Numerical analysis of flame instabilities in narrow channels: Laminar premixed methane/air combustion

Premixed flames propagating within small channels show complex combustion phenomena that differ from flame propagation at conventional scales. Available experimental and numerical studies have documented stationary, non-stationary, or asymmetric modes that depend on properties of the incoming reactant flow as well as channel geometry and wall temperatures. This work seeks to illuminate mechanisms leading to symmetry breaking and limit cycle behavior that are fundamental to these combustion modes. Specifically, four cases of lean premixed methane/air combustion—two equivalence ratios (0.53 and 0.7) and two channel widths (2 mm and 5 mm)—are investigated in a 2D configuration with constant channel length and bulk inlet velocity, where numerical simulations are performed using detailed chemistry. External wall heating is simulated by imposing a linear temperature gradient as a boundary condition on both walls. In the 2 mm channel, both equivalence ratios produce flames that stabilize with symmetric flame fronts after propagating upstream. In the 5 mm channel, flame fronts start symmetrically, although symmetry is broken almost immediately after ignition. Further, 5 mm channels produce non-stationary combustion modes with dramatically different limit cycles: in the leaner case ( φ = 0.53), the asymmetric flame front flops periodically, whereas in the richer case ( φ = 0.7), flames with repetitive extinctions and ignitions (FREI) are observed. To further understand the flame dynamics, reaction fronts and flame fronts are captured and differentiated. Results show that the loss of flame front symmetry originates in a region close to the flame cusp, where flow and chemical characteristics exhibit large gradients and curvatures. Limit cycle behavior is illuminated by investigating flame edges that are formed along the wall, and accompany local or global ignition and extinction processes. In the flopping mode ( φ = 0.53), local ignition and extinction in regions adjacent to the wall result in oblique fronts that advance and recede along the wall and redirect the flow ahead of the flame. In the FREI mode, asymmetric flames propagate much farther upstream, where they experience global extinction due to heat losses, and re-ignite far downstream with opposite flame front orientation. In both cases, an interaction of flow and chemical effects drives the asymmetric limit cycles. The lack of instabilities and asymmetries for the 2mm cases is attributed to insufficient wall separation, which is of the same order of magnitude as the flame thickness.

Limit-Cycle Analysis of Three-Dimensional Flexible Shaft/Rigid Rotor/Autobalancer System With Symmetric Rigid Supports

In recent years, there has been much interest in the use of automatic balancing devices (ABD) in rotating machinery. Autobalancers consist of several freely moving eccentric balancing masses mounted on the rotor, which, at certain operating speeds, act to cancel rotor imbalance. This “automatic balancing” phenomenon occurs as a result of nonlinear dynamic interactions between the balancer and rotor wherein the balancer masses naturally synchronize with the rotor with appropriate phase to cancel the imbalance. However, due to inherent nonlinearity of the autobalancer, the potential for other undesirable nonsynchronous limit-cycle behavior exists. In such situations, the balancer masses do not reach their desired synchronous balanced positions resulting in increased rotor vibration. To explore this nonsynchronous behavior of ABD, the unstable limit-cycle analysis of three-dimensional (3D) flexible shaft/rigid rotor/ABD/rigid supports described by the modal coordinates has been investigated here. Essentially, this paper presents an approximate harmonic analytical solution to describe the limit-cycle behavior of ABD–rotor system interacting with flexible shaft, which has not been fully considered by ABD researchers. The modal shape of flexible shaft is determined by using well-known fixed–fixed boundary condition due to symmetric rigid supports. Here, the whirl speed of the ABD balancer masses is determined via the solution of a nonlinear characteristic equation. Also, based upon the analytical limit-cycle solutions, the limit-cycle stability of three primary design parameters for ABD is assessed via a perturbation and Floquet analysis: the size of ABD balancer mass, the ABD viscous damping, and the relative axial location of ABD to the imbalance rotor along the shaft. The coexistence of the stable balanced synchronous condition and undesirable nonsynchronous limit-cycle is also studied. It is found that for certain combinations of ABD parameters and rotor speeds, the nonsynchronous limit-cycle can be made unstable, thus guaranteeing asymptotic stability of the synchronous balanced condition at the supercritical shaft speeds between each flexible mode. Finally, the analysis is validated through numerical simulation. The findings in this paper yield important insights for researchers wishing to utilize ABD in flexible shaft/rigid rotor systems and limit-cycle mitigation.

Stability of a Proportional Valve Control System With Backlash and Saturation

In this work, the describing function technique is used to study the stability of a nonlinear system. All of dynamic systems in industrial and fluid power systems are nonlinear and include uncertainties to some degree. Thus, unexpected changes in the stability can be exhibited and can lead these systems to become unstable or exhibit oscillatory behavior. Engineers have developed nonlinear mathematical models to be able to predict whether or not a designed system will be exposed to such an oscillation before considering building and implementing the system. The focus of this study is to predict the existence of nonlinear oscillation behavior in a dynamic system using a simplified approach. A nonlinear model validation of a solenoid operated proportional control valve was performed using open loop testes. The type of two-stage hydraulic valve considered in this research is used to control the velocity of hydraulic cylinders. The pilot valve, which is the focus of this research, is a pressure control 3-way valve. A number of 30 replications of this pilot spool valve were studied and tested experimentally along with a single main stage valve. The model consists of linear and nonlinear parts. The linear part of the model was developed by linearizing the nonlinear governing equations at nominal conditions. The nonlinear part was constructed by analyzing open loop experimental test data. The data showed that two major nonlinearities are found that are key to describing the behavior of the system: saturation of the current input and backlash hysteresis behavior. These nonlinearities were considered to be the cause of limit cycle behavior. Each one of these nonlinearities was represented by its describing function and limit cycles were predicted using the describing function analysis method. In using the describing function method, the complexities of working with the nonlinear physics based model to determine limit cycle behavior were avoided.

Modeling Unsteady Flow of a Lean Partially Premixed Flame on a Dry Low NOx Combustion System

The phenomenon of combustion dynamics (CD) is one of the most important operational challenges facing the gas turbine (GT) industry today. The Limousine project, a Marie Curie Initial Training network funded by the European Commission, focuses on the understanding of the limit cycle behavior of unstable pressure oscillations in gas turbines, and on the resulting mechanical vibrations and materials fatigue. In the framework of this project, a full transient CFD analysis for a Dry Low NOx combustor in a heavy duty gas turbine has been performed. The goal is to gain insight on the thermo-acoustic instability development mechanisms and limit cycle oscillations. The possibility to use numerical codes for complex industrial cases involving fuel staging, fluid-structure interaction, fuel quality variation and flexible operations has been also addressed. The unsteady U-RANS approach used to describe the high-swirled lean partially premixed flame is presented and the results on the flow characteristics as vortex core generation, vortex shedding, flame pulsation are commented on with respect to monitored parameters during operations of the GT units at Electrabel/GDF-SUEZ sites. The time domain pressure oscillations show limit cycle behavior. By means of Fourier analysis, the coupling frequencies caused by the thermo-acoustic feedback between the acoustic resonances of the chamber and the flame heat release has been detected. The possibility to reduce the computational domain to speed up computations, as done in other works in literature, has been investigated.

Limit-Cycle Analysis of Three Dimensional Rigid Rotor/Shaft/Autobalancer System With Symmetric Bearing Support

In recent years, there has been much interest in the use of automatic balancing devices (ABDs) in rotating machinery. Autobalancers consist of several freely moving eccentric balancing masses mounted on the rotor, which, at certain operating speeds, act to cancel rotor imbalance. This “automatic balancing” phenomena occurs as a result of nonlinear dynamic interactions between the balancer and rotor wherein the balancer masses naturally synchronize with the rotor with appropriate phase to cancel the imbalance. However, due to inherent nonlinearity of the autobalancer, the potential for other undesirable non-synchronous limit-cycle behavior exists. In such situations, the balancer masses do not reach their desired synchronous balanced positions resulting in increased rotor vibration. Although several researchers have explored limit-cycle behavior of single-plane ABD-rotor systems, a limit-cycle analysis of a full three dimensional rigid ABD/shaft/rotor considering transverse deflection, out-plane tilting and gyroscopic effects has not been investigated. This paper considers an approximate harmonic analytical solution to describe the limit-cycle behavior in a three dimensional rigid rotor/ABD system. Essentially, the solutions presented here capture both in-plane transverse deflection and out-plane tilting motion of the system under the limit-cycle condition. Here the whirl speed of the ABD balancer masses is determined via the solution of a non-linear characteristic equation. Also, based upon the limit-cycle solutions, the limit-cycle stability is assessed via a perturbation and Floquet analysis exploring three main parameters; ABD balancer mass, ABD damping, and axial location of ABD along the shaft. The coexistence of the stable balanced synchronous condition and undesired non-synchronous limit-cycle is studied. It is found that for certain combinations of ABD parameters and rotor speeds, the non-synchronous limit-cycle can be made unstable thus guaranteeing global asymptotic stability of the synchronous balanced condition. Finally, the analysis is validated through numerical simulation. The findings in this paper yield important insights for researchers wishing to utilize automatic balancing devices in rotor/shaft systems and limit-cycle mitigation.