Detonation combustion of hydrogen in a convergent-divergent nozzle with a central coaxial cylinder

The feasibility of steady detonation combustion of a hydrogen-air mixture entering at a supersonic velocity in an axisymmetric convergent-divergent nozzle with a central coaxial cylinder is considered. The problem of the nozzle starting and the initiation of detonation combustion is numerically solved with account for the interaction of the outflowing gas with the external supersonic flow. The modeling is based on the gasdynamic Euler equations for an axisymmetric flow. The calculations are carried out using the Godunov scheme on a fine fixed grid which allows one to study in detail the interaction of an oblique shock wave formed in the diffuser with the nozzle axis. It is shown that a central coaxial cylinder ensures the starting with the formation of supersonic flow throughout the entire nozzle and stable detonation combustion of a stoichiometric hydrogen-air mixture in the divergent section of the nozzle.     

Numerical modeling of detonation combustion of hydrogen-air mixtures in a convergent-divergent nozzle

The flow of igniting hydrogen-air mixtures entering an axisymmetric convergent-divergent nozzle at a supersonic velocity is considered. A possibility of stabilizing detonation combustion is numerically investigated at different freestream Mach numbers with account for nonuniform distribution of hydrogen concentration at the nozzle entry. The investigation is performed on the basis of the two-dimensional gasdynamic Euler equations for a multicomponent reacting gas. A detailed model of chemical reactions is used. The calculated thrust is compared with the drag of a conical housing containing the supersonic nozzle considered.     

Investigation of certain techniques for stabilizing detonationwaves in a supersonic flow

The salient features of detonation wave propagation in a supersonic flow of a stoichiometric hydrogen-air mixture in plane channels of both constant and variable cross-section are numerically investigated for the purpose of determining the conditions ensuring stabilized detonation. The propagation of a detonation wave formed in a variable-cross-section channel is studied. For different inflow Mach numbers the geometric parameters of a channel providing the detonation combustion stabilization are determined. An investigation of detonation wave stabilization in a supersonic flow of a combustible gas mixture in a plane channel with parallel walls using additional weak discharges is continued. The effects of the flow Mach number, the additional discharge energy, and the discharge location on detonation wave stabilization are studied.     

Stability of detonation combustion with respect to the variation in the hydrogen concentration at the supersonic nozzle inlet

Detonation combustion of hydrogen-air mixtures entering an axisymmetric convergent-divergent nozzle at a supersonic velocity is considered. The nozzle geometry does not ensure gas self-ignition; for this reason, forced ignition is used, which, under certain conditions, leads to the formation of stationary detonation combustion in the case of both uniform and nonuniform hydrogen distribution at the channel entry. The nonlinear problem of the stability of these combustion regimes against periodic disturbances of the hydrogen concentration in the oncoming flow is numerically solved. The study is performed on the basis of the two-dimensional gasdynamic Euler equations for a multicomponent reacting gas. A detailed model of chemical reactions is used.     

Stability of gas mixture flow with a stabilized detonation wave in a plane channel with a constriction

The stability of a flow with a stabilized detonation wave is studied within the framework of a detailed kinetic mechanism of the chemical interaction. The flow is due to the initiation of detonation combustion of a stoichiometric hydrogen-air mixture that enters into a plane channel with a constriction at a supersonic velocity greater than that of the self-sustained detonation propagation. The flow under consideration is numerically investigated using the software package developed by the authors. It is established that the flow formed in the channel, whose geometric parameters ensure the detonation stabilization in the case of the inflow Mach number M₀ = 5.2, is stable against strong disturbances of a certain type. The effect of an increase in the inflow Mach number and the dustiness of the combustible gas mixture entering into the channel on the stabilization of detonation combustion in the flow is investigated.     

Calculation of hydrogen-air combustion behind detached shock wave for supersonic flow past a sphere

Many of the published theoretical studies of quasi-one-dimensional flows with combustion have been devoted to combustion in a nozzle, wake, or streamtube behind a normal shock wave [1–6].Recently, considerable interest has developed in the study of two-dimensional problems, specifically, the effective combustion of fuel in a supersonic air stream.In connection with experimental studies of the motion of bodies in combustible gas mixtures using ballistic facilities [7–9], the requirement has arisen for computer calculations of two-dimensional supersonic gas flow past bodies in the presence of combustion.In preceding studies [10–12] the present author has solved the steady-state problem under very simple assumptions concerning the structure of the combustion zone in a detonation wave.In the present paper we obtain a numerical solution of the problem of supersonic hydrogen-air flow past a sphere with account for the nonequilibrium nature of eight chemical reactions. The computations encompass only the subsonic and transonic flow regions.The author thanks G. G. Chernyi for valuable comments during discussion of the article.     

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.     

Distinctive features of galloping detonation in a supersonic combustible-mixture flow under an inert gas layer

The problem of detonation initiation in a supersonic flow of a stoichiometric propane-air mixture occupying partially or completely the cross-section of a plane channel is considered. The initiation in the flow is produced by a step or a wall completely cutting off the flow. The study is conducted within the framework of one-stage combustion kinetics. A numerical method based on the Godunov scheme is employed. The critical conditions for detonation formation are determined in terms of the oncoming flow velocity. A previously unknown mechanism of detonation propagation is found; it is related with the presence of the combustible mixture in the wall layer under an inert gas layer. It is due to the formation of a complicated wave structure of the flow characterized by the penetration of a shock wave formed in the inert gas layer into a combustible mixture layer ahead of the detonation wave with the result that the latter layer is heated and ignited. The process as a whole is periodic in nature, as distinct from the conventional cellular detonation in a homogeneous fluid. Many problems arise in connection with the use of detonation in engines and other power plants. The most important among them are detonation excitation and stabilization in combustion chambers. The detonation initiation within a layer under conditions of unbounded space and a fluid at rest was experimentally investigated in [1]. In the case of a combustion chamber bounded in the transverse direction, some new effects accompanying the detonation might be expected.     

多循环脉冲爆震发动机流场数值研究

针对二维带有收敛扩张喷管的脉冲爆震发动机模型，采用带基元化学反应的Euler方程组和H2、空气的9组分20基元反应，对发动机在前六个工作循环的流场进行了数值模拟。通过对前几个循环流场进行比较，发现脉冲爆震发动机在第五个循环后流场就基本稳定，单循环得到的流场和多循环稳定后的流场有很大的差别，同时喷管对发动机内流场影响特别大。     

Generation and stabilization of detonation in a plane elbowed channel

The problem of detonation initiation in a supersonic flow of a stoichiometric propane-air mixture in a plane elbowed channel of constant width is considered. In the bend zone the channel walls are made in the shape of circles of given radii, whose lengths are determined by the given angle of the channel turn. An investigation is performed within the framework of the single-stage combustion kinetics using a numerical method based on the Godunov scheme and included in an original program complex, or a “virtual experimental setup”, developed for performing multiparameter calculations and flow visualization. The critical conditions of detonation generation are determined as functions of the oncoming flow velocity, the channel turn angle and width, and the radii of curvature of the walls.     

Stabilization of detonation combustion in a high-velocity flow of a hydrogen-oxygen mixture

The flow of a hydrogen-oxygen mixture diluted with argon in a supersonic axisymmetric nozzle consisting of an inlet cylinder, a convergent region, a cylindrical throat, and a divergent region is considered. The supersonic flow enters the channel along the axis of symmetry. The flow structure is calculated with allowance for hydrogen ignition. A possibility of stabilizing the combustion zone is studied and the forces acting on the nozzle from the flow are determined. The problem is solved in the two-dimensional approximation with account for detailed combustion kinetics.     

Supersonic flow of combustible gas mixture past sphere with account for ignition delay time

Assume an axisymmetric blunt body or a symmetric profile is located in a uniform supersonic combustible gas mixture stream with the parameters M₁, p₁, and T₁. A detached shock is formed ahead of the body and the mixture passing through the, shock is subjected to compression and heating. Various flow regimes behind the shock wave may be realized, depending on the freestream conditions. For low velocities, temperatures, or pressures in the free stream, the mixture heating may not be sufficient for its ignition, and the usual adiabatic flow about the body will take place. In the other limiting case the temperature behind the adiabatic shock and the degree of gas compression in the shock are so great that the mixture ignites instantaneously and burns directly behind the shock wave in an infinitesimally thin zone, i. e., a detonation wave is formed. The intermediate case corresponds to the regime in which the width of the reaction zone is comparable with the characteristic linear dimension of the problem, for example, the radius of curvature of the body at the stagnation point.The problem of supersonic flow of a combustible mixture past a body with the formation of a detonation front has been solved in [1, 2]. The initial mixture and the combustion products were considered perfect gases with various values of the adiabatic exponent .These studies investigated the effect of the magnitude of the reaction thermal effect and flow velocity on the flow pattern and the distribution of the gasdynamic functions behind the detonation wave.In particular, the calculations showed that the strong detonation wave which is formed ahead of the sphere gradually transforms into a Chapman-Jouguet wave at a finite distance from the axis of symmetry. For planar flow in the case of flow about a circular cylinder it is shown that the Chapman-Jouguet regime is established only asymptotically, i. e., at infinity.This result corresponds to the conclusions of [3, 4], in which a theoretical analysis is given of the asymptotic behavior of unsteady flows with planar, spherical, and cylindrical detonation waves.Available experimental data show that in many cases the detonation wave does not degenerate into a Chapman-Jouguet wave as it decays, bur rather at some distance from the body it splits into an adiabatic shock wave and a slow combustion front.The position of the bifurcation point cannot be determined within the framework of the zero thickness detonation front theory [1], and for the determination of the location of this point we must consider the structure of the combustion zone in the detonation wave. Such a study was made with very simple assumptions in [5].The present paper presents a numerical solution of the problem of combustible mixture flow about a sphere with a very simple model for the structure of the combustion zone, in which the entire flow behind the bow shock wave consists of two regions of adiabatic flow-an induction region and a region of equilibrium flow of products of combustion separated by the combustion front in which the mixture burns instantaneously. The solution is presented only for subsonic and transonic flow regions.     

Detonation combustion of hydrogen in an axisymmetric channel with a central body

The problem of initiation and stabilization of detonation combustion of a hydrogen–air mixture injected into an axisymmetric channel with a finite-length central body in a flow with a Mach number M₀ = 5–9 is solved. It is numerically demonstrated that the presence of the central body both in a convergent–divergent nozzle and in an expanding channel leads to stabilization of detonation combustion of a stoichiometric hydrogen–air mixture at free-stream Mach numbers M₀ > 7. Various channel configurations that ensure different values of thrust generated by detonation combustion of a stoichiometric hydrogen–air mixture are compared.     

Nozzle startup in an oncoming flow

Three variants of the startup of an axisymmetric convergent-divergent nozzle are considered with the static pressures at the entry and exit of the nozzle being the same at the beginning of the process. The subsonic startup corresponds to open nozzle acceleration in air. The supersonic startup simulates the sudden opening of a cover at the nozzle inlet under supersonic flight conditions. A successful nozzle startup with the formation of steady supersonic flow along the whole channel is realized in the third variant of supersonic startup with gas injection through a small region of the wall of the divergent nozzle section. The investigation is performed numerically, on the basis of the Euler equations for axisymmetric gas flows.     

旋转爆震燃烧室轴向和周向长度对其出口流场压力和温度的影响

为了研究旋转爆震燃烧室与涡轮的匹配特性,利用二维欧拉方程数值研究了基于当量H₂/Air燃烧的旋转爆震燃烧室出口流场特性,对比分析了不同燃烧室轴向长度和周向长度出口总压脉动、总压畸变以及出口温度分布规律。结果表明:旋转爆震燃烧室在稳定工作状态下,其出口总压的脉动值会呈现周期性振荡;燃烧室尺度对发动机出口流场的不均匀性有很大影响,随着燃烧室轴向长度的增大或周向尺寸的减小,其出口总压脉动均值、畸变指数和出口温度分布系数均会减小,其出口流场均匀性提高。此外,爆震波高度随着周向尺寸的增大而增大;轴向尺寸对爆震波高度几乎不产生影响。     

Propagation of detonation waves in plane channels with obstacles

The detonation wave propagation in plane channels filled with a stoichiometric hydrogen-air mixture at rest under standard conditions is numerically modeled with account for the actual kinetics of the chemical interaction. The calculations show that the stable cellular structure of the detonation wave formed in a plane channel with parallel walls is not always uniquely determined by its width. The effect of transverse walls and sharp expansion of the channel on the propagation of the cellular detonation wave is studied. The conditions of conservation and restoration of detonation are determined.     

Detonation and deflagration initiation at the focusing of shock waves in combustible gaseous mixture

Abstract. Detonation and deflagration initiation under focusing conditions in a lean hydrogen-air mixture was experimentally investigated. The experiments were carried out in a shock tube equipped with the laser schlieren system and pressure transducers. Two-dimensional wedges (53° and 90°), semi-cylinder and parabola, were used as the focusing elements. The peculiarities of mild and strong ignition inside the reflector cavity were visualized. A hydrogen-nitrogen mixture was taken for comparison between reactive and inert mixture. It was found that mild ignition inside the reflector cavity can lead to detonation initiation outside the cavity. Schlieren pictures of the process were obtained and the dependence of the distance of detonation initiation on Mach number of the incident shock wave was established. Received 30 August 1999 / Accepted 23 February 2000     

斜爆轰发动机的推力性能理论分析

爆轰燃烧具有释热快、循环热效率高的特点. 斜爆轰发动机利用斜爆轰波进行燃烧组织, 在高超声速吸气式推进系统中具有重要地位. 以往研究主要关注斜爆轰波的起爆、驻定以及波系结构等, 缺少从整体层面出发对斜爆轰发动机开展推力性能分析. 本文将斜爆轰发动机内的流动和燃烧过程分解成进气压缩、燃料掺混、燃烧释热和排气膨胀4个基本模块并分别进行理论求解, 建立了斜爆轰发动机推力性能的理论分析模型. 在斜爆轰波系研究成果的基础上, 选取了过驱动斜爆轰、Chapman?Jouguet斜爆轰、过驱动正爆轰和斜激波诱导等容燃烧等4种燃烧模式来描述燃烧室内的燃烧释热过程, 并对比分析了不同燃烧模式对发动机比冲性能的影响. 此外, 还获得了不同来流参数、燃烧室参数和进排气参数等对发动机推力的影响规律, 发现来流马赫数和尾喷管的膨胀面积比是发动机理论燃料比冲的主要影响因素. 最后, 结合以往关于受限空间内斜爆轰波驻定特性等方面的研究成果, 提出了斜爆轰发动机燃烧室的设计方向.      

关于超声速燃烧与高超动力

先进发动机是航空工业的核心技术,而吸气式高超声速发动机一直是宇航飞行技术研发的首位难题.发动机的性能依赖于其能量转换模式和燃烧组织方法,相关理论研究具有基础性和启发性意义.论文首先讨论了超声速燃烧,它一直是超燃冲压发动机技术的理论基础.然后综述了相关研究进展,提出了吸气式高超声速冲压推进技术的3个临界条件,或者称为临界...