In §II. Theory, two reduced-order models are proposed, which the authors have termed: the quasi-steady model (§II.A. Quasi-steady one-dimensional model) & the inertial/hybrid model (§II.B. Quasi-one-dimensional pointmass model), respectively. N.b., in both cases time dependence isn’t explicitly modeled, i.e., technically speaking both models are quasi-steady. Ergo, in hindsight, it would have been more apt to call the model proposed in §II.A.: the matching-condition model. With that in mind, the readership is encouraged to substitute “matching-condition model/modeling regime” instead of “quasi-steady model/modeling regime,” when reading this conference paper. Moreover, the following title would have been more suitable: “Entropy-patch chokednozzle interaction: matching-condition and inertial modeling-regimes mapped”.

Indirect combustion noise due to the interaction of flow inhomogeneities with a choked combustion-chamber exit is an important cause of combustion instability in solid rocket motors. Moreover, it is believed to be an issue in electrical-power generation turbines and aero-engines. If these flow inhomogeneities are essentially characterized by the fluid having a locally appreciably-different thermodynamic state, the acoustic response engendered by its interaction with the combustion-chamber exit is commonly referred to as entropy noise. In this paper, dedicated numerical-simulation results of entropy-patch choked-nozzle interactions are presented. Two types of entropy patches were considered: rectangular slugs and circular spots. Moreover, analytical-model-based analysis, of said simulation results, is presented. Based on said analysis, the authors posit the existence of three modeling regimes: the quasi-steady-modeling regime, the blended-physical-effects regime, and the inertial-modeling regime.

Entropy inhomogeneities and vorticity spots induce so-called indirect combustion noise when passing through a choked nozzle; referred to as entropy noise and vorticity noise, respectively. We note that vorticity noise depends on the orientation of the vorticity; viz., oriented normal or parallel to the axial main flow. An experimental investigation of parallel component vorticity noise is presented. In the experiment a time-dependent swirling flow was induced by unsteady tangential injection in the pipe upstream of a choked convergent-divergent nozzle. As the resulting swirling flow passes through the nozzle, the axial stretching of the fluid caused an increase in rotation energy. The steady energy conservation in an isentropic flow implies a Mach number higher than unity at the throat and an associated reduction of density. Ergo, the critical mass-flow rate (for fixed reservoir pressure and temperature) decreases quadratically with increasing swirl intensity. The acoustic waves radiated downstream of the nozzle are due to the change in the mass flow through the nozzle. These are a direct measure for this mass-flow modulation. Using a semi-empirical model, this sound production mechanism is demonstrated to be quasi steady.

An experimental cold-gas study of the response of a choked convergent–divergent nozzle to swirl perturbations is presented. The perturbations were obtained by means of upstream unsteady tangential injections into initially steady flows with different values of steady background swirl. The swirl perturbations induced changes in the axial mass-flow rate, due to either their ingestion or evacuation by the nozzle. This in turn caused a downstream acoustic response. For low-intensity background swirl the responses were found to be similar to those obtained without steady background swirl. Perturbations of a high-intensity background swirl led to different effects. For long injection times, the negative mass-flow rate modulation occurred in two stages. The first stage was similar to that of the background-swirl free case. The second stage occurred after a short time delay, and induced a much stronger negative acoustic response. This unexpected behavior suggests that a significant part of the tangentially injected fluid flows upstream inducing an accumulation of swirl, which is – after tangential injection is ceased – suddenly cleared out through the nozzle. A scaling rule for the amplitudes of these acoustic responses is reported. Furthermore, quasi-steady models, based on steady-state measurements are proposed. These models predict the downstream acoustic response amplitude within a factor two. Additionally, preliminary empirical evidence of the effect of swirl on the downstream acoustic response due to the interaction of entropy patches with a choked nozzle is reported. This was obtained by comparison of sound produced by abrupt radial or tangential sonic injection, upstream from the choked nozzle, of air from a reservoir at room temperature to that from a reservoir with a higher stagnation temperature. Because the mass flow through the nozzle does not increase instantaneously, the injected higher-enthalpy air accumulates upstream of the injection-port position in the main flow. This eventually induces a large downstream acoustic pulse when tangential injection is interrupted. The magnitude of the resulting sound pulse can reach that of a quasi-steady response of the nozzle to a large air patch with a uniform stagnation temperature equal to that of the upstream-injected heated air. This hypothesis is consistent with the fact that the initial indirect-sound pulse is identical to one obtained with unheated air injection. The authors posit that – given all of the insight gleaned from them in this case – acoustic measurements of indirect sound appear to be a potentially useful diagnostic tool.

The downstream acoustic response due to the interaction of main-flow oriented vorticity with a choked nozzle in a swirl-free flow was experimentally demonstrated. The response was obtained by means of impulsive radial air injection in the pipe upstream from the nozzle. The resulting downstream acoustic data are shown to obey a scaling rule that differs, from the one for swirl-nozzle interaction, which according to the literature is proportional to the square of the swirl number. In contrast, here evidence is presented that points to the scaling of main-flow oriented vorticity noise with the cross-sectional average of the square of the transversal velocity at the throat divided by the square of the critical sound speed.

Indirect noise due to the interaction of flow inhomogeneities with a choked nozzle is an important cause of combustion instability in solid rocket motors and is believed to be important in aircraft engines. A previously published experiment (Kings, N., and Bake, F., “Indirect Combustion Noise: Noise Generation by Accelerated Vorticity in a Nozzle Flow,” International Journal of Spray and Combustion Dynamics, Vol. 2, No. 3, 2010, pp. 253–266.) demonstrated that interaction of a nozzle with time-dependent axial swirl can also be a source of sound. This axial swirl was generated by intermittent tangential mass injection upstream from a choked nozzle in a so-called vortex wave generator. The present work discusses the impact of swirl–nozzle interaction in this experiment on the acoustic waves detected downstream of the nozzle. The main source of sound appears to be the reduction in mass flux through the choked nozzle, which depends quadratically on the swirl number. This effect is quantitatively predicted by a quasi-steady and quasi-cylindrical analytical model. The model, combined with empirical data for the decay of axial swirl in pipe flows, predicts the observed influence of the distance between the vortex wave generator and the nozzle. The findings presented here contradict the hypothesis found in the literature, which presumes that sound production in the aforementioned experiment is due to the acceleration of vorticity waves through the nozzle.

View Video Presentation: https://doi-org.tudelft.idm.oclc.org/10.2514/6.2021-2286.vid

Quantitative measurements of sound due to swirl-nozzle interaction are presented for the first time. In the experiment a swirl structure was generated by means of tangential injection into a steady swirl-free flow upstream from a choked convergent-divergent nozzle. Ingestion of swirl by the choked nozzle caused a mass-flow rate change, which resulted in a downstream measured acoustic response. The amplitude of this acoustic response was found to be proportional to the square of the tangential mass-flow rate used to generate swirl. This was, assuming that the upstream generated swirl intensity is proportional to the tangential injection mass-flow rate, predicted by a previously published quasi-steady model for the swirl-nozzle interaction sound source (Hirschberg, L., Hulshoff, S. J., and Bake, F., “Sound Production due to Swirl-Nozzle Interaction: Model-Based Analysis of Experiments,” AIAA Journal, Published online on Nov. 11th 2020, doi: 10.2514/1.J059669.). The tangential-injection time was varied, and found to not influence the amplitude of the acoustic response. This indicates that quasi-steady modelling remains applicable, even for smallest achievable upstream swirl structure with an axial length of ca. three upstream diameters.

Measurements of sound due to swirl–nozzle interaction are presented. In the experiment a swirl structure was generated by means of unsteady tangential injection into a steady swirl-free flow upstream from a choked convergent–divergent nozzle. Ingestion of swirl by the choked nozzle caused a mass-flow rate change, which resulted in a downstream-measured acoustic response. The downstream acoustic pressure was found to remain negative as long as the swirl is maintained and reflections from the open downstream pipe termination do not interfere. The amplitude of this initial acoustic response was found to be proportional to the square of the tangential mass-flow rate used to generate swirl. When the tangential injection valve was closed, the mass-flow rate through the nozzle increased, resulting in an increase of the downstream acoustic pressure. This increase in signal was compared to the prediction of an empirical quasi-steady model, constructed from steady-state flow measurements. As the opening time of the valve was varied, the signal due to swirl evacuation showed an initial overshoot with respect to quasi-steady behavior, after which it gradually decayed to quasi-steady behavior for tangential injection times long compared to the convection time in the pipe upstream of the nozzle. This demonstrates that the acoustic signal can be used to obtain quantitative information concerning the time dependence of the swirl in the system. This could be useful for understanding the dynamics of flow in engines with swirl-stabilized combustion. Graphic abstract: [Figure not available: see fulltext.].

Indirect noise due to the interaction of flow inhomogeneities with a choked nozzle is as an important cause of combustion instability in solid rocket motors and is believed to be important in aircraft engines. A previously published experiment demonstrated that interaction of the nozzle with time-dependent axial swirl can also be a source of sound. This axial swirl was generated by intermittent circumferential mass injection upstream from a choked nozzle in a so-called Vortex Wave Generator. The present work discusses the impact of swirl-nozzle interaction in this experiment on the acoustic waves detected downstream of the nozzle. The main source of sound appears to be the reduction in mass flux through the choked nozzle, which depends quadratically on the swirl number. This effect is quantitatively predicted by a quasi-steady and quasi-cylindrical analytical model. The model, combined with empirical data for the decay of axial swirl in pipe flows, predicts the observed influence of the distance between the Vortex Wave Generator and the nozzle. The findings presented here contradict the hypothesis found in the literature, which presumes that sound production in the above-mentioned experiment is due to the acceleration of vorticity waves through the nozzle.