Heat Transfer in Oscillating Flows and its Impact on the Damping Characteristics of Acoustic Resonators
by Simon van Buren and Wolfgang Polifke
Motivation
Within the framework of the “DFG Sonderforschungsbereich Transregio 40”, the technological fundamentals of space vehicle as launcher systems are studied to contribute to the design process of components, exposed to high thermal and mechanical loads. In this context, the Thermo-Fluid-Dynamics Group focuses on the damping characteristics of acoustic resonators. These characteristics strongly depend on the transient temperature field within the resonator and thus are directly coupled to the heat transfer between wall components and the fluid flow.
Propulsion systems as rocket motors are prone to thermo-acoustic instabilities that are triggered by the feedback-loop between fluctuating heat release in the combustion zone and acoustic waves that are reflected by the confinement of the combustion chamber. Possible consequences are a reduced efficiency as well as fatal effects as the shut-down of the engine or structural damage. Acoustic resonators are utilized for the thermo-acoustic stabilization of the combustion chamber, exploiting their capability to absorb acoustic energy. Accounting for linear effects, the damping characteristics only depend on the acoustic forcing frequency. At frequencies close to the eigenfrequency, increased acoustic flow velocities are observed close to the resonator mouth. Thus, high thermo-viscous losses are generated within the boundary layer, resulting in considerable sound absorption. At high acoustic forcing amplitudes, flow separation contributes to additional non-linear losses. In this domain, the damping characteristics not only depend on the acoustic frequency but also on the forcing amplitude.
Objectives and Strategy
Objective of the current study is the evaluation of transient temperature distributions and their impact on the damping characteristics. In contrast to previous studies, where homogeneous temperatures were assumed, high temperature gradients are expected to develop in the resonator: at the resonator mouth the hot gases of the combustion predominate, while, at the back of the resonator, low temperatures are induced by chamber cooling mechanisms. Analytical correlations show that the damping characteristics are influenced by temperature inhomogeneities. A shift of the eigenfrequency may lead to a off-tune of the resonator.
In a generic configuration the effect of temperature inhomogeneities is investigated by the help of numerical simulations. Using the computational fluid dynamics (CFD) code OpenFOAM, laminar as well as turbulent cases are considered. In previous work, it was shown that Large-Eddy-Simulations (LES) provide a reliable approach to determine the damping characteristics for turbulent flows. Methods from the field of system identification are utilized to obtain the quantitative characteristics from the simulation results. Particular focus for the determination of the local temperature distribution lies on heat transfer mechanisms that prevail in the acoustically oscillating turbulent flow. The effects of enhanced heat transfer (EHT) in fluid regions close to the wall is of crucial importance and requires a deeper numerical investigation.
Based on the generic approach, an application oriented configuration shall serve as a reference of a combustion chamber at operating condition. Due to the geometric and fluid-dynamic complexity, a simulation of the complete chamber is unfeasible. Therefore, only a small geometric region around the resonator is resolved numerically in the CFD simulation, while the remaining fluid flow is modeled by one-dimensional state space systems that can be derived by the inhouse code tax. The coupling between the CFD domain and the state space models is realized by the Characteristic Based State Space Boundary Condition (CBSBC) [1]. This approach allows for a significant reduction in computational cost by numerically focusing on the geometric region of interest, without neglecting the proper acoustic interactions to the adjoining domains. A test rig at the chair of turbomachinery and flight propulsion (Prof. Haidn) may serve for validation purposes.
[1] Jaensch, S., Sovardi, C., Polifke, W.: On the Robust, Flexible and Consistent Implementation of Time Domain Impedance Boundary Conditions for Compressible Flow Simulations. Journal of Computational Physics, 2016
Acknowlegment
Financial support has been provided by the German Research Foundation (DFG) in theframework of the DFG TRR40, whose support is gratefully acknowledged.