Damkohler Number Research Articles

Combustion of H2/air supersonic mixing layers with splitter plate: Flame structure and statistical characteristics

H2/air supersonic mixing layers were calculated with different splitter plates thickness. The accumulation of OH radicals between the most reactive and stoichiometric mixture fraction causes the corresponding change of reactions. With the increase of plate thickness, flame surfaces tend to be more wrinkling. Especially in the initial developing stage, the distribution of temperature, scalar dissipation, Damkohler number and Takeno index is closely related to plate thickness. However in the developed stage, the distribution shows similarity. The symmetry of scalar dissipation rate built in the initial developing zone is broken in the developed stage, corresponding to the distribution about production terms of scalar variance [1]. Different from circulation and developed zone, premixed combustion take a more important part in the initial developing stage. Same as the change of flame curvature, autoignition effect dominating heat release increases first and decreases lately along streamwise direction.

Low pressure flame blowoff of the stagnation region of cast PMMA cylinders in axial mixed convective flow

Low-pressure blowoff experiments were conducted with a stagnation flame stabilized on the forward tip of cast PMMA rods in a vertical wind tunnel. Pressure, forced flow velocity, gravity, and ambient oxygen concentration were varied. Both normal gravity and microgravity tests were conducted to determine the influence of buoyant flow velocity on the blowoff limits. A linear shift of a buoyant flow of ~ 25 cm/s was adequate to match the microgravity data. The flame standoff distance before blowoff varies with the inverse square root of pressure and stretch rate via the gas phase length scale δ = (α/a)1/2, where the thermal diffusivity varies inversely with pressure. For a constant critical Damkohler number, the reaction rate must increase in tandem with the flow rate. The flame standoff distance responds to environment changes to maintain both the critical Damkohler number and the molar flux of oxygen along the blowoff boundary. Via Fick's law, there is a ubiquitous linear relationship between the partial pressure of oxygen at blowoff and the total pressure regardless of forced flow velocity and gravity level. At very low pressures, reactant leakage appears to cause a two-stage reaction zone. For very dilute oxidizer mixtures, an apparent high pressure blowoff limit is found, believed to be caused by chain-terminating three body reactions. The overall reaction order becomes negative along the high pressure limit. A normal gravity materials flammability screening methodology is suggested for spacecraft exploration atmospheres where the blowoff partial pressure of oxygen versus total pressure blowoff limits are measured for the expected exploration atmospheres (oxygen concentrations). As long as the blowoff boundary is above the Earth-normal partial pressure of oxygen (21 kPa) threshold, the material is safe for use in exploration spacecraft.

Magnesium Modified Mesh-TYPE Cu/γ-Al2O3/Al Catalysts: Low Acid Density Catalysts for Methanol Steam Reforming

Methanol steam reforming (MSR) is regarded as one of the effective technologies for in-situ hydrogen generation. A novel mesh-type γ-Al2O3/Al support was prepared by anodization technology. To decrease dimethyl ether (DME) yield in MSR system, magnesium was doped to the γ-Al2O3/Al to modify acidity. The results show that the acid density of the γ-Al2O3/Al support can be decreased from 1.423 μmol/m2 to 1.122 μmol/m2, resulting in the decrease in DME yield from 70.2 to 16.7%. Meanwhile, various CuMgx/γ-Al2O3/Al catalysts were prepared and the effects of MgO on the distribution and reducibility of CuO on the support were investigated. The results show that the dispersion of CuO was improved and reduction temperature was decreased with Mg doping. Finally, four pieces of mesh structured CuMg/γ-Al2O3/Al catalysts (4*8 cm2) were applied into the microreactor with the channel height of 2 mm. CuMg/γ-Al2O3/Al catalyst showed excellent catalytic performance with 100% methanol conversion, 98.2% hydrogen yield, without DME at 250 °C, 4000 mL/(g h) GHSV. Furthermore, the diffusion limitation was investigated by Damkohler number (Da), the results indicated the diffusion influence can be neglected in the microreactor over mesh-type catalysts.

Effect of volumetric expansion on shock-induced ignition of H2–NO2/N2O4 mixtures

The competition between chemical energy release rate and volumetric expansion related to shock wave’s dynamics is of primary importance for a number of situations relevant to explosion safety. While studies have been performed on this topic over the years, they have been limited to mixtures with monotonous energy release profile. In the present study, the ignition of H2–NO2/N2O4 mixtures, which exhibit a single-step or a two-step energy release rate profile depending on the equivalence ratio, has been investigated under volumetric expansion conditions. The rate of expansion has been calculated using the Taylor–Sedov solution and accounted for using 0-D numerical simulations with time-dependent specific volume. The results were analyzed in terms of a Damkohler number defined as the ratio of the expansion to ignition times. For mixtures with non-monotonous energy release rate profiles, two critical Damkohler numbers can be identified for individual steps of energy release. It was also shown that the fluid element behind a shock propagating at the Chapman–Jouguet velocity is most likely to ignite. The thermo-chemical dynamics have been analyzed about the critical conditions using energy release rate per reaction, rate of production and sensitivity analyses.

Upscaling diffusion–reaction in porous media

In this work, we present the outlines of the periodic homogenization of the diffusion equation with chemical reaction at the interface, for different orders of magnitude of the Damkohler number. For large values of the Damkohler number, a non-classical homogenized model is obtained, where the homogenized diffusion tensor is strongly coupled with the chemical reaction rate. This homogenized model is particularly well adapted to describe, at the macroscopic level, diffusion with strong chemical reactions at the pore interfaces. The aim of this article is to highlight the transition between different regimes of diffusion–reaction according to the order of magnitude of the Damkohler number. In the last part of this work, we first consider a simple analytical example between two parallel plates, to understand the transition between the different possible regimes of diffusion–reaction. Finally, numerical simulations are performed on more complex two-dimensional elementary cells.

Global spectral analysis for convection-diffusion-reaction equation in one and two-dimensions: Effects of numerical anti-diffusion and dispersion

Convection-diffusion-reaction (CDR) equation plays a central role in many disciplines of engineering, science and finances. As a consequence, importance of analysis of numerical methods for the accurate solution of CDR equation has motivated the present research. We have used the global spectral analysis to characterize all the three important physical processes in terms of the non-dimensional numerical parameters, namely, the non-dimensional wavenumber (kh); Courant-Friedrich-Lewy (CFL) number, Nc; the Peclet number (Pe) and the Damkohler number (Da). For the purpose of illustration, we have focused on two space-time discretization schemes known for accuracy and robustness. The basic properties relate to numerical issues arising for the numerical amplification factor, numerical diffusion coefficient, numerical phase speed and numerical group velocity. With the help of model one-dimensional (1D) and two-dimensional (2D) CDR equations, we have reported the numerical property charts for the cases: (i) When all the processes of convection, diffusion and reaction are of same order, with critical numerical behaviour enforcing low values of Da for the 1D CDR equation studied here. (ii) The 2D CDR equation considered is diffusion-reaction dominated, and as a consequence, this enforces Da to be larger. We have thoroughly analyzed these cases to identify the essential roles of anti-diffusion on the critical Nc and Pe values, which in turn decides admissible space and time steps to be used with the discretization schemes. The property charts have been used to calibrate the analysis with two model equations, one of which has an exact solution for a 1D CDR equation, and the second case for the 2D CDR equation has numerical solution available in the literature. These cases help to identify the importance of such analysis in explaining the utility of the choice one can exercise in fixing the numerical parameters. This also identifies and explains some hitherto unknown numerical problems for CDR equation and their alleviation techniques.

Unsteady solute dispersion by electrokinetic flow in a polyelectrolyte layer-grafted rectangular microchannel with wall absorption

The dispersion of a neutral solute band by electrokinetic flow in polyelectrolyte layer (PEL)-grafted rectangular/slit microchannels is theoretically studied. The flow is assumed to be both steady and fully developed and a first-order irreversible reaction is considered at the wall to account for probable surface adsorption of solutes. Considering low electric potentials, analytical solutions are obtained for electric potential, fluid velocity and solute concentration. Special solutions are also obtained for the case without wall adsorption. To track the dispersion properties of the solute band, the generalized dispersion model is adopted by considering the exchange, the convection and the dispersion coefficients. The solutions developed are validated by comparing the results with the predictions of finite-element-based numerical simulations. Even though the solutions can take any form of initial solute concentration into account, the results are presented by considering a solute band of rectangular shape. The results reveal that, while the short-term transport coefficients are strongly affected by the initial concentration profile, the long-term values are not dependent upon the initial conditions. In addition, it is shown that the mass transport coefficients are strong functions of the channel aspect ratio; hence, approximating a rectangular geometry by the space between two parallel plates may lead to considerable errors in the estimation of mass transport characteristics. This is particularly important for the dispersion coefficient for which the long-term values for a slit microchannel are quite different from those for a rectangular channel of very high aspect ratio. It is also illustrated that the exchange and convection coefficients increase on increasing the Damkohler number, whereas the opposite is true for the dispersion coefficient. The convection and dispersion coefficients are generally increasing functions of the PEL fixed charge density and the PEL thickness and decreasing functions of the PEL friction coefficient. Last but not least, a thicker electric double layer is found to provide a larger degree of solute dispersion, which is the opposite of that observed in a microchannel with bare walls.

Production of metallic iron nanoparticles in a baffled stirred tank reactor: Optimization via computational fluid dynamics simulation

The aim of this work is to optimize iron nanoparticle production in stirred tank reactors equipped with two classical impellers: Rushton and four-pitched blade turbines, which are largely used in batch industrial synthesis and efficient scale-up. The main operative parameters of nanoparticle synthesis are the precursor initial concentration, reducing agent/precursor molar ratio, impeller–tank clearance, and impeller rotational velocity. These parameters were varied during the synthesis to find the optimal operating values based on the Fe(0) (%) production, zeta potential, particle size distribution, and powder X-ray diffraction pattern obtained. We found that the optimal operating conditions for nanoparticle production were an impeller velocity of 1500rpm, initial iron precursor concentration of 20mM, molar ratio of reducing agent to iron precursor of 3mol/mol, and impeller clearance of 0.25 and 0.4 times the vessel diameter for Rushton and four-pitched blade impellers, respectively. Setting these conditions achieved a total conversion of 0.94–0.98 and yielded a product with a unimodal size distribution and average diameters in the range 30–50nm. The computational fluid dynamics results agreed with the expectations, and the obtained mixing Damkohler numbers show that the process is mixed controlled.

MILD Combustion Limit Phenomena

This work contains an analysis of the existence of critical phenomena in MILD combustion systems through an exploration of classical results from high-energy asymptotics theory for extinction conditions of non-premixed flames and well-stirred reactors. Through the derivation of an expression linking burning rate to Damkohler number, the criteria for a folded S-Shaped Curve, representative of a combustion system with sudden extinction and ignition behaviour, was derived. This theory is discussed in detail, with particular focus on the limitations of the global chemistry it presents. The conditions reported by various previously-published numerical and experimental investigations are then discussed in the context of this theory. Of these investigations, those with the highest level of preheat and dilution had monotonic rather than folded S-Shaped Curves, indicating a lack of sudden extinction phenomena. It suggests that MILD combustion systems are those which lack sudden ignition and extinction behaviour, therefore exhibiting a smooth, stretched S-Shaped Curve rather than a folded one with inflection points. The results suggest that the delineation between folded versus monotonic S-Shaped Curves may provide a useful alternative definition of MILD combustion.

Reactive fluid flow topology optimization with the multi-relaxation time lattice Boltzmann method and a level-set function

This paper presents a topology optimization algorithm based on the lattice Boltzmann method coupled with a level-set method for increasing the efficiency of reactive fluid flows. The multi-relaxation time model is considered for the lattice Boltzmann collision operator, allowing higher Reynolds numbers flow simulations compared to the ordinary single-relaxation time model. The cost function gradient is obtained with the derivation of the adjoint-state formulation for the fully coupled problem. The proposed method is tested successfully on several numerical applications involving Reynolds numbers from 10 up to 1,000, as well as with different Damkohler and Peclet numbers. A limitation of the maximal pressure drop is also applied. The obtained results demonstrate that the proposed numerical method is robust and efficient for solving topology optimization problems of reactive fluid flows, in different operating conditions.

CONJUGATE MASS TRANSFER FOR THE REMOVAL OF HYDROGEN SULFIDE GAS CIRCULATING IN A SLIT MICROCHANNEL ON A HOMOGENEOUS BIOFILM UNDER THE INFLUENCE OF THE DAMKÖHLER NUMBER

CONJUGATE MASS TRANSFER FOR THE REMOVAL OF HYDROGEN SULFIDE GAS CIRCULATING IN A SLIT MICROCHANNEL ON A HOMOGENEOUS BIOFILM UNDER THE INFLUENCE OF THE DAMKÖHLER NUMBER

Preparation and optimization of nano-sized cocrystals using a quality by design approach

Nano-cocrystals were optimized using the L-18 Hunter design. Selection of solvent and antisolvent was made using the Damkohler number.

LES of Subsonic Reacting Mixing Layers

We study a class of chemically reacting, spatially evolving, subsonic mixing layers via large eddy simulations (LES). A primary goal is to assess the inflow conditions, numerical methods, and physical models requirement to reproduce experimental results on molecular mixing and effects of inflow conditions in high-Reynolds number mixing layers: here, we target experiments performed by Slessor et al. (J. Fluid Mech. 376, 115–138 1998). The streams forming the mixing layer carry small amounts of hydrogen and fluorine, initiating a hypergolic reaction upon mixing at large Damkohler number. In this regime, product formation and temperature rise in the flow is mixing limited. The chemical compositions considered for this study correspond to low levels of heat release and results in adiabatic flame temperature rise of 171K and 267K. Both reacting and non-reacting simulations are performed with the Vreman sub-grid scale model (Vreman Phys. Fluids 16(10), 3670–3681 2004). A grid resolution study is done and comparisons are made with the available experimental data. To mitigate dispersive errors and ensure boundedness in species mass fractions that occur in simulations of non-premixed combustion, non-linear scaling limiters are used for reconstructing species densities during flux evaluation. The simulations show good agreement of the velocity and temperature rise profiles with experiment, and reveal differences in the flow field attributed to changes in the inflow conditions.

Effect of first order chemical reactions on the dispersion coefficient associated with laminar flow through fibrosis affected lung

In this paper, we worked on the effective area average concentration and dispersion coefficient associated with the unsteady flow, to understand the dispersion in the fibrosis-affected lung. We assumed that the tube wall (i.e. alveolar or pulmonary capillary wall) is thicker than its normal size due to fibrosis and chemical species may go through linear first-order kinetic reactions, one is reversible phase exchange with the wall material and other is irreversible absorption into the tube wall. By considering diffusivity as a function of thickness, the dispersion can be calculated by the distribution of concentration of gas along a tube. Mathematical modeling is done by using diffusion equation; and effects of various dimensionless parameters e.g., the Damkohler number (DA), phase partitioning number (α), dimensionless absorption number (Γ), thickness and permeability of wall are observed. Numerical simulation shows that the diffusion rate through the respiratory wall is decreased significantly as the thickness of wall increases, while it increased with the increment in the porosity of wall, the concentration of species increased when the tube wall thickness increases; which cause reduction in the spread of the species; additionally, the dispersion coefficient achieves the steady-state values in a very short time when 0 < DA ⩽1 and absorption rate < 1, while for 1 < DA ⩽20 and absorption rate = 1 long time dispersion is achieved.

Effect of soluble surfactant on the motion of a confined droplet in a square microchannel

Surfactants are widely used in the manipulation of drop motion in microchannels, which is commonly involved in many applications, e.g., surfactant assisted oil recovery and droplet microfluidics. This study is dedicated to a crucial fundamental problem, i.e., the effects of a soluble surfactant on drop motion and their underlying mechanisms, which is an extension of our previous work of an insoluble-surfactant-covered droplet in a square microchannel [Z. Y. Luo, X. L. Shang, and B. F. Bai, “Marangoni effect on the motion of a droplet covered with insoluble surfactant in a square microchannel,” Phys. Fluids 30, 077101 (2018)]. We make essential improvements to our own three-dimensional front-tracking finite-difference model, i.e., by further integrating the equation governing surfactant transport in the bulk fluid and surfactant mass exchange between the drop surface and bulk fluid. We find that the soluble surfactant generally enlarges the droplet-induced extra pressure loss compared to the clean droplet, and enhancing surfactant adsorption tends to intensify such an effect. We focus specifically on the influences of four soluble-surfactant-relevant dimensionless parameters, including the Biot number, the dimensionless adsorption depth, the Damkohler number, and the bulk Peclet number. Most importantly, we discuss the mechanisms underlying the soluble surfactant effect, which consists of two aspects similar to the insoluble case, i.e., the reduced surface tension to decrease droplet-induced extra pressure loss and the enlarged Marangoni stress playing the opposite role. Surprisingly, we find that the enlarged Marangoni stress always makes the predominant contribution over the reduced surface tension in the effects of above-mentioned four soluble-surfactant-relevant dimensionless parameters on drop motion. This finding explains why the droplet-induced extra pressure loss increases with the film thickness, which is opposite to that observed for clean droplets.

Random walk particle tracking simulation on scalar diffusion with irreversible first-order absorption boundaries.

Scalar transport in an open channel with irreversible first-order absorption boundaries is investigated through random walk particle tracking method (RWPT). We provide the pre-asymptotic behavior of scalar transport as well as a comparison with existing asymptotic formulations. The RWPT method is based on the development of the probability that a particle is absorbed at the boundary. The random walk model is applied to simulate three main parameters of the scalar transport in the laminar flow with sorption boundaries. The three parameters are (1) the attenuation coefficient reflecting the depletion rate of the total mass; (2) the effective velocity coefficient representing the effective advection of the total mass; and (3) the effective longitudinal dispersion coefficient expressing the effective spreading rate of the solute plume. When the Peclet number is large, numerical results agree well with previous theoretical solutions. Results show that (1) the three coefficients reach their asymptotic values when the dimensionless time τ (= Dt/H2) is about 0.5, where t is the time, H is the water depth, and D is the molecular diffusion coefficient and (2) when the Damkohler number reaches a value around 100, the boundary can be treated as a totally absorptive boundary.

Deposition of Colloidal Particles during the Evaporation of Sessile Drops: Dilute Colloidal Dispersions

The deposition of colloidal silica particles during the evaporation of sessile drops on a smooth substrate has been modeled by the simultaneous solution of the Navier–Stokes equations, the convective-diffusive equation for particles, and the diffusion equation for evaporated vapor in the gas phase. Isothermal conditions were assumed. A mapping was created to show the conditions for various deposition patterns for very dilute suspensions. Based on values of the Peclet (Pe) number and Damkholer numbers (Da and Da−1), the effects of adsorption and desorption were discussed according to the map. Simulations were also done for suspensions with a high particle concentration to form a solid phase during the evaporation by using a packing criterion. The simulations predicted the height and width of the ring deposit near the contact line, and the results compared favorably to experimental particle deposition patterns.

Three-dimensional simulation of microcapillary and microchannel photo reactors for organic pollutant degradation from contaminated water using computational fluid dynamics

A three-dimensional (3D) simulation of four photocatalytic microreactors is performed using mass and momentum balance equations. The simulated results are validated with the available experimental data for the photocatalytic removal of methylene blue (MB) in two microcapillaries as well as dimethylformamide (DMF) and salicylic acid (SA) in two microchannels. In the surface layers of the microreactor, a photo removal reaction takes place, and the kinetic rates are described by the Langmuir-Hinshelwood (L-H) model. The Damkohler number for these microreactors is less than one, which indicates that the mass transfer rate is limited by the reaction rate. The numerical study and kinetic constants determination are carried out by using computational fluid dynamic techniques. The 3D modelpredictionsare ingood agreementwith the availableexperimental data sets. The results of the parametric study show that by increasing the microreactor length from 50 to 90mm, the removal efficiency improves from 76% to 93%. Moreover, the removal rate is increased by about 40% by reducing the microchannel depth from 500 to 100 .

Analysis of permeability change in dissolving rough fractures using depth-averaged flow and reactive transport models

Many geophysical problems and engineering applications involve fluid flow through evolving faults and fractures. These situations are typical in CO2 injection scenarios where supercritical CO2 or CO2–saturated fluids are able to dissolve the solid matrix. Dissolution or precipitation within a fracture could lead to self-reinforcing or self-limiting behavior due to feedbacks from changes in permeability (k). There is limited predictive understanding of this phenomenon. Here, we investigated the case of fracture dissolution using a two-dimensional depth-averaged reactive transport model. The model simulated an acidic fluid dissolving a three-dimensional rough fracture. We observed different dissolution patterns across a wide range of geometric properties and different Peclet and Damkohler numbers (960 cases total). Despite this variation, a persistent linear increase in k with time (t) roughly manifested once the dissolution front advanced through the fracture. The time rate of change of k (k/t) is roughly constant for all simulations. The modeled rate is consistent with a theoretical value based on the parallel plates model and with experimentally derived values. The results confirm the common presence of linear time-dependence of fracture k due to self-reinforcement.

Cadmium-Bacteria Complexation and Subsequent Bacteria-Facilitated Cadmium Transport in Saturated Porous Media.

Cadmium (Cd) contamination is becoming a significant environmental concern due to its persistency in soil. In the subsurface, the fate and transport of Cd are significantly affected by the presence of organic carriers, including bacteria, which are ubiquitous. In this research, facilitated Cd transport by four different bacterial strains in zeolite was investigated by column experiments under three different Cd introduction scenarios (i.e., a Cd and bacteria mixture, Cd and bacteria introduced separately but simultaneously, and Cd added to the column, followed by bacterial flushing), through which Cd-bacteria complexes formed. In turn, Cd-bacteria complexation affected bacterial transport. Bacteria were least retarded when Cd was pre-deposited, with mass recovery>90% for all strains. More Cd was recovered when introduced as a mixture with bacteria (i.e., Cd mass recovery ranging from 16 to 25%). Obtained bacteria and Cd breakthrough curves were simulated by the attachment-detachment model in Hydrus-1D. Damkohler number and reversibility were both found to be suitable to control the mass recovery of Cd and bacteria in all investigated scenarios.