Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem

https://hal.archives-ouvertes.fr/hal-01320509/document

Exploration of combustion instability triggering using Large Eddy Simulation of a multiple injector Liquid Rocket Engine

An experimental study of spontaneous longitudinal high-frequency combustion instabilities in a high-pressure model rocket combustor is described. The experiment is designed to efficiently obtain stability data under variable resonance conditions in a single test. A traversing choked axial oxidizer inlet is used to vary the coupled resonances between the variable-length oxidizer tube and the fixed-length combustion chamber, thereby changing the temporal and spatial relationship between the fluid mechanical resonances in the oxidizer tube and the local pressure oscillations at the head end of the combustor. Marked transitions between pressure-fluctuation amplitudes and spectral contents are observed as the injector tube length changes. Stable-to-unstable and unstable-to-stable transitions are observed. Depending on the injector tube length, the first dominant injector-coupled resonance ranged from1200 to 1500Hz.The high-frequency pressure oscillation amplitudes varied from less than 10%ofmean pressure to greater than 30% of chamber pressure. Spectrograms are used to assess the global frequency contributions, and power spectral densities are used as a quantitative measure of the stability characteristics and to identify the most unstable geometry. The combustor was also operated in fixed-tube-length mode to measure linear growth rates and compare limit cycle amplitudes. The experimental results provide a basis for comparison with stability models, and their use in conjunction with reliable computational fluid dynamics models can potentially provide detailed insight into the physics of self-excitation and limit cycle behavior in a practical system.

Spontaneous Longitudinal Combustion Instability in a Continuously-Variable Resonance Combustor

The unsteady gas dynamic field in a closed combustor is determined by the nonlinear interactions between chamber acoustics, hydrodynamics, and turbulent combustion that can energize these modes. These interactions are studied in detail using hybrid RANS/large eddy simulations (RANS = Reynolds Averaged Navier-Stokes) of a non-premixed, high-pressure laboratory combustor that produces self-excited longitudinal instabilities. The main variable in the study is the relative acoustic length between the combustion chamber and the tube that injects oxidizer into the combustor. Assuming a half-wave (closed-closed) combustion chamber, the tube lengths approximately correspond to quarter-, 3/8-, and half-wave resonators that serve to vary the phasing between the acoustic modes in the tube and the combustion chamber. The simulation correctly predicts the relatively stable behavior measured with the shortest tube and the very unstable behavior measured with the intermediate tube. Unstable behavior is also predicted for the longest tube, a case for which bifurcated stability behavior was measured in the experiment. In the first (stable) configuration, fuel flows into the combustor uninterrupted, and heat release is spatially continuous with a flame that remains attached to the back step. In the second (unstable) configuration, a cyclic process is apparent comprising a disruption in the fuel flow, subsequent detachment of the flame from the back step, and accumulation of fuel in the recirculation zone that ignites upon arrival of a compression wave reflected from the downstream boundary of the combustion chamber. The third case (mixed stable/unstable) shares features with both of the other cases. The major difference between the two cases predicted to be unstable is that, in the intermediate length tube, a pressure wave reflection inside the tube pushes unburnt fuel behind the back step radially outward, leading to a post-coupled reignition mechanism, while in the case of the longest tube, the reignition is promoted by vortex convection and combustor-wall interaction. Other flow details indicated by the simulation include the relative phase between flow resonances in the tube and the combustor, increased mixing due to baroclinic torque, and the presence of an unsteady triple flame.

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Coupling between hydrodynamics, acoustics, and heat release in a self-excited unstable combustor

A combustion instability in a combustor terminated by a nozzle is analysed and modelled based on a low-order Helmholtz solver. A large eddy simulation (LES) of the corresponding turbulent, compressible and reacting flow is first performed and analysed based on dynamic mode decomposition (DMD). The mode with the highest amplitude shares the same frequency of oscillation as the experiment (approximately 320 Hz) and shows the presence of large entropy spots generated within the combustion chamber and convected down to the exit nozzle. The lowest purely acoustic mode being in the range 700–750 Hz, it is postulated that the instability observed around 320 Hz stems from a mixed entropy–acoustic mode, where the acoustic generation associated with entropy spots being convected throughout the choked nozzle plays a key role. The DMD analysis allows one to extract from the LES results a low-order model that confirms that the mechanism of the low-frequency combustion instability indeed involves both acoustic and convected entropy waves. The delayed entropy coupled boundary condition (DECBC) (Motheau, Selle & Nicoud, J. Sound Vib., vol. 333, 2014, pp. 246–262) is implemented into a numerical Helmholtz solver where the baseline flow is assumed at rest. When fed with appropriate transfer functions to model the entropy generation and convection from the flame to the exit, the Helmholtz/DECBC solver predicts the presence of an unstable mode around 320 Hz, in agreement with both LES and experiments.

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Mixed acoustic–entropy combustion instabilities in gas turbines

A single injector element liquid rocket combustion experiment was designed and conducted to investigate the combustion dynamics of a gas-centered, liquid-swirled coaxial injector element. The oxidizer was a mixture of superheated water and oxygen, and kerosene was used as the fuel. The mean chamber pressure ranged from 2.14 to 2.38 MPa. The combustion chamber length was discretely varied between 25.4 and 88.9 cm to determine the dependence of combustion stability characteristics on resonant frequency and mode shape. Strong spontaneous instabilities were measured with peak-to-peak amplitudes of 0.69 to 1.38 MPa, and wave slopes on the order of 1000 MPa/s. The frequencies of the strongest instabilities ranged from 1184 to 1721 Hz. The most amplified modes ranged from the first longitudinal for the 38.1-cm chamber to the third longitudinal for the 88.9-cm chamber. One test, with a 25.4-cm chamber, was classically stable with pressure oscillation amplitudes less than 5% of the mean pressure. Resonant frequencies calculated with a model of the chamber acoustics compared well with measured values. For this injector, the data suggest that the observed stability behavior is a result of the combined effects of chamber mode shape and a driving combustion mechanism that limits the frequency range over which instability occurs.

Combustion instability with a single-element swirl injector

An experimental investigation of high-frequency longitudinal combustion instability using a continuously variable resonance combustor (CVRC) is described. The continuously variable resonance condition is provided by varying the length of a tube carrying oxidizer into a combustor with a rearward-facing step. The a coustic length of the tube is varied between a quarter- and half-wave resonator. The data are analyzed and compared with the analytical results calculated using linearized Eule r equations. As the tube length changes the system transitions between stable and highly unstable operation, allowing the observation of several unique stability behaviors. When the system transitions into instability, higher harmonics appear simultaneously and instantaneously. The transition is accompanied by transitory, unorganized, high amplitude, sub-harmonic pressure fluctuations. When the system transitions into stability regime, the highe r harmonics disappear sequentially, led by the highest order. Small but measurable differences are measured in oscillation amplitude depending on the direction of the sweep (Ω wave to o wave or vice versa). For gaseous fuel experiments, the highest amplitudes of instability do not occur at the least damped acoustic configuration suggested by classical acoustic model s (Ω wave, perfectly coupled resonance condition). This indicates that the gas dynamic eff ects of the system on combustion is important. Comparisons are made between the measured frequency and mode shape data and results from a linearized Euler equation, indic ating generally good agreement, but highlight the need for an accurate combustion respo nse submodel.

Experimental Study of High-Frequency Combustion Instability in a Continuously Variable Resonance Combustor (CVRC)

The development of a Linearized Euler Equation (LEE) model for analyzing high frequency longitudinal combustion instability is described. The model includes mean flow effects and is generalized for multiple domains as well as natural boundary conditions that deviate from acoustically perfect conditions. These effects are systematically evaluated. Calculated spatial mode shapes and resonant frequencies are compared to experimental measurements and good agreements are obtained. Demonstrative results using a prescribed unsteady heat release model are also analyzed. Observations made from analytical results include mean flow decreases resonant frequencies and shifts the antinode locations; effects of entropy wave and mean flow property changes are location-dependent; application of natural boundary conditions produces more resonant modes and shifts the nodal locations; and the primary effect of unsteady heat release is a change in the linear growth rate. The LEE model is shown to be a useful platform for deve...

Effects of Mean Flow, Entropy Waves, and Boundary Conditions on Longitudinal Combustion Instability

In staged-bipropellant rocket combustors that use decomposed hydrogen peroxide as the oxidizer, a liquid fuel is injected into the hot decomposition products comprising oxygen and water vapor. For a well-designed combustor, the oxidizer is at a sufficiently high temperature to vaporize and to autoignite the liquid fuel; however, experimental autoignition data in key chamber contraction ratio and propellant equivalence ratio ranges are missing. In this study a transverse injector was used in a dump-combustor configuration to investigate the autoignition characteristics of JP-8 in decomposed hydrogen peroxide, specifically fuel-rich autoignition limits at contraction ratios less than 6 and with high hydrogen peroxide concentrations. The chamber contraction ratio was varied between 3 and 5 to evaluate the effects of chamber gas Mach number (0.45 and 0.27), and the hydrogen peroxide concentration was varied from 85 to 98% by weight to evaluate the effects of oxidizer temperature. Three regimes were noted: strong, weak, and no autoignition. Chamber pressure oscillations with a dominant frequency between 27 and 47 Hz occurred in the weak-autoignition regime. Results showed that as hydrogen peroxide concentration and/or contraction ratio was increased the equivalence ratio that defined the autoignition boundary increased as well. At a contraction ratio of 3.0, no autoignition was achieved at equivalence ratios of 1.37 and above using 85% hydrogen peroxide, but with 98% hydrogen peroxide autoignition occurred at an equivalence ratio as high as 2.06. When the contraction ratio was increased to 5.0, autoignition was achieved at an equivalence ratio of 1.38 using 85% hydrogen peroxide. These data provide a starting point for the development of an accurate autoignition model and an empirical basis for the design of efficient combustors.

James C. Sisco

Papers

Spontaneous Longitudinal Combustion Instability in a Continuously-Variable Resonance Combustor

Combustion instability with a single-element swirl injector

Experimental Study of High-Frequency Combustion Instability in a Continuously Variable Resonance Combustor (CVRC)

Effects of Mean Flow, Entropy Waves, and Boundary Conditions on Longitudinal Combustion Instability

Autoignition of kerosene by decomposed hydrogen peroxide in a dump-combustor configuration