Moritz Schulze

Linearized Navier-Stokes and Euler equations for the Determination of the Acoustic Scattering Behaviour of an Area Expansion

In this paper, we investigate the scattering behaviour of plane acoustic waves at an area expansion. Therein, the mean flow separates at the trailing edge and expands into a jet in the downstream duct. This configuration supports complex interaction effects between acoustic waves and mean flow field. The methodology involves a two step hybrid approach. First, a highly resolved large eddy simulation (LES) is performed to extract the mean flow field. Then, the acoustic field is computed in frequency space, yielding the unknown scattering matrix coefficients. Two different sets of governing equations are used for this task: the linearized Navier-Stokes equations (LNSEs) and linearized Euler equations (LEEs). By definition, these sets of equations are convection dominated and are therefore susceptible to numerical instabilities. In this paper a consistent finite element Galerkin/least-squares (GLS) approach is used to stabilize the different sets of equations. Unlike the introduction of artificial viscosity, this technique partially preserves the accuracy of the discretization order. The results show that both equation sets, viz. LNSEs and LEEs capture the complex interaction between acoustic waves and the free shear layer in detail. It is shown that acoustic diffusion effects of the LNSEs are of small order and may be neglected for the acoustic determination of the scattering behaviour of sudden area expansions.

Quantitative Stability Analysis Using Real-Valued Frequency Response Data

Models for the analysis of thermoacoustic instabilities are conveniently formulated in the frequency domain. In this case one often faces the difficulty that the response behavior of some elements of the system is only known at real-valued frequencies, although the transfer behavior at complex-valued frequencies is required for the quantification of the growth rates of instabilities. The present paper discusses various methods for extrapolation of frequency response data at real-valued frequencies into the complex plane. Some methods have been used previously in thermoacoustic stability analysis, others are newly proposed. First the pertinent mathematical background is reviewed, then the sensitivity of predicted growth rates on the extrapolation scheme is explored. This is done by applying different methods to a simple thermoacoustic system, i.e. a ducted premixed flame, for which an analytical solution is known. A short analysis determining the region of confidence of the extrapolated transfer function is carried out to link the present study to practical applications. The present study can be seen as a practical guideline for using frequency response data collected for a set of real-valued frequencies in quantitative linear stability analysis.Copyright

A Conceptional Approach for the Prediction of Thermoacoustic Stability in Rocket Engines

A methodology to predict thermoacoustic stability in rocket engines is presented. It is based on a divide and conquer principle. The central elements, consisting of the combustion chamber and the nozzle are calculated together directly by a hybrid approach using an extended version of the DLR’s acoustic solver PIANO. Beside these central elements, the different components affecting the overall thermoacoustic stability are simulated separately and their properties are lumped into an adequate mathematical description, which is then integrated into PIANO. Each component is analyzed and optimized in its individual environment to reduce the complexity of the interaction processes, which govern thermoacoustics. The challenging step however is the incorporation of all components into a complete stability analysis and thereby keep the computational cost within reasonable limits to make this approach attractive for industrial purposes. In this report the fundamental approach is explained as well as the different components are described by means of their relevance for thermoacoustics and used modelling approaches are shown. Finally the strengths of the approach are confronted with its disadvantages. Especially its realizability and future prospects are discussed.

Interaction of Combustion with Transverse Velocity Fluctuations in Liquid Rocket Engines

The verification of thermoacoustic stability is one of the most essential steps in the framework of the development of liquid rocket engines. In hybrid methods, which allow fast and detailed evaluation of the flame/acoustics interaction, the simulation of wave propagation is separated from the analysis of flame response to acoustic perturbations. This requires a feedback model for the interaction of combustion and acoustics. Transverse modes, which are particularly prone to combustion instabilities due to their low nozzle damping, are dominated by velocity fluctuations in the transverse direction. The interaction of these fluctuations with the combustion process in liquid rocket engines is numerically studied in the paper, employing a rocket engine configuration with hypergolic propellants as an example. It is shown that the fluctuations lead to major changes in the mean flow near the injector as evaporation and mixing are accelerated. Furthermore, the study reveals that the displacement of the flame cent...

Linear stability assessment of a cryogenic rocket engine

The linear high frequency stability of DLR’s cryogenic H2/O2 BKD test chamber is assessed using a hybrid computational fluid dynamic/computational aeroacoustic methodology, which is based on single flame simulations for the generation of an adequate mean flow and for the calibration of feedback models as well as on frequency space transformed linearized Euler equations. The application of a realistic mean flow field including combustion explains the spatial separation of transverse modes into a near face plate mode, which is found linearly unstable under certain operation conditions for the first transverse and a rear part mode. The axial mode shape length as well as eigenfrequencies is affected by propellant injection specifications and, in consequence, decisively influence pressure and transverse velocity sensitive dynamic flame response. The stability assessment procedure is finally applied to four operation conditions and the linear stability is predicted for the first transverse mode.

Impact of Injector Mass Flow Fluctuations on Combustion Dynamics in Liquid Engines

Reynolds-averaged Navier–Stokes simulations were carried out to study the influence of acoustically driven injector mass flow fluctuations on combustion dynamics in a liquid propellant rocket engine. First, a framework of transfer functions is introduced, showing the links between pressure fluctuations in the chamber and resulting heat release modulation on the basis of the subprocesses involved. An analytical model for the injector admittance is evaluated, and computational-fluid-dynamics results for a single-injector configuration are obtained. The impact of mass flow fluctuations on evaporation dynamics and on heat release modulation is studied for four load points. Results show that the combustion dynamics are controlled by the droplet evaporation time. Dynamic mode decomposition results explain the convective transport of the droplets and give a detailed insight into the fluctuating fields. A weak mutual influence of the fuel evaporation is observed, whereas the fluctuations of the heat release rate ...

Low-Order Modelling of the Non-Local Acoustic Reacting Combustion Chamber-Dome Interface in Rocket Engines

A low-order model of the complex non-local reacting acoustic interface between the combustion chamber and the oxygen dome volume of typical rocket engine configurations is presented. Herein, computational effort is reduced by not resolving the complex face plate geometry comprising a potentially big number of injectors but by providing an adequate describing function of the interface in its entirety. The acoustic properties of the interface are described by so-called scattering matrices. The determination of the scattering matrix is performed in a separated procedure, which can be conducted analytically, numerically or by using experimental methods. Detailed evaluations of these lead to matrices that capture even small scale effects. For the usage of the scattering matrices in a time-domain solver digital filters are applied. This paper presents first results for the case of an orifice located in a straight pipe, which is considered as a simplified face plate configuration for longitudinal waves. The objective is to verify that the imposed scattering matrix can be reconstructed by using the two-source location method.

Influence of atomization quality modulation on flame dynamics in a hypergolic rocket engine

For the numerical evaluation of the thermoacoustic stability of rocket engines often hybrid methods are applied, which separate the computation of wave propagation in the combustor from the analysis of the flame response to acoustic perturbations. Closure requires a thermoacoustic feedback model which provides the heat release fluctuation in the source term of the employed wave transport equations. The influence of the acoustic fluctuations in the combustion chamber on the heat release fluctuations from the modulation of the atomization of the propellants in a hypergolic upper stage rocket engine is studied. Numerical modeling of a single injector provides the time mean reacting flow field. A network of transfer functions representing all aspects relevant for the feedback model is presented. Analytical models for the injector admittances and for the atomization transfer functions are provided. The dynamics of evaporation and combustion are studied numerically and the numerical results are analyzed. An analytical approximation of the computed flame transfer function is combined with the analytical models for the injector and the atomization quality to derive the feedback model for the wave propagation code. The evaluation of this model on the basis of the Rayleigh index reveals the thermoacoustic driving potential originating from the fluctuating spray quality.

Frequency Domain Predictions of Acoustic Wave Propagation and Losses in a Swirl Burner With Linearized Navier-Stokes Equations

A low-cost, high-quality hybrid CFD/CAA-methodology is used to predict the acoustic properties of a swirl burner including its complex swirl flow conditions. The numerically determined burner transfer matrix is validated against experimental data. The results demonstrate the capability of this low-cost hybrid approach to predict the acoustic characteristics of combustor components with high geometrical complexity. Most importantly it captures the effect of mean flow quantities on the fluctuating field. This causes the loss of acoustic energy and thus constitutes sources of acoustic damping. In this regard, reliable data can be obtained to characterize complex acoustic components at relatively low computational cost. Therefore, experimental efforts can be reduced which are generally required to provide data e.g. to set up low-order network models.The insight into the field of fluctuating quantities allows the analysis of linear acoustic damping phenomena. Essentially, in the context of isentropic conditions acoustic energy is lost due to the formation of vorticity disturbances. Source regions for vorticity disturbances are identified at flow separation edges and within the multiple shear layers of the complex swirl flow.Copyright

Frequency domain simulations for the determination of liner effects on longitudinal wave propagation

Frequency domain simulations are carried out in order to determine the effects of a liner on the propagation of longitudinal waves. On the basis of a CFD/CAA approach, three-dimensional linearized Euler equations (LEE) are transformed into frequency space and discretized using a stabilized Finite-Element technique to provide stable solution procedures and meaningful results. The code is validated on a Grazing Incidence Tube (GIT), which is operated at the NASA Langley Research Center. Results show that the frequency transformed LEE are very suitable to predict the acoustic propagation using experimentally determined liner impedances for different Mach numbers in the tube and further acoustic boundary conditions both at inlet and outlet of the test rig. In comparison to time-domain based approaches, computational times are reduced substantially and numerical instability issues are prevented. Furthermore, the relevance of detailed mean flow profiles and Myers impedance boundary conditions for the accurate prediction of the liner effect on the acoustic wave propagation is addressed.