Spatial Direct Numerical Simulation of the Large Vortical Structures in Forced Plumes

Direct numerical simulation (DNS) of forced plumes arising frominput of both momentum and buoyancy into an ambient fluid is presented.The large vortical structures in the near field of thermal and reactiveplumes are investigated. Boundary conditions associated with the spatialDNS of open-boundary buoyant flows that are compatible with the modernnon-dissipative, high-order, finite-difference schemes have beendeveloped. The governing equations for flow and combustion at the plumecenterline are put into a special form to circumvent the singularity atthe axis associated with the cylindrical coordinates. Mixing is found tobe stronger in the planar thermal plume than in the axisymmetric case.An explanation is provided based on the vorticity budget. Axisymmetricreactive plumes with a one-step reaction governed by the Arrheniuskinetics have also been studied. The unsteady effects of chemical heatrelease and combustion-induced buoyancy on the flow structures areinvestigated. Budgets of the vorticity transport are examined to revealthe mechanisms leading to the formation and evolution of large vorticalstructures in forced plumes. It is found that volumetric expansion dueto chemical heat release tends to destroy vorticity, whilecombustion-induced buoyancy under the gravitational effect generatesvorticity. The gravitational term in the vorticity transport equation isfound to be the main mechanism for the buoyant flow instability and thedevelopment of counter-rotating vortices in reactive plumes.     

A computational study of supersonic combustion behind a wedge-shaped flameholder

In this study, large eddy simulation (LES) has been used to examine supersonic flow, mixing, self-ignition and combustion in a model scramjet combustor and has been compared against the experimental data. The LES model is based on an unstructured finite-volume discretization, using monotonicity-preserving flux reconstruction of the filtered mass, momentum, species and energy equations. Both a two-step and a seven-step hydrogen–air mechanism are used to describe the chemical reactions. Additional comparisons are made with results from a previously presented flamelet model. The subgrid flow terms are modeled using a mixed model, whereas the subgrid turbulence–chemistry interaction terms are modeled using the partially stirred reactor model. Simulations are carried out on a scramjet model experimentally studied at Deutsches Zentrum für Luft- und Raumfahrt consisting of a one-sided divergent channel with a wedge-shaped flame holder at the base of which hydrogen is injected. The LES predictions are compared with experimental data for velocity, temperature, wall pressure at different cross sections as well as schlieren images, showing good agreement for both first- and second-order statistics. In addition, the LES results are used to illustrate and explain the intrinsic flow, and mixing and combustion features of this combustor.     

Comparison Between Numerically Simulated and Experimentally Measured Flowfield Quantities Behind a Pulsejet

Pulsed combustion is receiving renewed interest as a potential route to higher performance in air breathing propulsion and ground based power generation systems. Pulsejets offer a simple experimental device with which to study unsteady combustion phenomena and validate simulations. Previous computational fluid dynamics (CFD) simulations focused primarily on pulsejet combustion and exhaust processes. This paper describes a new inlet sub-model which simulates the fluidic and mechanical operation of a valved pulsejet head. The governing equations for this sub-model are described. Sub-model validation is provided through comparisons of simulated and experimentally measured reed valve motion, and time averaged inlet mass flow rate. The updated pulsejet simulation, with the inlet sub-model implemented, is validated through comparison with experimentally measured combustion chamber pressure, inlet mass flow rate, operational frequency, and thrust. Additionally, the simulated pulsejet exhaust flowfield, which is dominated by a starting vortex ring, is compared with particle imaging velocimetry (PIV) measurements on the bases of velocity, vorticity, and vortex location. The results show good agreement between simulated and experimental data. The inlet sub-model is shown to be critical for the successful modeling of pulsejet operation. This sub-model correctly predicts both the inlet mass flow rate and its phase relationship with the combustion chamber pressure. As a result, the predicted pulsejet thrust agrees very well with experimental data.     

Interpretation of wake instability at slip line in rotating detonation

ABSTRACT

In studies on instabilities of flowfield in rotating detonation, one of the most common concerns is the instability at the slip line originating from the conjunction of the detonation wave and oblique shock. Using Euler equations associated with the 7-species-and-8-reaction finite-rate chemical reaction model of hydrogen/air mixtures, further studies are performed to simulate the 2-D rotating detonation, and the flow mechanism of instability at the slip line is investigated in depth. The results show that the distinct wake profile exists at the slip line, which is different from the typical mixing layer. Analysis indicates that the generation of wake is caused by the transition shock between the detonation wave and oblique shock. Because of the wake profile, the vorticity distribution therein appears in a double-layer layout, and different evolutions exist in different vorticity layers. Based on the velocity profile across the slip line, the analysis by the linear stability theory is made, and two main unstable modes which have different shape profiles and phase velocities are found. Discrete Fourier transformation is utilised to analyse the numerical results, and similar shape profiles are obtained. A general coincidence in velocity of vortex movement is also attained between the theoretical predictions and simulations. Investigations show that the wake instability is responsible for the unstable mechanism, and corresponding unstable structures differ from the canonical ones in typical mixing layers.     

Effect of boundary vorticity discretization on explicit stream‐function vorticity calculations

The numerical solution of the time‐dependent Navier–Stokes equations in terms of the vorticity and a stream function is a well tested process to describe two‐dimensional incompressible flows, both for fluid mixing applications and for studies in theoretical fluid mechanics. In this paper, we consider the interaction between the unsteady advection–diffusion equation for the vorticity, the Poisson equation linking vorticity and stream function and the approximation of the boundary vorticity, examining from a practical viewpoint, global iteration stability and error. Our results show that most schemes have very similar global stability constraints although there may be small stability gains from the choice of method to determine boundary vorticity. Concerning accuracy, for one model problem we observe that there were cases where the boundary vorticity discretization did not propagate to the interior, but for the usual cavity flow all the schemes tested had error close to second order. Copyright © 2005 John Wiley & Sons, Ltd.     

Accessed Compositions in Turbulent Reactive Flows

At a given position and time in a turbulent reactive flow involving many chemical species, the thermochemical composition corresponds to a point in the multi-dimensional composition space. The union of all such points, for all positions, times and realizations, is defined to be the accessed region of the composition space. The geometry of the accessed region is investigated from several perspectives. Many existing models of turbulent nonpremixed combustion (e.g., equilibrium chemistry, the steady flamelet model, and the conditional moment closure) implicitly assume that the accessed region is a low-dimensional manifold of dimension one or two. It is shown from the conservation equations that the simultaneous actions of mixing and reaction can lead to an accessed region of significantly higher dimension than occurs when mixing and reaction act separately or sequentially. For a laminar flame, the accessed region is a curved manifold of the same dimensionality as the flow; whereas for a turbulent reactive flow it is a plane manifold, generally of higher dimension. Several processes are identified which can lead to the edge of the manifold being nonconvex.     

Numerical study of an inviscid incompressible flow through a channel of finite length

A two‐dimensional inviscid incompressible flow in a rectilinear channel of finite length is studied numerically. Both the normal velocity and the vorticity are given at the inlet, and only the normal velocity is specified at the outlet. The flow is described in terms of the stream function and vorticity. To solve the unsteady problem numerically, we propose a version of the vortex particle method. The vorticity field is approximated using its values at a set of fluid particles. A pseudo‐symplectic integrator is employed to solve the system of ordinary differential equations governing the motion of fluid particles. The stream function is computed using the Galerkin method. Unsteady flows developing from an initial perturbation in the form of an elliptical patch of vorticity are calculated for various values of the volume flux of fluid through the channel. It is shown that if the flux of fluid is large, the initial vortex patch is washed out of the channel, and when the flux is reduced, the initial perturbation evolves to a steady flow with stagnation regions. Copyright © 2008 John Wiley & Sons, Ltd.     

激波冲击火焰的涡量特性研究

激波冲击火焰的现象涉及一系列复杂的物理化学过程,其中涡量的生成与演化对控制火焰发展起重要作用。为系统分析激波冲击火焰过程中的涡量特性,采用二维带化学反应的Navier-Stokes方程对平面入射激波及其反射激波与球形火焰作用的现象进行了数值研究,通过引入并行计算达到高网格分辨率的要求。计算结果表明,斜压项对火焰区内涡量生成起主导作用,压缩项和耗散项在火焰膨胀阶段抑制涡量生成,此外,火焰在激波压缩阶段主要受物理过程而非化学反应过程影响。     

Magnetogasdynamic generation of electrical energy in models of aircraft with a high-speed jet engine

The possibility of generating electric power in a plane model of an integral high-speed hydrogen-burning jet engine by mounting a magnetogasdynamic (MHD) generator at the combustion chamber exit is discussed. Attention is concentrated on clarifying the effect of MHD energy extraction from the stream on the aircraft’s thrust characteristics. The internal and external flows are simulated numerically. The two-dimensional supersonic gasdynamic flow inside the engine (in the air-intake, combustion chamber, MHD generator, and nozzle) and the supersonic flow past the aircraft are described on the basis of the complete averaged system of Navier-Stokes equations (in the presence of turbulence), which includes MHD force and heat sources, a one-parameter turbulence model, the electrodynamic equations for an ideal segmented MHD generator, and the equations of the detailed chemical kinetics of hydrogen burning in air. The numerical solution is obtained by means of a computer program that uses a relaxation scheme and an implicit higher-order version of the Godunov method. It is shown that MHD electric power generation can be realized without disturbing the positive balance in the relation between the thrust and the drag of the aircraft with the engine operating with allowance for the MHD drag, but with some loss of effective thrust.     

Buoyancy-Driven Coherent Structures in Free Round Flame

Complex interactions between fluid dynamics and combustion processes areamong the topics most often undertaken in recent years. The free roundflames dominated by large-scale vortex structures seem to be a veryinteresting type of flow as indicated by the many experimental resultsavailable in literature. The so-called outer coherent structures whichare believed to be generated as a result of buoyancy-driven instabilitywere experimentally investigated by means of laser Doppler anemometry.The results of spectral analysis of fluctuating velocity componentsrevealed the regular oscillations of the flow field with well-defineddiscrete frequencies depending upon the mixture composition. Theexternal excitation of coherent structures at a frequency matching theirnatural shedding frequency allowed the construction of velocity vectormaps of organised vorticity. From the results obtained one may statethat the coherent vortices are located in the outer part of flame withthe trajectory of their centres moving far from the flame front. Theirlocation and very large sizes (comparable with the flow width) suggesttheir important role in mixing and, especially, in the entrainmentprocesses which are the essential in combustion systems.The dimensionalanalysis taking into account the characteristic parameters of vorticesand thermal structure of the flame suggests that buoyancy forces havesignificant impact on organised vorticity and can be considered asresponsible for its origin.     

The influence of fuel injection and heat release on bulk flow structures in a direct-injection, swirl-supported diesel engine

Particle image velocimetry is applied to measure the vertical (r–z) plane flow structures in a light-duty direct-injection diesel engine with a realistic piston geometry. The measurements are corrected for optical distortions due to the curved piston bowl walls and the cylindrical liner. Mean flow fields are presented and contrasted for operation both with and without fuel injection and combustion. For operation with combustion, the two-dimensional divergence of the measured mean velocity fields is employed as a qualitative indicator of the locations of mean heat release. In agreement with numerical simulations, dual-vortex, vertical plane mean flow structures that may enhance mixing rates are formed approximately mid-way through the combustion event. Late in the cycle a toroidal vortex forms outside the bowl mouth. Imaging studies suggest that soot and partially oxidized fuel trapped within this vortex are slow to mix with surrounding fluid; moreover, the vortex impedes mixing of fluid exiting the bowl with air within the squish volume.     

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.     

Joint RANS/LES Approach to Premixed Flame Modelling in the Context of the TFC Combustion Model

We present an original timesaving joint RANS/LES approach to simulate turbulent premixed combustion. It is intended mainly for industrial applications where LES may not be practical. It is based on successive RANS/LES numerical modelling, where turbulent characteristics determined from RANS simulations are used in LES equations for estimation of the subgrid chemical source and viscosity. This approach has been developed using our TFC premixed combustion model, which is based on a generalization of the Kolmogorov’s ideas. We assume existence of small-scale statistically equilibrium structures not only of turbulence but also of the reaction zones. At the same time, non-equilibrium large-scale structures of reaction sheets and turbulent eddies are described statistically by model combustion and turbulence equations in RANS simulations or follow directly without modelling in LES. Assumption of small-scale equilibrium gives an opportunity to express the mean combustion rate (controlled by small-scale coupling of turbulence and chemistry) in the RANS and LES sub-problems in terms of integral or subgrid parameters of turbulence and the chemical time, i.e. the definition of the reaction rate is similar to that of the mean dissipation rate in turbulence models where it is expressed in terms of integral or subgrid turbulent parameters. Our approach therefore renders compatible the combustion and turbulent parts of the RANS and LES sub-problems and yields reasonable agreement between the RANS and averaged LES results. Combining RANS simulations of averaged fields with LES method (and especially coupled and acoustic codes) for simulation of corresponding nonstationary process (and unsteady combustion regimes) is a promising strategy for industrial applications. In this work we present results of simulations carried out employing the joint RANS/LES approach for three examples: High velocity premixed combustion in a channel, combustion in the shear flow behind an obstacle and the impinging flame (a premixed flame attached to an obstacle).     

A Fully Implicit, Compact Finite Difference Method for the Numerical Solution of Unsteady Laminar Flames

Forced laminar diffusion flames form an important class of problems that can help to bridge the significant gap between steady laminar flames in simple burner configurations and the turbulent flames found in many practical combustors. Such flames offer a much wider range of interactions between convection, diffusion, and chemical reaction than can be examined under steady-state conditions, and yet detailed simulations of them should be feasible without having to resort to “modeling” any of the relevant physics, above all without having prematurely to reduce the large kinetic mechanisms typical of hydrocarbon fuels. Nevertheless, the computation of time-dependent laminar diffusion flames with conventional numerical methods is hindered by technical challenges that, while not new, are more troublesome to surmount than in the calculation of otherwise similar, unforced flames. First, the intricate spatiotemporal coupling between fluid dynamics and combustion thermochemistry ensures that spurious numerical diffusion or spatial under-resolution of the mixing process at any stage of the computation can lead to inaccurate prediction of flame characteristics for the remainder thereof. Second, relatively long simulated flow times and extremely short chemical time scales make many standard time integration algorithms impractical on all but the largest parallel computer clusters. This paper introduces a new numerical approach for time-varying laminar flames that addresses these challenges through the use of high order compact finite difference schemes within a robust, fully implicit solver based on a Jacobian-free Newton–Krylov method. The capabilities of this implicit-compact solver are demonstrated on a periodically forced axisymmetric laminar jet diffusion flame with one-step Arrhenius chemistry, and the results are compared to those of a conventional low order finite difference solver.     

激波诱导火焰变形、混合和燃烧的数值研究

为了深入研究激波诱导的火焰变形以及由此带来的混合和燃烧变化特性,采用带单步化学反应的Navier-Stokes方程和高网格分辨率,对平面入射激波及其反射激波诱导球形火焰变形的现象进行了二维数值研究,计算结果与实验结果较好吻合。研究结果显示,在反射激波作用前,火焰的变形和皱褶主要受入射激波诱导等物理过程影响;而在反射激波与失稳火焰作用后,燃烧放热率、火焰有效面积和界面长度均迅速增加,控制火焰变形的机制逐渐向化学反应(燃烧)过程过渡;在失稳火焰发展的后期,增强的燃烧过程能够削弱火焰界面的皱褶,进而抑制未燃气和可燃气的混合。由此可以得出结论,激波诱导的火焰界面通过变形可促进界面两侧未燃气与可燃气的混合,进而强化燃烧过程,但燃烧的增强却反过来能抑制混合;认识两者之间的关系有助于利用或控制激波 火焰相互作用过程。     

Similarity solutions for MHD thermosolutal Marangoni convection over a flat surface in the presence of heat generation or absorption effects

The problem of steady, laminar, thermosolutal Marangoni convection flow of an electrically-conducting fluid along a vertical permeable surface in the presence of a magnetic field, heat generation or absorption and a first-order chemical reaction effects is studied numerically. The general governing partial differential equations are converted into a set of self-similar equations using unique similarity transformations. Numerical solution of the similarity equations is performed using an implicit, iterative, tri-diagonal finite-difference method. Comparisons with previously published work is performed and the results are found to be in excellent agreement. Approximate analytical results for the temperature and concentration profiles as well as the local Nusselt and sherwood numbers are obtained for the conditions of small and large Prandtl and Schmidt numbers are obtained and favorably compared with the numerical solutions. The effects of Hartmann number, heat generation or absorption coefficient, the suction or injection parameter, the thermo-solutal surface tension ratio and the chemical reaction coefficient on the velocity, temperature and concentration profiles as well as quantitites related to the wall velocity, boundary-layer mass flow rate and the Nusselt and Sherwood numbers are presented in graphical and tabular form and discussed. It is found that a first-order chemical reaction increases all of the wall velocity, Nusselt and Sherwood numbers while it decreases the mass flow rate in the boundary layer. Also, as the thermo-solutal surface tension ratio is increased, all of the wall velocity, boundary-layer mass flow rate and the Nusselt and Sherwood numbers are predicted to increase. However, the exact opposite behavior is predicted as the magnetic field strength is increased.     

Particle Simulation of Swirling Flows

The vortex particle method has been applied to the axisymmetric swirling flow of a viscous fluid. The formulation used yields two transport equations which have been solved within the lagrangian framework of particle method. The diffusion operator for both equations has been approximated by means of a Particle Strength Exchange scheme. Applications to the cases of one isolated vortex ring and two co-rotating vortex rings illustrate the interest of this new method. Special attention has been devoted to the vorticity production resulting from the interaction between the azimuthal components of vorticity and velocity. The generation of small eddies at the boundary of the vortex ring cross-section has been particularly investigated. This revised version was published online in July 2006 with corrections to the Cover Date.     

Steady vortex structures in inviscid flows in channels

The problem of inviscid incompressible flow through a rectangular channel is considered under the normal velocity component given at the chanel boundaries and the fluid vorticity at the entry. Nonconventional steady flows with recirculation zones and different functional dependences of the vorticity on the stream function are found by analytical and numerical methods. The stability of the steady regimes obtained is analyzed using the numerical solution of the time-dependent problem by the particle-in-cells method.