Visualization of deflagration-to-detonation transitions in a channel with repeated obstacles using a hydrogen–oxygen mixture

The deflagration-to-detonation transition in a 100 mm square cross-section channel was investigated for a highly reactive stoichiometric hydrogen oxygen mixture at 70 kPa. Obstacles of 5 mm width and 5, 10, and 15 mm heights were equally spaced 60 mm apart at the bottom of the channel. The phenomenon was investigated primarily by time-resolved schlieren visualization from two orthogonal directions using a high-speed video camera. The detonation transition occurred over a remarkably short distance within only three or four repeated obstacles. The global flame speed just before the detonation transition was well below the sound speed of the combustion products and did not reach the sound speed of the initial unreacted gas for tests with an obstacle height of 5 and 10 mm. These results indicate that a detonation transition does not always require global flame acceleration beyond the speed of sound for highly reactive combustible mixtures. A possible mechanism for this detonation initiation was the mixing of the unreacted and reacted gas in the vicinity of the flame front convoluted by the vortex present behind each obstacle, and the formation of a hot spot by the shock wave. The final onset of the detonation originated from the unreacted gas pocket, which was surrounded by the obstacle downstream face and the channel wall.     

A compressible two-layer model for transient gas–liquid flows in pipes

This work is dedicated to the modeling of gas–liquid flows in pipes. As a first step, a new two-layer model is proposed to deal with the stratified regime. The starting point is the isentropic Euler set of equations for each phase where the classical hydrostatic assumption is made for the liquid. The main difference with the models issued from the classical literature is that the liquid as well as the gas is assumed compressible. In that framework, an averaging process results in a five-equation system where the hydrostatic constraint has been used to define the interfacial pressure. Closure laws for the interfacial velocity and source terms such as mass and momentum transfer are provided following an entropy inequality. The resulting model is hyperbolic with non-conservative terms. Therefore, regarding the homogeneous part of the system, the definition and uniqueness of jump conditions is studied carefully and acquired. The nature of characteristic fields and the corresponding Riemann invariants are also detailed. Thus, one may build analytical solutions for the Riemann problem. In addition, positivity is obtained for heights and densities. The overall derivation deals with gas–liquid flows through rectangular channels, circular pipes with variable cross section and includes vapor–liquid flows.     

A growth model for dynamic slugs in gas–liquid horizontal pipes

Long liquid slugs, with sizes reaching 500 pipe diameters or more, may form in gas–liquid horizontal pipe flow at intermediate liquid loadings. Such slugs cause serious operational upsets due to the strong fluctuations in flow supply and pressure. Therefore, predicting the transition from short (hydrodynamic) to long slug flow regimes may play a significant role in preventing or reducing the negative effects caused by the long slugs.     

A theoretical model for gas–liquid slug flow in down inclined ducts

Analytical solutions are obtained for flows in downwardly inclined ducts, partly filled by a liquid and containing finite amplitude moving jumps. A unified theory for both roll waves and periodic slug flows in rounded ducts of arbitrary cross-section is worked out by means of some simplifications. The article is focused on slugs: a set of equations is obtained, which predicts the transition between roll waves and slug regimes and gives access to all flow characteristics without any need of closure laws concerning either the speed of propagation or the slug length. As a result, we gain a new insight on the physical structure of slug flow. The proposed model is valid for sufficient inclination, small pressure gradient along the duct and negligible superficial tension. Owing to assumptions, only main trends and orders of magnitude observed in experiments are to be checked. In this connection the model fits most of the previously published experimental results obtained in ducts of circular cross-section: the domain of occurrence of downwardly propagating slugs is satisfactorily predicted, the limitations in drift velocity and in liquid layer thickness are demonstrated and upwardly propagating slugs are possible.     

Analysis of gas–solid flow and shaft-injected gas distribution in an oxygen blast furnace using a discrete element method and computational fluid dynamics coupled model

Ironmaking using an oxygen blast furnace is an attractive approach for reducing energy consumption in the iron and steel industry. This paper presents a numerical study of gas–solid flow in an oxygen blast furnace by coupling the discrete element method with computational fluid dynamics. The model reliability was verified by previous experimental results. The influences of particle diameter, shaft tuyere size, and specific ratio (X) of shaft-injected gas (SIG) flowrate to total gas flowrate on the SIG penetration behavior and pressure field in the furnace were investigated. The results showed that gas penetration capacity in the furnace gradually decreased as the particle diameter decreased from 100 to 40 mm. Decreasing particle diameter and increasing shaft tuyere size both slightly increased the SIG concentration near the furnace wall but decreased it at the furnace center. The value of X has a significant impact on the SIG distribution. According to the pressure fields obtained under different conditions, the key factor affecting SIG penetration depth is the pressure difference between the upper and lower levels of the shaft tuyere. If the pressure difference is small, the SIG can easily penetrate to the furnace center.     

An empirical model for the thermal conductivity of compacted bentonite and a bentonite–sand mixture

The thermal conductivities of compacted bentonite and a bentonite–sand mixture were measured to investigate the effects of dry density, water content and sand fraction on the thermal conductivity. A single expression has been proposed to describe the thermal conductivity of the compacted bentonite and the bentonite–sand mixture once their primary parameters such as dry density, water content and sand fraction are known.     

On a generalized nonlinearK-ɛ model for turbulence that models relaxation effects

In this paper, based on a similarity that exists between the constitutive relations for turbulent mean flow of a Newtonian fluid and that for the laminar flow of a non-Newtonian fluid, and making use of extended thermodynamics, we develop a generalized nonlinearK- model, whose approximate form includes the standardK- model and the nonlinearK- model of Speziale (1987) as special cases. Our nonlinearK- model, which is frame indifferent, can predict relaxation of the Reynolds stress, unlike most standardK- models. Also, our model is in keeping with that of Yakhotet al. (1992). Most interestingly, the linearized form of our model bears a striking resemblance to the model due to Yoshizawa and Nisizima (1993); however, it has been obtained from a totally different perspective.     

Simulations of vertical jet penetration using a filtered two-fluid model in a gas–solid fluidized bed

The influence of a vertical jet located at the distributor in a cylindrical fluidized bed on the flow behavior of gas and particles was predicted using a filtered two-fluid model proposed by Sundaresan and coworkers. The distributions of volume fraction and the velocity of particles along the lateral direction were investigated for different jet velocities by analyzing the simulated results. The vertical jet penetration lengths at the different gas jet velocities have been obtained and compared with predictions derived from empirical correlations; the predicted air jet penetration length is discussed. Agreement between the numerical simulations and experimental results has been achieved.     

Roll waves in a gas–liquid medium

The onevelocity motion of a gas–liquid medium with a variable mass fraction of the gas phase, which is equilibrium in terms of phase pressures, is considered. The existence conditions of nonlinear periodic wave packets similar in structure to roll waves in open inclined channels are found. The structure of travelling waves in the medium with continuous addition of energy to the gas phase is studied.     

Numerical simulation of gas–solid flow with two fluid model in a spouted-fluid bed

The flow characteristics in a spouted-fluid bed differ from those in spouted or fluidized beds because of the injection of the spouting gas and the introduction of a fluidizing gas. The flow behavior of gas–solid phases was predicted using the Eulerian–Eulerian two-fluid model (TFM) approach with kinetic theory for granular flow to obtain the flow patterns in spouted-fluid beds. The gas flux and gas incident angle have a significant influence on the porosity and particle concentration in gas–solid spouted-fluid beds. The fluidizing gas flux affects the flow behavior of particles in the fountain. In the spouted-fluid bed, the solids volume fraction is low in the spout and high in the annulus. However, the solids volume fraction is reduced near the wall.     

Rich spatial–temporal dynamics in a diffusive population model for pioneer–climax species

Nonlinear Dynamics - A general diffusive population model for interactions of pioneer and climax species subject to the no-flux boundary condition is considered. Local and global steady-state...     

Chapman–Enskog solutions to arbitrary order in Sonine polynomials II: Viscosity in a binary,rigid-sphere,gas mixture

The Chapman–Enskog solutions of the Boltzmann equations provide a basis for the computation of important transport coefficients for both simple gases and gas mixtures. These coefficients include the viscosity, the thermal conductivity, and the diffusion coefficient. In a preceding paper (I), for simple, rigid-sphere gases (i.e. single-component, monatomic gases) we have shown that the use of higher-order Sonine polynomial expansions enables one to obtain results of arbitrary precision that are error free. It is our purpose in this paper to report the results of our investigation of relatively high-order, standard, Sonine polynomial expansions for the viscosity-related Chapman–Enskog solutions for binary gas mixtures of rigid-sphere molecules. We note that in this work we have retained the full dependence of the solution on the molecular masses, the molecular sizes, the mole fractions, and the intermolecular potential model via the omega integrals. For rigid-sphere gases, all of the relevant omega integrals needed for these solutions are analytically evaluated and, thus, results to any desired precision can be obtained. The values of viscosity obtained using Sonine polynomial expansions for the Chapman–Enskog solutions converge monotonically from below and, therefore, the exact viscosity solution to a given degree of convergence can be determined with certainty by expanding to sufficiently high an order. We have used Mathematica® for its versatility in permitting both symbolic and high precision computations. Our results also establish confidence in the results reported recently by other authors who used direct numerical techniques to solve the relevant Chapman–Enskog equations. While in all of the direct numerical methods more-or-less full calculations need to be carried out with each variation in molecular parameters, our work utilizes explicit, general expressions for the necessary matrix elements that retain the complete parametric dependence of the problem and, thus, only a matrix inversion at the final step is needed as a parameter is varied. This work also indicates how similar results may be obtained for more realistic intermolecular potential models and how other gas-mixture problems may also be addressed with some additional effort.     

Generalized Timoshenko–Reissner model for a multilayer plate

A multilayer plate with isotropic (or transversally isotropic) layers strongly differing in rigidity is considered. This plate is reduced to an equivalent homogeneous transversally isotropic Timoshenko–Reissner plate whose deflections and free transverse vibration frequencies are close to those of the multilayer plate. By comparison with the exact solution of test three-dimensional problems of elasticity, the error of the proposed method is estimated both for the static problem and for free vibrations. This comparison can readily be carried out for the hinged edges of the plate, and explicit approximate formulas are obtained for the vibration frequencies. The scope of the proposed model turned out to be rather wide (the Young moduli of soft and rigid layers can differ by a factor of 1000). In the case of boundary conditions other than hinged support, a closed-form solution cannot be constructed in general. For rigidly fixed edges, the asymptotic method proposed by V. V. Bolotin is generalized to the case of a Timoshenko–Reissner plate.     

Bifurcation and stability analysis in predator–prey model with a stage-structure for predator

A predator–prey system with Holling type II functional response and stage-structure for predator is presented. The stability and Hopf bifurcation of this model are studied by analyzing the associated characteristic transcendental equation. Further, an explicit formula for determining the stability and the direction of periodic solutions bifurcating from positive equilibrium is derived by the normal form theory and center manifold argument. Some numerical simulations are also given to illustrate our results.     

Dynamics of an elastic cylindrical shell with a gas–liquid medium subject to two-frequency vibrational excitation

The paper presents experimental results on nonlinear dynamic processes such as the deformation of the elastic wall of a cylindrical shell filled with a fluid and the formation and clustering of gas bubbles, which interact under two-frequency excitation Translated from Prikladnaya Mekhanika, Vol. 44, No. 11, pp. 112–122, November 2008.     

Numerical investigations on gas–solid flow in circulating fluidized bed risers using a new cluster-based drag model

A cluster-based drag model is proposed for the gas–solid circulating fluidized bed (CFB) riser by including the cluster information collected from image processing and wavelet analysis into the calculation of system drag. The performance of the proposed drag model is compared with some commonly used drag models. A good agreement with the experimental data is achieved by the proposed cluster-based drag model. Error analysis of the proposed cluster-based drag model based on the local distributions of solids holdup and particle velocity is conducted. The clustering phenomenon in the low-density and high-density CFB risers and the effect of the cluster size on the simulation accuracy are also numerically studied by the proposed drag model.     

Finite differences study of ignition in a methane–air mixture flow

A detailed simulation of the ignition process and premixed flames propagation, taking into account molecular transport, chemical reaction, thermodynamics and convection, is built by making use of the implicit finite difference scheme with the help of the Tridiagonal Matrix Algorithm. The velocity of chemical reaction is expressed by means of Arrhenius form of first order in both fuel and oxygen. The main objective of this work is to define numerically in two cases, u=0.1 m/s and u=0.4 m/s, the ignition temperature of the methane–air mixture with different air excess coefficients in the mixture. In addition, the effect of the thickness of the region ignition and of ignition location on the transient behavior of the flame was studied.