Generalized Riemann problem for gas dynamic combustion

The generalized Riemann problem for gas dynamic combustion in a neighborhood of the origin t > 0 in the (x, t) plane is considered. Under the modified entropy conditions, the unique solutions are constructed, which are the limits of the selfsimilar Zeldovich-von Neumann-Dring (ZND) combustion model. The results show that, for some cases, there are intrinsical differences between the structures of the perturbed Riemann solutions and the corresponding Riemann solutions. Especially, a strong detonation in the...     

Non‐linear analysis of solid propellant burning rate behavior

The parametric analysis of the thermal wave model of the non‐steady combustion of solid propellants is carried out under a sudden compression. First, to observe non‐linear effects, solutions are obtained using a computer under prescribed pressure variations. Then, the effects of rearranging the spatial mesh, additional points, and the time step on numerical solutions are evaluated. Finally, the behavior of the thermal wave combustion model is examined under large heat releases (H) and a dynamic factor (β). The numerical predictions show that (1) the effect of a dynamic factor (β), related to the magnitude of dp/dt, on the peak burning rate increases as the value of β increases. However, unsteady burning rate ‘runaway’ does not appear and will return asymptotically to apⁿ, when β≥10.0. The burning rate ‘runaway’ is a numerical difficulty, not a solution to the models. (2) At constant β and m, the amplitude of the burning rate increases with increasing H. However, the increase in the burning rate amplitude is stepwise, and there is no apparent intrinsic instability limit. A damped oscillation of burning rate occurs when the value of H is less. However, when H>1.0, the state of an intrinsically unstable model is composed of repeated, amplitude spikes, i.e. an undamped oscillation occurs. (3) The effect of the time step on the peak burning rate increases as H increases. Copyright © 2000 John Wiley & Sons, Ltd.     

Convergence issues in using high‐resolution schemes and lower–upper symmetric Gauss–Seidel method for steady shock‐induced combustion problems

This paper reports numerical convergence study for simulations of steady shock‐induced combustion problems with high‐resolution shock‐capturing schemes. Five typical schemes are used: the Roe flux‐based monotone upstream‐centered scheme for conservation laws (MUSCL) and weighted essentially non‐oscillatory (WENO) schemes, the Lax–Friedrichs splitting‐based non‐oscillatory no‐free parameter dissipative (NND) and WENO schemes, and the Harten–Yee upwind total variation diminishing (TVD) scheme. These schemes are implemented with the finite volume discretization on structured quadrilateral meshes in dimension‐by‐dimension way and the lower–upper symmetric Gauss–Seidel (LU–SGS) relaxation method for solving the axisymmetric multispecies reactive Navier–Stokes equations. Comparison of iterative convergence between different schemes has been made using supersonic combustion flows around a spherical projectile with Mach numbers M = 3.55 and 6.46 and a ram accelerator with M = 6.7. These test cases were regarded as steady combustion problems in literature. Calculations on gradually refined meshes show that the second‐order NND, MUSCL, and TVD schemes can converge well to steady states from coarse through fine meshes for M = 3.55 case in which shock and combustion fronts are separate, whereas the (nominally) fifth‐order WENO schemes can only converge to some residual level. More interestingly, the numerical results show that all the schemes do not converge to steady‐state solutions for M = 6.46 in the spherical projectile and M = 6.7 in the ram accelerator cases on fine meshes although they all converge on coarser meshes or on fine meshes without chemical reactions. The result is based on the particular preconditioner of LU–SGS scheme. Possible reasons for the nonconvergence in reactive flow simulation are discussed.Copyright © 2012 John Wiley & Sons, Ltd.     

Existence of planar flame fronts in convective-diffusive periodic media

We prove the existence of planar travelling wave solutions in a reaction-diffusion-convection equation with combustion nonlinearity and self-adjoint linear part in R ⁿ, n1. The linear part involves diffusion-convection terms and periodic coefficients. These travelling waves have wrinkled flame fronts propagating with constant effective speeds in periodic inhomogeneous media. We use the method of continuation, spectral theory, and the maximum principle. Uniqueness and monotonicity properties of solutions follow from a previous paper. These properties are essential to overcoming the lack of compactness and the degeneracy in the problem.     

Steady,oblique, detonation waves

Normal and oblique, steady planar detonation waves have been theoretically and computationally examined using the Zeldovich, von Neumann, Döring model. Combustion is between a methane/hydrogen mixture and dry air assuming, first, complete combustion, then an equilibrium solution. Prescribed parameters are the upstream values for the pressure, temperature, and Mach number, the fuel/air equivalence ratio, a hydrogen/methane ratio, and the detonation wave angle. For a given upstream state, the angle varies from its normal wave value in increments of 10 ^o to non-integer wave angles that correspond to the Chapman-Jouguet state for complete combustion and for an equilibrium solution. For each solution, detailed results are provided for the upstream state, the state just downstream of the shock, and the two downstream states. Over 340 solutions in a report (Emanuel and Tuckness 2002) are provided, thereby establishing, for the first time, comprehensive tables that can be used to provide quick estimates, establish trends, and check CFD results. This paper describes the basis for the model, briefly outlines the analytical and numerical method, and discusses several insights.     

A generalized Zel’dovich-Neumann-Döring model of steady gaseous detonation

A model of N-component gas mixture detonation whose combustion zone is formed by n (1 ≤ n ≤ N − 1) independent reactions satisfying the kinetic formulation of the mass action law is studied. In the framework of this model, it is found that there exist two possible types of self-sustaining detonation waves with asymptotically stable combustion zones. It is shown that it is possible to observe only a strong wave propagating in the Chapman-Jouguet regime relative to the flow on the critical surface. It is also shown that, for a perfect gas mixture, this wave appears only when a combustion zone is formed by one or two reactions.     

Theory of convective combustion of an aerosuspension of fuel which contains an oxidant

In earlier papers [1, 2], the author and Nigmatulin developed a theory of the unsteady propagation of combustion in aerosuspensions of a unitary fuel (a fuel containing an oxidant) at low subsonic velocities of the gas. The assumption of low velocities permits a number of simplifications which reduce the equations describing the mechanics of multiphase reacting media [3, 5] to the equations of unsteady homobaric (with uniform pressure [1, 3, 4, 6]) motion of gas with distributed blowing and heat release. At a constant mass rate of combustion of the particles, these equations have a class of analytic solutions describing the initial stage of convective combustion of aerosuspensions in open and closed regions with allowance for the possible formation of weak shock waves. In the present paper, these solutions are generalized to the case of a more realistic law of combustion of a particle of a unitary fuel [7]. The results are given of a numerical solution to the problems, and these results make it possible, in particular, to analyze the conditions of applicability of the model with a constant mass rate of combustion of the particles.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 152–155, October–December, 1981.     

Influence of Inlet Dilution of Reactants on Premixed Combustion in a Recuperative Furnace

This paper presents a numerical study by RANS modeling that investigates the effect of external dilution on the premixed combustion occurring in a recuperative furnace. Calculations are performed using the detailed GRI-Mech 3.0 mechanism to ensure the accuracy of the modeling. Results of the in-furnace flow, temperature, and concentrations of OH, O₂, CO₂ and NO _x are provided. It is found that the external dilution with the inert gas CO₂ plays a significant role in establishing the premixed MILD (Moderate or Intense Low-oxygen Dilution) combustion. Externally diluting the reactant mixture not only reduces the initial concentration of O₂ but also ensures a stronger internal dilution by recirculation of more hot combustion products. Importantly, the latter effect is more significant for achieving the MILD regime. There is a critical mass fraction of the diluent CO₂ present, below which MILD combustion cannot occur. While the traditional premixed flame produces much more NO _x than the MILD combustion, the emission of NO _x appears to result most from the thermal-NO route and least from the N₂O route no matter which mode occurs. Moreover, the present simulation demonstrates that the MILD mode occurs over a wider range of initial reactant conditions for premixed combustion than for diffusion combustion.     

Supersonic flow of a combustible gas mixture past a sphere

In recent years considerable interest has developed in the problems of steady-state supersonic flow of a mixture of gases about bodies with the formation of detonation waves and slow combustion fronts. This is due in particular to the problem of fuel combustion in a supersonic air stream.In [1] the problem of supersonic flow past a wedge with a detonation wave attached to the wedge apex is solved. This solution is based on using the equation of the detonation polar obtained in [2]-the analog of the shock polar for the case of an exothermic discontinuity. In [3] a solution is given of the problem of cone flow with an attached detonation wave, and [4] presents solutions of the problems of supersonic flow past the wedge and cone with the formation of attached adiabatic shocks with subsequent combustion of the mixture in slow combustion fronts. In the two latter studies two different solutions were also found for the problem of flow past a point ignition source, one solution with gas combustion in the detonation wave, the other with gas combustion in the slow combustion front following the adiabatic shock. These solutions describe two different asymptotic pictures of flow of a combustible gas mixture past bodies.In an experimental study of the motion of a sphere in a combustible gas mixture [5] it was found that the detonation wave formed ahead of the sphere splits at some distance from the body into an ordinary (adiabatic) shock and a slow combustion front. Arguments are presented in [6] which make it possible to explain this phenomenon and in certain cases to predict its occurrence.The present paper presents examples of the calculation of flow of a combustible gas mixture past a sphere with a detonation wave in the case when the wave does not split. In addition, the flow near the point at which the detonation wave splits is analyzed for the case when splitting occurs where the gas velocity behind the wave is greater than the speed of sound. This analysis shows that in the given case the flow calculation may be carried out without any particular difficulties. On the other hand, the calculation of the flow for the case when the point of splitting is located in the subsonic portion of the flow behind the wave (or in the region of influence of the subsonic portion of the flow) presents difficulties. This flow case is similar to the problem of the supersonic jet of finite width impacting on an obstacle.     

Numerical simulation of a low-emission gas turbine combustor using KIVA-II

A numerical study was performed to investigate chemically reactive flows with sprays inside a staged turbine combustor (STC) using a modified version of the KIVA-II code. This STC consists of a fuel nozzle (FN), a rich-burn (RB) zone, a converging connecting pipe, a quick-quench (QQ) zone, a diverging connecting pipe and a lean-combustion (LC) zone. From the computational viewpoint, it is more efficient to split the STC into two subsystems, called FN/RB zone and QQ/LC zones, and the numerical solutions were obtained separately for each subsystem. This paper addresses the numerical results of the STC which is equipped with an advanced airblast fuel nozzle. The airblast nozzle has two fuel injection passages and four air flow passages. The input conditions used in this study were chosen similar to those encountered in advanced combustion systems. Preliminary results generated illustrate some of the major features of the flow and temperature fields inside the STC. Velocity, temperature and some critical species information inside the FN/RB zone are given. Formation of the co- and counter-rotating bulk flow and the sandwiched-ring-shaped temperature field, typical of the confined inclined jet-in-cross-flow, can be seen clearly in the QQ/LC zones. The calculations of the mass-weighted standard deviation and the pattern factor of temperature revealed that the mixing performance of the STC is very promising. The temperature of the fluid leaving the LC zone is very uniform. Prediction of the NO_x emission shows that there is no excessive thermal NO_x produced in the QQ/LC zones for the case studied. From the results obtained so far, it appears that the modified KIVA-II code can be used to guide the low-emission combustion experiments.     

Experimental and numerical investigations on PDE performance augmentation by means of an ejector

To improve the performance of pulse detonation engines, a 48 cm long cylindrical combustion chamber of 5cm internal diameter (i.d.) is fitted with an ejector of constant section. The role of the ejector is (i) to provide partial confinement of the detonation products escaping from the chamber and (ii) to suck in fresh air and then to increase the mass ejected compared to the ejection of burned gases alone.The combustion chamber is fully filled with a stoichiometric ethylene/oxygen mixture at ambient conditions. Three parameters of the ejector are varied: the i.d. D, the length L, and the position d relative to the thrust wall of the combustion chamber. For various configurations, the specific impulse (I _sp) is determined in single shot experiments. The maximum operating frequency (f _max) and the maximum thrust are then deduced. I _sp is measured by means of the ballistic pendulum method, and f _max is derived from the pressure signal recorded on the combustion chamber thrust wall.The addition of an ejector increases the specific impulse up to 60% in the best configuration tested, from 164s without ejector to 260s with ejector. The specific impulse can be represented by a single curve using suitable dimensionless parameters. The thrust results for the main ejector studied (D = 80mm) indicate an optimal (L, d) configuration that provides a 28% thrust gain. For the same ejector, f _max remains constant and equal to the frequency obtained without ejector in a large range of (L, d) values, before decreasing.Two-dimensional unsteady numerical computations agree reasonably with the experiments, slightly overestimating the experimental values. The results indicate that 80% of the I _sp gain comes from the action of the expanding detonation products on the annular end surface of the combustion chamber, governed by the tube wall thickness.This paper was based on the work that was presented at the 19th International Colloquium on the Dynamics of Explosions and Reactive Systems, Hakone, Japan, July 27–August 1, 2003 PACS 47.40.Rs     

Comparison of Combustion Models and Assessment of Their Applicability to the Simulation of Premixed Turbulent Combustion in IC-Engines

In order to simulate the turbulent combustion process occurring in spark-ignition (IC) engines, it is necessary to provide suitable and numerically economical models, the latter being particularly important in the application to industrial problems. Moreover, these models must deliver sufficiently accurate results for the unsteady operation of spark combustion engines, concerning variable geometries, temperatures, pressures and charge development in different configurations. In this work different turbulent combustion models for premixed hydrocarbon combustion are compared with respect to their ability to accurately predict the propagation of turbulent perfectly premixed flames. As a first configuration a cylinder of constant volume was studied. Transient calculations were used to simulate the propagation of the turbulent flame and to evaluate the resulting turbulent burning velocity. These calculations were performed for a perfect mixture of air and hydrocarbons at stoichiometric mixture and different initial conditions concerning pressure, temperature and turbulence intensity. As a second configuration a stationary turbulent bunsen-type flame with methane fuel was used to validate the turbulent combustion model of [Lindstedt and Vaos, Combust. Flame 116 (1999) 461] at different pressures. Calculated results were then compared to experimental data of [Kobayashi, Tamura, Maruta and Niioka. In: Proceedings of the 26th Symposium on Combustion, 1996, p. 389] and show excellent agreement for the turbulent burning velocity at several pressure levels using only a single set of model parameters.     

Numerical Simulation of Delft-Jet-in-Hot-Coflow (DJHC) Flames Using the Eddy Dissipation Concept Model for Turbulence–Chemistry Interaction

In this paper, we report results of a numerical investigation of turbulent natural gas combustion for a jet in a coflow of lean combustion products in the Delft-Jet-in-Hot-Coflow (DJHC) burner which emulates MILD (Moderate and Intense Low Oxygen Dilution) combustion behavior. The focus is on assessing the performance of the Eddy Dissipation Concept (EDC) model in combination with two-equation turbulence models and chemical kinetic schemes for about 20 species (Correa mechanism and DRM19 mechanism) by comparing predictions with experimental measurements. We study two different flame conditions corresponding to two different oxygen levels (7.6% and 10.9% by mass) in the hot coflow, and for two jet Reynolds number (Re = 4,100 and Re = 8,800). The mean velocity and turbulent kinetic energy predicted by different turbulence models are in good agreement with data without exhibiting large differences among the model predictions. The realizable k-ε model exhibits better performance in the prediction of entrainment. The EDC combustion model predicts too early ignition leading to a peak in the radial mean temperature profile at too low axial distance. However the model correctly predicts the experimentally observed decreasing trend of lift-off height with jet Reynolds number. A detailed analysis of the mean reaction rate of the EDC model is made and as possible cause for the deviations between model predictions and experiments a low turbulent Reynolds number effect is identified. Using modified EDC model constants prediction of too early ignition can be avoided. The results are weakly sensitive to the sub-model for laminar viscosity and laminar diffusion fluxes.     

Experimental investigation of combustion mechanisms of kerosene-fueled scramjet engines with double-cavity flameholders

A scramjet combustor with double cavitybased flameholders was experimentally studied in a directconnected test bed with the inflow conditions of M = 2.64,Pt = 1.84 MPa,Tt = 1 300 K.Successful ignition and selfsustained combustion with room temperature kerosene was achieved using pilot hydrogen,and kerosene was vertically injected into the combustor through 4×φ 0.5 mm holes mounted on the wall.For different equivalence ratios and different injection schemes with both tandem cavities and parallel cavities,flow fields were obtained and compared using a high speed camera and a Schlieren system.Results revealed that the combustor inside the flow field was greatly influenced by the cavity installation scheme,cavities in tandem easily to form a single side flame distribution,and cavities in parallel are more likely to form a joint flame,forming a choked combustion mode.The supersonic combustion flame was a kind of diffusion flame and there were two kinds of combustion modes.In the unchoked combustion mode,both subsonic and supersonic combustion regions existed.While in the choked mode,the combustion region was fully subsonic with strong shock propagating upstream.Results also showed that there was a balance point between the boundary separation and shock enhanced combustion,depending on the intensity of heat release.     

Combustion Fronts in a Porous Medium with Two Layers

We study a model for the lateral propagation of a combustion front through a porous medium with two parallel layers having different properties. The reaction involves oxygen and a solid fuel. In each layer, the model consists of a nonlinear reaction–diffusion–convection system, derived from balance equations and Darcy’s law. Under an incompressibility assumption, we obtain a simple model whose variables are temperature and unburned fuel concentration in each layer. The model includes heat transfer between the layers. We find a family of traveling wave solutions, depending on the heat transfer coefficient and other system parameters, that connect a burned state behind the combustion front to an unburned state ahead of it. These traveling waves are strong: they correspond to connecting orbits of a system of five ordinary differential equations that lie in the unstable manifold of a hyperbolic saddle and the stable manifold of a nonhyperbolic equilibrium. We argue that for physically relevant initial conditions, traveling waves that correspond to connecting orbits that approach the nonhyperbolic equilibrium along its center direction do not occur. When the heat transfer coefficient is small, we prove that strong traveling waves exist for a small range of system parameters, near parameter values where the two layers individually admit strong traveling waves with the same speed. When the heat transfer coefficient is large, we prove that strong traveling waves exist for a very large range of parameters. For small heat transfer, combustion typically does not occur simultaneously in the two layers; for large heat transfer, it does. The proofs use geometric singular perturbation theory. We give a numerical method to solve the nonlinear problem, and we present numerical simulations that indicate that the traveling waves we have found are in fact the dominant feature of solutions.     

Viscosity Solutions of a Degenerate Parabolic-Elliptic System Arising in the Mean-Field Theory of Superconductivity

In a Type‐II superconductor the magnetic field penetrates the superconducting body through the formation of vortices. In an extreme Type‐II superconductor these vortices reduce to line singularities. Because the number of vortices is large it seems feasible to model their evolution by an averaged problem, known as the mean-field model of superconductivity. We assume that the evolution law of an individual vortex, which underlies the averaging process, involves the current of the generated magnetic field as well as the curvature vector. In the present paper we study a two‐dimensional reduction, assuming all vortices to be perpendicular to a given direction. Since both the magnetic field H and the averaged vorticity ω are curl‐free, we may represent them via a scalar magnetic potential q and a scalar stream function ψ, respectively. We study existence, uniqueness and asymptotic behaviour of solutions (ψ, q) of the resulting degenerate elliptic‐parabolic system (with curvature taken into account or not) by means of viscosity and weak solutions. In addition we relate (ψ, q) to solutions (ω, H) of the mean‐field equations without curvature. Finally we construct special solutions of the corresponding stationary equations with two or more superconducting phases. (Accepted August 8, 1997)     

Supersonic H2-air combustions behind oblique shock waves

In order to study the mechanisms of initiation and stabilization of H₂-Air combustions (stoechiometric mixture initially atT ₀=293 K andp ₀=0.5 bar) in supersonic flow conditions behind an oblique shock wave (OSW), an original technique is used where OSW is generated in this mixture by the lateral expansion of the burnt gas behind a normal CJ gaseous detonation propagating into a bounding reactive mixture. Four Mach numberM of propagation of OSW are considered in the study, namelyM=7.7-6.1-4.4 and 3. Depending on the Mach numberM and inclinaison angle of OSW different regimes of combustion may occur in the driven mixture. For high values ofM (6.1 and 7.7) delayed steady overdriven oblique detonation waves (SODW) were obtained with a near CJ detonation wave as the critical regime. It was found that SODW obtained correspond quite well to prediction of the polar method. When thermal conditions behind the OSW are lower, either for high Mach number 6.1 and 7.7 for smaller angle than the previous case, or for lower Mach number, 4.4 and 3, the flame initiated at the apex is stabilized as a turbulent oblique flame behind the OSW. With much lower conditions, no combustion appears in the H₂-Air mixture.     

Direct Numerical Simulations of Localised Forced Ignition in Turbulent Mixing Layers: The Effects of Mixture Fraction and Its Gradient

The effects of mixture fraction value ξ and the magnitude of its gradient |∇ξ| at the ignitor location on the localised forced ignition of turbulent mixing layers under decaying turbulence is studied based on three-dimensional compressible Direct Numerical Simulations (DNS) with simplified chemistry. The localised ignition is accounted for by a spatial Gaussian power distribution in the energy transport equation, which deposits energy over a prescribed period of time. In successful ignitions, it is observed that the flame shows a tribrachial structure. The reaction rate is found to be greater in the fuel rich side than in stoichiometric and fuel-lean mixtures. Placing the ignitor at a fuel-lean region may initiate ignition, but extinction may eventually occur if the diffusion of heat from the hot gas kernel overcomes the heat release due to combustion. It is demonstrated that ignition in the fuel lean region may fail for an energy input for which self-sustained combustion has been achieved in the cases of igniting at stoichiometric and fuel-rich locations. It is also found that the fuel reaction rate magnitude is negatively correlated with density-weighted scalar dissipation rate in the most reactive region. An increase in the initial mixture fraction gradient at the ignition centre for the ignitor placed at stoichiometric mixture decreases the spreading of the burned region along the stoichiometric mixture fraction isosurface. By contrast, the mass of the burned region increases with an increase in the initial mixture fraction gradient at the ignition location, as for a given ignition kernel size the thinner mixing layer includes more fuel-rich mixture, which eventually makes the overall burning rate greater than that compared to a thicker mixing layer where relatively a smaller amount of fuel-rich mixture is engulfed within the hot gas kernel. Submitted as a full-length article to Flow Turbulence and Combustion.     

Asymptotic Behavior of Solutions to a Model for the Flow of a Reacting Fluid

We give a complete analysis of solutions of a model for the flow of a multispecies reacting fluid occupying a thin cylinder whose walls may be semipermeable with respect to some or all of the chemical species. We prove the global existence of solutions and establish a number of time-independent a priori bounds sufficient to determine the corresponding time-asymptotic steady-state. We then derive necessary conditions and sufficient conditions ensuring that this steady-state reflects complete combustion, that is, that at least one of the reactant species is depleted.     

UNSTEADY CONFINED VISCOUS FLOWS WITH OSCILLATING WALLS AND MULTIPLE SEPARATION REGIONS OVER A DOWNSTREAM-FACING STEP

This paper presents computational solutions for unsteady viscous flows in channels with a downstream-facing step, followed by an oscillating floor. These solutions of the unsteady Navier–Stokes equations are obtained with a time-integration method using artificial compressibility in a fixed computational domain, which is obtained via a time-dependent coordinate transformation from the fluid domain with moving boundaries. The computational method is first validated for steady viscous flows past a downstream-facing step by comparison with previous numerical solutions and experimental results. This method is then used to obtain solutions for unsteady viscous flows with multiple separation regions over a downstream-facing step with oscillating walls, for which there are no previously known solutions. Thus, the present results may be used as benchmark solutions for the unsteady viscous flows with multiple separation regions between fixed and oscillating walls.