Effects of enhanced heat transfer in oscillating flows on the thermal load and damping behavior of resonators

1 Motivation

Liquid propellant rocket engines tend to thermo-acoustic instabilities, which occur due to a feedback between the heat release (combustion process) and the acoustic field of the thrust chamber, resulting in an amplification of the oscillations. To limit the amplitude of these oscillations, the use of acoustic cavities, so called resonators, is a common practice.Usually, resonators dissipate acoustic energy in small frequency ranges around their eigenfrequency values, and thus they have to be tuned according to the oscillation modes of the combustion chamber. This is not a simple task. Among other effects, the eigenfrequency of a cavity depends on the speed of sound of the gas inside it. Under operation, the superimposed oscillations may flush hot exhaust gases into the cavity, changing the gas composition and temperature distribution inside it. Furthermore, several investigations report a significantly enhanced heat transfer in oscillating flows under certain conditions, which could lead to higher thermal loads in the cavity and chamber walls and again to different temperature distributions. These two effects modify the speed of sound inside the cavity, the resonator might be put out of tune delivering perhaps not enough dissipation for the stabilization of the thrust-chamber. An accurate prediction of the damping behavior of resonators under real operation conditions taking the previous effects into account would be of great interest for the development of more reliable space transportations systems.

2 Objectives and strategy

The effects of periodic insertion of hot exhaust gases into acoustic cavities through high frequency oscillations on the temperature and gas composition distribution, heat flux, eigenfrequencies and dissipation rates of the resonators will be systematic studied. For that, a detailed analysis of momentum- and heat transfer mechanisms in oscillating and pulsating flows is intended.

Computational methods applied to simplified geometries allow a detailed analysis of the complex interaction mechanisms between fluid mechanics, acoustic and heat transfer. The focus is set on the use of LES and DNS simulations approaches. In addition, acoustic calculations using for example the wave equation for the prediction of the impedance and dissipation power of resonators respectively influenced by the previous mentioned effects are planed too.

3 Background

3.1 Oscillating and pulsating flows

The velocity of unsteady flows might be decomposed into three parts: a time-average or mean, a periodic and a turbulent part. Per definition the mean part is only position dependent, while the periodic and turbulent fluctuations are position and time dependent. Figure 1 shows a schematic representation of this triple decomposition. The difference between the last two is that the periodic fluctuations display an organized character with evident frequency f, while the turbulent part displays chaotic random fluctuations. Using the previous notation, two further distinctions of unsteady flows can be made. If the mean part is equal to zero, one speaks of an oscillating flow and if the mean doesn't vanish, of a pulsating flow.

Pulsating and oscillating flows have been studied since many years, and several interesting effects of these flows have been pointed out. In many investigations an enhanced heat transfer under special conditions has been reported. The responsible mechanisms for this effect are not yet totally clarified, however several suggestions exist.

An other interesting effect, is the creation of secondary flows near to the boundary layer induced by viscous forces. The most common experiment is that of a circular cylinder performing harmonic linear oscillations perpendicular to is axis in stagnating fluid. The harmonic motion of the cylinder induces stationary flows near to the boundary and yields to jets propagating from or to the stagnation points. In literature this phenomenon is usually referred to as “streaming”. Figure 2 shows the results of a CFD-simulation displaying this effect.

3.2 Acoustic cavities

To increase the stability margin of operation, acoustic cavities such as Helmholtz or quarter-wave resonators are commonly used not only in rocket engines but also in other combustions systems like gas turbines. Figure 3 shows schematically the assembly for a rocket engine with the cavities placed usually on the perimeter near to the injectors.

The eigenmodes of combustion chambers can be approximated by the ones of simple circular cylinders. However, the addition of the acoustic cavities with large open area to the combustion chamber significantly alters the shape and frequency of the modes in the coupled system. This might already affect the driving mechanism of the instability. Furthermore, it is expected that the cavities will have a maximal response with high acoustic velocity oscillation at their inlet. In this case, acoustic energy dissipation occurs both through viscous losses at the walls and turbulent dissipation at cavity vertices.

In order to get an accurate description of the stability behavior of a combustion system it is necessary to include both the driving and damping mechanisms in the analysis such as combustion zone and nozzle response, mean flow, flow fluctuations and resonator behavior.

References

• Lighthill, M. J. The Response of Laminar Skin Friction and Heat Transfer to Fluctuations in the Stream Velocity Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, The Royal Society, 1954, 224, 1-23
• Riley Oscillatory Viscous Flows Inst. Maths Applies, 1967, 3, 419-434
• Oberg, C. L. Combustion stabilization with acoustic cavities Journal of Spacecraft and Rockets, 1971, 8, 1220?1225