Ahmed F. Ghoniem

Response of a laminar premixed flame to flow oscillations: A kinematic model and thermoacoustic instability results

Combustion instability is a resonance phenomenon that arises due to the coupling between the system acoustics and the unsteady heat release. The constructive feedback between the two processes, which is known to occur as a certain phase relationship between the pressure and the unsteady heat release rate is satisfied, depends on many parameters among which is the acoustic mode, the flame holder characteristics, and the dominant burning pattern. In this paper, we construct an analytical model to describe the dynamic response of a laminar premixed flame stabilized on the rim of a tube to velocity oscillation. We consider uniform and nonuniform velocity perturbations superimposed on a pipe flow velocity profile. The model results show that the magnitude of heat release perturbation and its phase with respect to the dynamic perturbation depend primarily on the flame Strouhal number, representing the ratio of the dominant frequency times the tube radius to the laminar burning velocity. In terms of this number, high-frequency perturbations pass through the flame while low frequencies lead to a strong response. The phase with respect to the velocity perturbation behaves in the opposite way. Results of this model are shown to agree with experimental observations and to be useful in determining how the combustion excited mode is selected among all the acoustic unstable modes. The model is then used to obtain a time-domain differential equation describing the relationship between the velocity perturbation and the heat release response over the entire frequency range.

Numerical modelling of turbulent flow in a combustion tunnel

A numerical technique is presented for the analysis of turbulent flow associated with combustion. The technique uses Chorin’s random vortex method (r.v.m .), an algorithm capable of tracing the action of elementary turbulent eddies and their cumulative effects without imposing any restriction upon their motion. In the past, the r.v.m . has been used with success to treat non-reacting turbulent flows, revealing in particular the mechanics of large-scale flow patterns, the so-called coherent structures. Introduced here is a flame propagation algorithm , also developed by Chorin, in conjunction with volume sources modelling the mechanical effects of the exothermic process of combustion. As an illustration of its use, the technique is applied to flow in a combustion tunnel w here the flame is stabilized by a back-facing step. Solutions for both non-reacting and reacting flow fields are obtained. Although these solutions are restricted by a set of far-reaching idealizations, they nonetheless mimic quite satisfactorily the essential features of turbulent combustion in a lean propane—air mixture that were observed in the laboratory by means of high speed schlieren photography.

Numerical study of a three-dimensional vortex method

Abstract A three-dimensional vortex method based on the discretization of the vorticity field into vortex vector elements of finite spherical cores is constructed for the simulation of inviscid incompressible flow. The velocity is obtained by summing the contribution of individual elements using the Biot-Savart law desingularized according to the vorticity cores. Vortex elements are transported in Lagrangian coordinates, and vorticity is redistributed, when necessary, among larger number of elements arranged along its direction. The accuracy and convergence of the method are investigated by comparing numerical solutions to analytical results on the propagation and stability of vortex rings. Accurate discretization of the initial vorticity field is shown to be essential for the prediction of the linear growth of azimuthal instability waves on vortex rings. The unstable mode frequency, growth rate and shape are in agreement with analytical results. The late stages of evolution of the instability show the generation of small scales in the form of bair-pin vortex structures. The behavior of the turbulent vortex ring is in good qualitative agreement with experimental data.

Grid-free simulation of diffusion using random walk methods

Abstract The simulation of diffusion of a continuum field by the random walk displacement of a set of particles is investigated in detail. Computational particles are used to transport elements of the gradients of the diffusive concentration. One-dimensional and quasi-one-dimensional cases are treated for a generalized diffusion variable. Different types of boundary conditions of the diffusion equation are considered, as well as the extensions to a system of coupled diffusion equations, the reaction-diffusion equations and the convection-diffusion set of equations. It is shown that by using concentration gradients in the random walk process, statistical errors are reduced and each realization of the numerical solution is a representation of the exact solution. Moreover, transport of higher-order derivatives can be utilized to improve the smoothness. The algorithm is grid-free, and the computational elements move to follow the gradients, thus it is self-adaptive and uniform resolution is attained for all times. The method is particularly suitable for the simulation of diffusion in systems which involve more than one transport mechanism, when the diffusivity is small and when Lagrangian elements are used to model the other mechanisms.

Active control in combustion systems

Over the past decade, active control has been investigated in combustion systems as a means of preventing thermoacoustic instabilities from degrading the system performance. More recently, attempts to control instability and emissions as well as to satisfy other performance criteria have also been pursued. In this article, the authors review control problems in continuous combustion processes, the need for active control, and current status of the field. Despite the success reported in experimental investigations, a systematic procedure by which active control can be designed and implemented is currently not available. In particular, a theoretical framework which includes an investigation of the resonant nature of the thermoacoustic instability, an understanding of the significance of the mixing of modes and the dynamic impact of acoustic drivers, and the incorporation of the subtle coupling among the different physical processes of heat, mass, and momentum addition, as well as acoustics, turbulence, and chemistry, has not been developed. As an example of what can be accomplished using such a theoretically based approach, in this article the authors also review the results of their efforts expended thus far in the area of active control of a premixed combustor. The authors discuss the highlights of a feedback model proposed in Annaswamy et al. (1995) which captures the dominant dynamic features of the combustor. The authors demonstrate that their model captures the effects of several interacting modes, the mean-flow and mean-heat release in the combustor, and the locations of the actuator-sensor pair, and provides guidelines for an active control design. The authors suggest a systematic procedure for designing an active controller that provides an appropriate compensating action and results in improved performance.

Impact of Linear Coupling on the Design of Active Controllers for the Thermoacoustic Instability

Analysis of combustion instability has traditionally been based on the assumption that linear coupling among acoustic modes is insignificant. While this is reasonable when one is interested in determining the unstable mode frequency and growth rate, in this paper we show that this assumption in a model-based active control design may lead to serious errors. To explain the origin of these errors, we employ both analysis and numerical examples to investigate the effect of linear coupling on the resonance and anliresonance properties of a benchlop premised combuslor in the presence of external excitation. The analysis is carried out using one-dimensional flow dynamics in the presence of an oscillating heal release source based on laminar premised flame kinematics, and an external actuator in the form of a loudspeaker. We show that, for certain sensor-actuator configurations, a controller designed on the basis of a model where linear coupling is neglected may fail to suppress the thermoacoustic instability wh...

Biomass torrefaction: modeling of volatile and solid product evolution kinetics.

The aim of this work is the development of a kinetics model for the evolution of the volatile and solid product composition during torrefaction conditions between 200 and 300°C. Coupled to an existing two step solid mass loss kinetics mechanism, this model describes the volatile release kinetics in terms of a set of identifiable chemical components, permitting the solid product composition to be estimated by mass conservation. Results show that most of the volatiles released during the first stage include highly oxygenated species such as water, acetic acid, and carbon dioxide, while volatiles released during the second step are composed primarily of lactic acid, methanol, and acetic acid. This kinetics model will be used in the development of a model to describe reaction energy balance and heat release dynamics.

Active control of combustion instability: theory and practice

One of the most successful applications of control technology in fluid systems is in the context of dynamic instability in continuous combustion systems. Models of combustion instability have been derived using both physically based and system-identification-based methods. Optimal, time-delay, and adaptive controllers have been designed using these models and demonstrated to lead to an order of magnitude improvement in a range of combustion rigs over empirically designed control methods. We present a survey of the existing theory that includes modeling and control of pressure instability in combustion systems and the practical applications of active control to date in small-, medium-, and large-scale combustion rigs.

Thermoacoustic instability: model-based optimal control designs and experimental validation

Active control of thermoacoustic instability has been increasingly sought after in the past two decades to suppress pressure oscillations while maintaining other performance objectives such as low NO/sub x/ emission, high efficiency, and power density. We have developed a feedback model of a premixed laminar combustor which captures several dominant features in the combustion process such as heat release dynamics, multiple acoustic modes, and actuator effects. In this paper, we study the performance of optimal control designs including LQG-LTR and H/sub /spl infin// methods using the model with additional effects of mean heat and mean flow actuator dynamics, and input saturation. We also verify these designs experimentally using a 1 kW bench-top combustor rig and a 0.2-W loudspeaker over a range of flow rates and equivalence ratios. Our results show that the proposed controllers, which are designed using a two-mode finite dimensional model, suppress the thermoacoustic instability significantly faster than those obtained using empirical approaches in similar experimental setups without creating secondary resonances, and guarantee stability robustness.

A Model-Based Active Control Design for Thermoacoustic Instability

Abstract Active control has been pursued vigorously for combating thermoacoustic instabilities in combustion processes. Most experimental investigations employ empirical design procedure for determining the characteristic parameters of the filter and phase-shifter of the controller. Such procedure has been observed to result in resonance at frequencies which were not excited in the power spectrum of the uncontrolled combustor, though the dominant thermoacoustic instability was suppressed. In this paper, we present an alternative design methodology which is based on the underlying physical model of the combustor and modern control theory. We show that using this methodology, one can avoid the generation of secondary peaks and achieve short settling time using small control energy. The physical model takes into account multiple acoustic modes, the heat release dynamics of a premixed flame, and the effect of an actuator such as a loudspeaker, on the flow variables over a wide range of frequencies. The model-...