Pressure Oscillations In Combustion Chambers Research Articles

Three-step approach for prediction of limit cycle pressure oscillations in combustion chambers of gas turbines

Currently, gas turbine manufacturers frequently face the problem of strong acoustic combustion driven oscillations inside combustion chambers. These combustion instabilities can cause extensive wear and sometimes even catastrophic damages to combustion hardware. This requires prevention of combustion instabilities, which, in turn, requires reliable and fast predictive tools. This work presents a three-step method to find stability margins within which gas turbines can be operated without going into self-excited pressure oscillations. As a first step, a set of unsteady Reynolds-averaged Navier–Stokes simulations with the Flame Speed Closure (FSC) model implemented in the OpenFOAM® environment are performed to obtain the flame describing function of the combustor set-up. The standard FSC model is extended in this work to take into account the combined effect of strain and heat losses on the flame. As a second step, a linear three-time-lag-distributed model for a perfectly premixed swirl-stabilized flame is extended to the nonlinear regime. The factors causing changes in the model parameters when applying high-amplitude velocity perturbations are analysed. As a third step, time-domain simulations employing a low-order network model implemented in Simulink® are performed. In this work, the proposed method is applied to a laboratory test rig. The proposed method permits not only the unsteady frequencies of acoustic oscillations to be computed, but the amplitudes of such oscillations as well. Knowing the amplitudes of unstable pressure oscillations, it is possible to determine how these oscillations are harmful to the combustor equipment. The proposed method has a low cost because it does not require any license for computational fluid dynamics software.

Active Adaptive Combustion Control Using Neural Networks

The suppression of pressure oscillations in combustion chambers through the use of active feedback control is a new technology with high potential. In this article, we present a feedback control strategy based on an Internal Model Control System for nonlinear plants that uses artificial neural networks. This control system uses two neural networks: The Internal Model which approximates the plant forward dynamic; and a controller which gives the appropriate control input. The controller's parameters are updated adaptively for that purpose. We demonstrate numerically the capabilities of the developped control system in a numerical simulation of control of combustion instabilities. Then, we demonstrate the ability of this neural networks based control system to actively damp instabilities in a Rijke-tube burner.

Nonlinear Analysis and Modelling of Combustion Instabilities in a Laboratory Combustor

The spectra of pressure oscillations in combustion chambers often contain large peaks at frequencies corresponding to chamber acoustic modes. Pulsed combustors are designed to operate with fixed amplitude oscillations but in many systems the oscillations have undesirable consequences. An understanding of the nonlinear mechanisms responsible for the limiting-amplitude behavior is therefore desired. This paper is divided into two parts. First, characterization of the oscillations in terms of attractors in mathematical phase space has been performed on pressure signals measured in a laboratory combustor of premixed gases. The results for one set of operating conditions show a quasiperiodic attractor of dimension two over an order of magnitude of scales. Next, the nonlinear combustion response to oscillations of a single acoustic mode are used to model autonomous or 'self-excited' behavior. Two simple models of nonlinear combustion processes observed in the laboratory combustor result in unstable oscillations that reach limiting-amplitudes. With the variation of model parameters, the periodic limit cycles undergo subharmonic bifurcations and transition to chaos.

Active control of nonlinear pressure oscillations in combustion chambers

A theoretical analysis of active control of nonlinear acoustic instabilities in combustion chambers is developed in this article. The formulation starts with a generalized wave equation that describes the dynamic behavior of second-order nonlinear oscillations with distributed feedback actions. Control inputs are provided by the burning of the injected seconday fuel in the chamber, with its instantaneous mass flow rate modulated by a proportionalplus-integral (PI) controller located between the pressure sensor and the fuel injection mechanism. Various nonlinear stability characteristics, including the existence and stability of limit cycles, are studied analytically using the method of time averaging. In addition, an optimization procedure is developed for selecting controller gains. Nomenclature Anij = parameters associated with nonlinear acoustic coupling a = speed of sound in mixture Bnij = parameters associated with nonlinear acoustic coupling b = spatial distribution of burning of control fuel, Eq. (5b), Cv - constant-volume specific heat for two-phase mixture c = amplification factor of sensor output Dni = linear parameters, Eq. (11) Eni = linear parameters, Eq. (11) e - error signal between desired response and actual measurement

State-feedback control of longitudinal combustion instabilities

Active control of longitudinal pressure oscillations in combustion chambers has been studied theoretically by means of a digital state-feedback control technique. The formulation is based on a generalized wave equation that accommodates all influences of combustion, mean flow, unsteady motions, and control actions. Following a procedure equivalent to the Galerkin method, a system of ordinary differential equations governing the amplitude of each oscillatory mode is derived for the controller design. The control actions are provided by a finite number of point actuators, with instantaneous chamber conditions monitored by multiple sensors. Several important control aspects, including sampling period, locations of sensors and actuators, controllability, and observability, have been investigated systematically. As a specific example, the case involving two controlled and two residual (uncontrolled) modes is studied. 20 refs.

Time-resolved velocities and turbulence in the oscillating flow of a pulse combustor tail pipe

The cyclic behavior of the oscillating velocity field in the tail pipe of a pulse combustor was studied using laser doppler velocimetry. In this flow, the oscillations result from an acoustic resonance and have amplitudes of up to 5 times the mean velocity. Oscillation frequencies were varied from 67 to 101 Hz. Streamwise velocity and turbulence-intensity boundary layer profiles were measured to within 130 μm of the wall, and transverse turbulence measurements were made to within 2 mm. The phase relationships of the velocity, turbulence intensity, and combustion chamber pressure oscillations are compared. Velocity oscillations near the wall are found to phase lead those in the center of the pipe, creating periodic flow reversals through the boundary layer. A comparison is made between this turbulent oscillating boundary layer and the laminar oscillating boundary layer for flow over a flat plate. The effects of axial position, pulsation frequency, pulsation amplitude, and mean flow rate on the velocity and turbulence profiles are discussed. Time-resolved wall shear stresses (directly calculated from the velocity measurements) are presented and compared with those of steady turbulent flow. Time-averaged velocity and turbulence profiles are also compared with those of conventional steady turbulent flows. The time-averaged velocity profile is found to be flatter than that of steady flow at the same mean Reynolds number, and both the streamwise and transverse turbulence intensities are found to be significantly higher than those of steady flow.

Triggering of Longitudinal Pressure Oscillations in Combustion Chambers. I: Nonlinear Gasdynamics

Based on spatial and temporal averaging of the conservation equations, an approximate analysis provides a convenient vehicle for analyzing the nonlinear behavior of unsteady motions in combustion chambers. Recent work has been concerned with the conditions for existence and stability of limit cycles, and in particular their dependence on the order of nonlinear terms contained in the equations of motion. It seems to be generally true that if only nonlinear gasdynamic terms to second order are accounted for, a stable nontrivial limit cycle is unique. This implies that no initial disturbance will cause a linearly stable system to execute a limit cycle, a result contrary to prior experience with, for example, solid propellant rocket motors. In this paper, we study some conditions under which true nonlinear instabilities may be found, with special attention focused on the effect of nonlinear gasdynamics. Our results indicate that third-order terms in the acoustic motions do not lead to triggering to either a stable or an unstable limit cycle; they only modify the stability domain of the system. However, the interactions between mean flow and nonlinear acoustic waves may trigger a linearly stable system to an unstable limit cycle. The influence of nonlinear combustion response may have quite different consequences and will be discussed in Part II of this work.

On the Existence and Stability of Limit Cycles for Transverse Acoustic Oscillations in a Cylindrical Combustion Chamber. 1: Standing Modes

Abstract Nonlinear pressure oscillations in combustion chambers have been studied using an approximate analysis which treats the unsteady motions as a collection of coupled nonlinear oscillators, each corresponding to an acoustic mode of the chamber. Based on spatial and temporal averaging of the conservation equations, the formulation provides a convenient means for analyzing the nonlinear behavior of acoustic wave motions. The work addresses the linear and nonlinear characteristics of transverse acoustic waves in a cylindrical chamber, with attention focused on the conditions for the existence and stability of limit cycles. As a result of the special structure of the equations, both general and precise conclusions can be reached. Explicit results are given for the special cases of two and three standing modes. Spinning wave motions will be treated in a subsequent paper.

The transfer function of premixed turbulent jet flames

For low-frequency pressure oscillations in combustion chambers, the transfer function of the flame is an important parameter. This transfer function represents the dependence between the burned and injected mass-flow rate on the pressure oscillations. The stability region of a system can be defined only if the transfer function is known. In this paper, the transfer function of a premixed turbulent city-gas flame has been determined by the frequency-response method, and an equation has been derived which describes the experimental behavior. It is shown that the transfer function of the, premixed turbulent flame consists of a transfer function of an extended time lag and a transfer function of a differential governor. The transfer function of an extended time lag is calculated from the flow pattern and the position of the reaction zone. Comparison of the calculations made with these equations shows good agreement with experimental data.