Combustion tube studies of dust flame acceleration

A new pneumatic dispersion system for obtaining a good quality uniform dust suspension in a horizontal dust combustion tube was developed. The effect of three different dispersion techniques on self-sustained dust flame acceleration in such a combustion tube was examined. The importance of the dispersion quality in the test tube for maintaining a self-sustained dust flame acceleration was demonstrated. A combustion tube for studies of flame acceleration in fine aluminum dust-air mixture and its transition to detonation under industrial ignition conditions was constructed in the course of the present study. It consists mainly of an initiation section and a test section. The initiation section must be equipped in a well-developed dispersion system for creating a good dispersion condition in the test tube. The length of this section is 3 meters. The test tube requires only to distribute uniformly the dust over the bottom of the tube prior to the experiment. The aluminum dust spherical in shape with 6 μm in diameter was used for tests. Experimental results demonstrated that the increase in flame velocity is roughly linear through the entire length of the test tube. The highest flame propagation velocity in fine aluminum dust-air mixture approaches some 1200m/s at a distance of 4.8m from the ignition plane.     

Experimental and numerical studies on interactions of a spherical flame with incident and reflected shocks

Observations are presented from experiments and calculations where a laminar spherical CH4/air flame is perturbed successively by incident and reflected shock waves. The experiments are performed in a standard shock tube arrangement, in which a high-speed shadowgraph imaging system is used to record evolutions of the flame. Numerical simulations are conducted by using second-order wave propagation algorithms, based on two-dimensional axisymmetric Navier-Stokes equations with detailed chemical reactions. Qualitative agreements are obtained between the experimental and numerical results. Under actions of incident shock waves, Richtmyer-Meshkov instability responsible for the flame deformation is induced in the flame, and the distoned flame takes a barrel shape. Then, under subsequent actions of the shock wave reflected from a planar wall, the flame takes an inclined non-symmetrical kidney shape in a symmetric cross section, which means a mushroom-like shape of the flame comes finally into being. The vorticity direction in the ring cap has been altered by the reflected shock＇s action, which makes the head of the mushroom-like flame extend quickly to the side wall.     

Nonlinear dynamics of a resonant gas sensor

We develop a mathematical model for a resonant gas sensor made up of an microplate electrostatically actuated and attached to the end of a cantilever microbeam. The model considers the microbeam as a continuous medium, the plate as a rigid body, and the electrostatic force as a nonlinear function of the displacement and the voltage applied underneath the microplate. We derive closed-form solutions to the static and eigenvalue problems associated with the microsystem. The Galerkin method is used to discretize the distributed-parameter model and, thus, approximate it by a set of nonlinear ordinary-differential equations that describe the microsystem dynamics. By comparing the exact solution to that associated with the reduced-order model, we show that using the first mode shape alone is sufficient to approximate the static behavior. We employ the Finite Difference Method (FDM) to discretize the orbits of motion and solve the resulting nonlinear algebraic equations for the limit cycles. The stability of these cycles is determined by combining the FDM discretization with Floquet theory. We investigate the basin of attraction of bounded motion for two cases: unforced and damped, and forced and damped systems. In order to detect the lower limit of the forcing at which homoclinic points appear, we conduct a Melnikov analysis. We show the presence of a homoclinic point for a loading case and hence entanglement of the stable and unstable manifolds and non-smoothness of the boundary of the basin of attraction of bounded motion.     

Frequency characteristics of a laminar flame

A theoretical study is made of the effect of harmonic pressure oscillations on a flat laminar flame. Frequency characteristics of the flames are obtained at amplitudes of the pressure oscillations which are small compared with the average pressure. It is established that in a broad range of frequencies the disturbances in the integral rate of heat release occur in phase with the pressure oscillations and depend weakly on the frequency.Translated trom Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 84–94, January–February, 1974.The authors thank V. E. Doroshenko for attention to the work and discussions.     

Modelling of a resonant inertial oscillation within a torus

Summary  We consider the air contained in a pneumatic tyre with the purpose of investigating its inertial oscillations. We model the tyre as a torus limited by a membrane in contact with the ground. According to this model, we prove that the flow within this torus may be considered as one at low Mach number and that it is ruled by oscillations of incompressible rotating fluid. Investigating such inertial oscillations, we show that the geostrophic oscillation is resonant, and we study the resonance phenomenon. Received 6 June 2000; accepted for publication 22 November 2000     

多次激波诱导正弦扰动预混火焰界面失稳的数值研究

激波诱导火焰失稳是实际中常见的现象,为深入研究火焰失稳特性,采用三维单步化学反应的Navier-Stokes方程和9阶weighted essentially non-oscillatory (WENO)的高精度格式,对不同马赫数的入射激波及其反射激波多次诱导正弦型预混火焰界面失稳的现象进行了三维数值模拟,并对计算结果的可靠性进行了验证。研究结果显示,在激波的多次作用下,火焰界面的演变过程主要受Richtmyer-Meshkov (RM)不稳定特性和化学反应特性的双重影响,且随着入射激波强度的增强,上述2种特性均得到进一步强化。为构造体现反应性RM不稳定特性的参数,根据火焰界面混合区平均涡量和化学反应速率,提出了表征界面受不稳定性和化学反应影响的量纲一参数。通过分析发现,在同一入射激波强度下,该参数的对数形式随入射激波和反射激波的多次作用呈基本相同的线性增长趋势;对不同马赫数的入射激波,该参数对数形式的线性增长率也基本一致。这样的变化表明该量纲一参数能够反映反应性RM不稳定过程中火焰界面发展的内在规律。     

On resonant reflection by a plane grating

The resonant minimum of the transmission coefficient (maximum of the reflection coefficient) of an infinite, periodic, plane grating for normal incidence of a plane wave is determined analytically.     

One-to-three resonant Hopf bifurcations of a maglev system

This paper studies the dynamics of a maglev system around 1:3 resonant Hopf–Hopf bifurcations. When two pairs of purely imaginary roots exist for the corresponding characteristic equation, the maglev system has an interaction of Hopf–Hopf bifurcations at the intersection of two bifurcation curves in the feedback control parameter and time delay space. The method of multiple time scales is employed to drive the bifurcation equations for the maglev system by expressing complex amplitudes in a combined polar-Cartesian representation. The dynamics behavior in the vicinity of 1:3 resonant Hopf–Hopf bifurcations is studied in terms of the controller’s parameters (time delay and two feedback control gains). Finally, numerical simulations are presented to support the analytical results and demonstrate some interesting phenomena for the maglev system.     

Digital image analysis of a turbulent flame

Digital image analysis of cine pictures of an unconfined rich premixed turbulent flame has been used to determine structural characteristics of the turbulent/non-turbulent interface of the flame. The results, comprising various moments of the interface position, probability density functions and correlation functions, establish that the instantaneous flame-interface position is essentially a Gaussian random variable with a superimposed quasi-periodical component. The latter is ascribable to a pulsation caused by the convection and the stretching of ring vortices present within the flame. To a first approximation, the flame can be considered similar to a three-dimensional axisymmetric turbulent jet, with superimposed ring vortices, in which combustion occurs.     

Transient behaviors of a flame over a Tsuji burner

The present study investigated numerically the physical mechanisms underlying the transient behaviors of the flame over a porous cylindrical burner. The numerical results showed that a cold flow structure at a fixed inflow velocity of Uin = 0.6 m/s in a wind tunnel could be observed in two co-existing recirculation flows. Flow variations occur repeatedly until t = 4.71 s, and then a vortex existed steadily behind the burner and no shading occurred. The ignition of flammable mixture led to a rapid rise in gas temperature and a sudden gas expansion. When it reached the stable envelope flame condition, Uin is adjusted to an assigned value. Two blow-off mechanisms were identified. It was also found in the study flame shapes with buoyancy effects agreed with the ones observed experimentally by Tsai. Furthermore, the lift-off flame would appear briefly between the envelopes and wake ones, and was stabilized as a wake flame.     

Axisymmetric resonant disturbances in a homogeneous wave guide

The initial boundary-value linear stability problem for small localised axisymmetric disturbances in a homogeneous elastic wave guide, with the free upper surface and the lower surface being rigidly attached to a half-space, is formally solved by applying the Laplace transform in time and the Hankel transforms of zero and first orders in space. An asymptotic evaluation of the solution, expressed as a sum of inverse Laplace-Hankel integrals, is carried out by using the approach of the mathematical formalism of absolute and convective instabilities. It is shown that the dispersion-relation function of the problem D₀ (κ, ω), where the Hankel parameter κ is substituted by a wave number (and the Fourier parameter) κ, coincides with the dispersion-relation function D₀ (k, ω) for two-dimensional (2-D) disturbances in a homogeneous wave guide, where ω is the frequency (and the Laplace parameter) in both cases. An analysis for localised 2-D disturbances in a homogeneous wave guide is then applied. We obtain asymptotic expressions for wave packets, triggered by axisymmetric perturbations localised in space and finite in time, as well as for responses to axisymmetric sources localised in space, with the time dependence satisfying e^−iω₀t + O(e^−εt) for t → ∞, where Im ω₀ = 0, ε > 0, and t denotes time, i.e. for signalling with frequency ω₀. We demonstrate that, for certain combinations of physical parameters, axisymmetric wave packets with an algebraic temporal decay and axisymmetric signalling with an algebraic temporal growth, as √t, i.e., axisymmetric temporal resonances, are present in a neutrally stable homogeneous wave guide. The set of physically relevant wave guides having axisymmetric resonances is shown to be fairly wide. Furthermore, since an axisymmetric part of any source is L²-orthogonal to its non-axisymmetric part, a 3-D signalling with a non-vanishing axisymmetric component at an axisymmetric resonant frequency will generally grow algebraically in time. These results support our hypothesis concerning a possible resonant triggering mechanism of certain earthquakes, see Brevdo, 1998, J. Elasticity, 49, 201–237.     

Predicting vibration-induced displacement for a resonant friction slider

A mathematical model is set up to quantify vibration-induced motions of a slider, sandwiched between friction layers with different coefficients of friction, and equipped with an imbedded resonator that oscillates at high frequency and small amplitude. This model is highly nonlinear, involving non-smooth functions with strong harmonic excitation terms. The method of averaging is extended to hold for systems of this class, and used to derive approximate expressions for predicting average velocities of the slider. These expressions are shown to produce results that agree very well with numerical integration of the full equations of motion. The expressions are used to estimate and explain the influence of system parameters.     

Efficient retrieval of the thermo‐acoustic flame transfer function from a linearized CFD simulation of a turbulent flame

The stability of thermo‐acoustic pressure oscillations in a lean premixed methane‐fired generic gas turbine combustor is investigated. A key element in predicting the acoustically unstable operating conditions of the combustor is the flame transfer function. This function represents the dynamic relationship between a fluctuation in the combustor inlet conditions and the flame's acoustic response. A transient numerical experiment involving spectral analysis in computational fluid dynamics (CFD) is usually conducted to predict the flame transfer function. An important drawback of this spectral method application to numerical simulations is the required computational effort. A much faster and more accurate method to calculate the transfer function is derived in this paper by using a most important basic assumption: the fluctuations must be small enough for the system to behave linear. This alternative method, which is called the linear coefficient method, uses a linear representation of the unsteady equations describing the CFD problem. This linearization is applied around a steady‐state solution of the problem, where it can consequently describe the dynamics of the system. Finally, the flame transfer function can be calculated from this linear representation. The advantage of this approach is that one only needs a steady‐state solution and linearization of the unsteady equations for calculating a dynamic transfer function, i.e. no time‐consuming transient simulations are necessary anymore. Nevertheless, as a consequence of the large number of degrees of freedom in a CFD problem, an extra order reduction step needs to be performed prior to calculating the transfer function from the linear representation. Still, the linear coefficient method shows a significant gain in both speed and accuracy when calculating the transfer function from the linear representation as compared to a spectral analysis‐based calculation. Hence, this method gives a major improvement to the application of the flame transfer function as a thermo‐acoustic design tool. Copyright © 2007 John Wiley & Sons, Ltd.     

LIF-LII measurements in a turbulent gas-jet flame

 Detection of soot by laser-induced incandescence (LII) and fuel-rich (PAH containing) regions by laser-induced fluorescence (LIF) is demonstrated in a turbulent, Re=2500, ethylene gas-jet diffusion flame. Simultaneous combined LIF–LII images allow identification of regions containing PAH or soot and their relative spatial relationship. Separate LII images confirm the identity of the soot containing regions shown in the LIF–LII images. Variations in the size, structure, spatial location and intensity of the PAH and soot containing regions are shown qualitatively in the images and quantified through histograms of image intensities and spatial extents. Received: 9 September 1996/Accepted: 4 February 1997     

Recent advances of hydrogel network models for studies on mechanical behaviors

Acta Mechanica Sinica - Current constitutive theories face challenges when predicting the extremely large deformation and fracture of hydrogels, which calls for the demands to reveal the...     

Experimental validation of a dynamic resonant wall shear stress sensor

Experimental measurements are used to validate a numerical model of a dynamic resonant wall shear stress sensor. The numerical model consists of an unsteady two-dimensional boundary-layer model for the flow and a simple mechanical model for the sensor itself. The sensor’s sensitivity to wall shear stress is experimentally determined in a flat-plate boundary layer, and the results agree closely with those from the numerical simulations. Using the validated model, it is determined that the energy lost in each sensor oscillation due to the interaction between the sensor and fluid increases with increasing mean wall shear stress.     

硅微谐振加速度计的模态分析与实验

针对硅微谐振加速度计在进行结构设计时,如何根据模态特性选取工作模态这一问题,比较分析了加速度计工作在两种不同振动模态下的性能参数。首先采用刚度法分析了谐振器的振动特性,得出能够反映谐振器振动状态的两种模态即同相振动模态和反相振动模态,结合理论推导和仿真结果得出两种振动模态下谐振频率差值与标度因数差值呈线性关系;其次通过分析两种振动模态下的能量分布情况,得出两种振动模态下谐振器的品质因数与振梁振动幅值之间的关系,同相模态振动一个周期所消耗能量约为反相模态所消耗能量的2倍;最后通过评估硅微谐振加速度计的噪声,阐明了两种振动模态下部分噪声分量不同的原因并进行了实验验证。实验结果表明,在相同驱动电压下,同相模态相比反相模态总体噪声增大25.7%。该研究为设计硅微谐振式加速度计时,确定谐振器的振动模态及驱动方案提供了参考依据。     

Non-linear effects on the resonant frequencies of a cantilevered plate

In this paper, we address experimentally and theoretically the non-linear effects on the resonance of a periodically-forced cantilevered plate immersed in a fluid at rest. Experiments are performed with small aspect-ratio plates made of two different materials. When forced harmonically at their leading edges, these plates exhibit resonances for their first 3 structural modes. The frequencies at these resonances decrease when the forcing amplitude is increased, revealing the presence of non-linear effects. To model this phenomenon, a theoretical model is employed, which takes into account both resistive and reactive forces exerted by the fluid on the plate. By carrying out a weakly non-linear analysis, the frequencies at the resonances can then be determined. Model and experiments are in good agreement, showing that a weakly non-linear approach is suited to this kind of fluid–structure interaction and could be applied, in the future, to engineering problems such as energy harvesting with a fluttering plate or the biological problem of aquatic propulsion with a flexible fin.