter wind speed, $f_{nat}$ is the natural frequency of the torsional vibration and $B$ is the deck width. Finally, apart from the actual vibration process in 1940, we perform more numerical simulations to investigate the roles of the free-stream velocity and vertical vibration in the growth of the torsional vibration.

Convective mesoscale turbulence at very low Prandtl numbers

Horizontally extended turbulent convection, termed mesoscale convection in natural systems, remains a challenge to investigate in both experiments and simulations. This is particularly so for very low molecular Prandtl numbers, such as occur in stellar convection and in the Earth's outer core. The present study reports three-dimensional direct numerical simulations of turbulent Rayleigh–Bénard convection in square boxes of side length $L$ and height $H$ with the aspect ratio $\varGamma =L/H$ of 25, for Prandtl numbers that span almost 4 orders of magnitude, $10^{-3}\le Pr \le 7$ , and Rayleigh numbers $10^5 \le Ra \le 10^7$ , obtained by massively parallel computations on grids of up to $5.36\times 10^{11}$ points. The low end of this $Pr$ -range cannot be accessed in controlled laboratory measurements. We report the essential properties of the flow and their trends with the Rayleigh and Prandtl numbers, in particular, the global transport of momentum and heat – the latter decomposed into convective and diffusive contributions – across the convection layer, mean vertical profiles of the temperature and temperature fluctuations and the kinetic energy and thermal dissipation rates. We also explore the degree to which the turbulence in the bulk of the convection layer resembles classical homogeneous and isotropic turbulence in terms of spectra, increment moments and dissipative anomaly, and find close similarities. Finally, we show that a characteristic scale of the order of the mesoscale seems to saturate to a wavelength of $\lambda \gtrsim 3H$ for $Pr\lesssim 0.005$ . We briefly discuss possible implications of these results for the development of subgrid-scale parameterization of turbulent convection.

An extended flamelet/progress variable model for coal/biomass co-firing flame

Coal/biomass co-firing (CBCF) is regarded as one of the sustainable alternatives to reduce emissions from the utilization of fossil fuels. It features complex reacting stages and fuel streams caused by the asynchronous reaction behaviors of coal and biomass particles, which cannot be represented well by the traditional two-mixture-fractions (2Z) coal flamelet/progress variable (FPV) model. To address this issue, we developed an extended FPV model for the CBCF flame in the present study. Firstly, a three-dimensional (3D) point-particle direct numerical simulation (PP-DNS) was conducted to explore the combustion characteristics of the co-firing flame and served as a reference for the model development. Secondly, an extended FPV model was developed by introducing an extra parameter to distinguish the volatiles sources, and the model performance was evaluated by the apriori study as well as comparison with those of the traditional coal-/bio- 2Z-FPV models. The results showed that there were three reacting stages with four fuel streams in the CBCF flame, and their corresponding flame behaviors were obviously different from each other as demonstrated in both the one-dimensional flamelets and 3D PP-DNS solutions. The apriori results showed that the coal-/bio- 2Z-FPV models would give large deviations in the predictions of gas temperature and major species due to the lack of distinguishing the volatiles sources. In contrast, the extended FPV model could well reproduce the flame behaviors (both temperature and species profiles) for different reacting stages with complex fuel streams in the CBCF flame. This validated the extended FPV model and demonstrated its superiority against the traditional 2Z-FPV models.

A single bubble rising in the vicinity of a vertical wall: A numerical study based on volume of fluid method

Single bubble rising in the close vicinity of a vertical wall is one of the focuses in the field of gas-liquid two-phase flow. In this work, three-dimensional direct numerical simulation based on volume of fluid (VOF) and adaptive mesh refinement method is performed to investigate the bubble rising and wake structures near a vertical wall. The bubble migration trajectory, deformation, velocity and wake structures were analyzed under various Galileo numbers and initial wall distances. Bubbles with a Galileo number of 8.8 significantly migrate away from the wall, which is driven by the repulsive force as a result of the suppression of the vortex diffusion on the bubble surface. As the Galileo number increases, the asymmetry of the shedding vortex tends to play a vital role on the repulsive force, which is exacerbated by the presence of the vertical wall. A periodic shedding of the vortex appears behind the bubble when the Galileo number reaches at 95. Meanwhile, the bubble trajectory changes from rectilinear to spiral along with a periodic oscillation. Due to the interaction between the vertical wall and the bubble wake, a transition from a rectilinear rising path to a spiral rising path is more likely to occur compared to that without a vertical wall. The presence of a vertical wall contributes to bubble-rising oscillations. A decrease of the bubble terminal velocity due to viscous effect near the vertical wall is observed for bubbles at low Galileo numbers. However, the viscous effect is less pronounced as the Galileo number increases.