<p dir="ltr">Thermo-acoustic interactions, characterized by the coupling between heat release and acoustic waves, are a phenomenon that can lead to combustion instability in high-speed propulsion devices. These interactions are highly undesirable as they can damage engine components and, in severe cases, cause catastrophic failure of the entire propulsion system. Mitigating these instabilities is crucial for ensuring reliable combustor operation. This work presents a computational investigation of combustion instability in Purdue's Continuously Variable Resonance Combustor (CVRC), focusing on the prediction of instability trend over the entire oxidizer-post length range. Computational fluid dynamics (CFD) studies in the past mainly focused on individual CVRC cases with specific oxidizer-post lengths. Those studies help understand the instability mechanism for individual CVRC cases but are limited in examining the applicability of model predictions over a wide range of instability conditions. No studies have been reported to assess the model predictivity over the entire oxidizer-post range in CVRC. </p><p dir="ltr">In this work, we first conduct a series of CFD simulations that cover the entire oxidizer-post length in CVRC to assess the models for a wide range of instability conditions. It is found that the CFD models generally fail to capture the instability trend over the entire oxidizer-post length although they can capture some individual cases. To understand the model failure, parametric studies are often deemed the first step of investigation. Such parameter studies, however, are expensive for CVRC since more than ten simulation cases to cover the entire oxidizer-post range are needed for each parametric study. Multiple parametric studies are typically needed to cover various uncertainties from numerics and physical models and those involved in the experimental conditions, making parametric studies for CVRC a computationally expensive task. Therefore, our focus next is on developing faster approaches.</p><p dir="ltr">The second part of this work is to develop a reduced-order model to quickly conduct the needed parametric studies. The developed reduced-order model leverages the instability mechanisms observed from the CFD simulations conducted in the first part. Monte Carlo approaches are employed to replace expensive CFD simulations by replicating the randomness in the combustor through statistical sampling. The developed reduced-order model is first validated by comparing its predictions with the CFD simulation results in a number of cases. The reduced-order model, despite its simplicity, reasonably reproduced the overall trend of instability from CFD simulations, making it an attractive alternative to the detailed model simulations for parametric studies. </p><p dir="ltr">The validated reduced-order model is then applied to parametric studies of CVRC to help identify the uncertainties of CFD predictions of CVRC. Four sets of parametric studies are conducted to provide a rapid examination of the effect of heat loss, the effect of oxidizer temperature, the effect of equivalence ratio, and the effect of turbulence on the instability predictions in CVRC. From the rapid reduced-order parametric studies, we found that the heat losses in upstream of the oxidizer inlet and the combustor wall are the two most contributing factors to the uncertainties of CFD model predictions. The turbulence level and the error involved in the equivalence ratio due to experimental uncertainties play an insignificant role in contributing to the CFD prediction uncertainties. </p><p dir="ltr">This work is a significant contribution to the combustion instability community by enabling an alternative rapid assessment of CFD model predictions. This capability facilitates the identification of major contributing factors of CFD modeling uncertainties with much less computational cost, thereby allowing for a more focused approach to CFD analysis and ultimately accelerating the improvement of CFD models for combustion instability studies. </p>

<div>Shock-wave/turbulent boundary-layer interactions (SWTBLIs) are characterized by low-frequency unsteadiness, amplified aerothermal loads, and a complex three-dimensional flowfield. Presence of a broad range of length and time-scales associated with compressible turbulence generates additional gasdynamic features that interact with different parts of the flowfield via feedback mechanisms. Determining the physics of such flows is of practical importance as they occur frequently in different components of a supersonic/hypersonic aircraft such as inlets operating in both on- and off-design conditions, exhaust nozzles, and control surfaces. SWTBLIs can cause massive flow separation which may trigger unstart by choking the flow in an inlet. On control surfaces, fatigue loading caused by low-frequency shock unsteadiness, coupled with high skin-friction and heat transfer at the surface, can result in failure of the structure.</div><div><br></div><div>The objective of this study is twofold. The first aspect involves examining the causes of unsteadiness in SWTBLIs associated with two geometries – a backward facing step flow reattaching on to a ramp, and a highly confined duct flow. Signal processing and statistical techniques are performed on the results obtained from Delayed Detached-Eddy Simulations (DDES) and Implicit Large-Eddy Simulations (ILES). Dynamic Mode Decomposition (DMD) is used as a complement to this analysis, by obtaining a low-dimensional approximation of the flowfield and associating a discrete frequency value to individual modes. </div><div><br></div><div>In case of the backward facing step, Fourier analysis of wall-pressure data brought out several energy dominant frequency bands such as separation bubble breathing, oscillations of the reattachment shock, shear-layer flapping, and shedding of vortices from the recirculation zone. The spectra of reattachment shock motion suggested a broadband nature of the oscillations, wherein separation bubble breathing affected the low-frequency motion and shear-layer flapping, and vortex shedding correlated well at higher frequencies. A similar exercise was carried out on the highly confined duct flow which featured separation on the floor and sidewalls. In addition to the low-frequency shock motions, the entire interaction exhibited a cohesive back-and-forth in the streamwise direction as well as a left-right motion along the span. Mode reconstruction using DMD was used in this case to recover complex secondary flows induced by the presence of sidewalls.</div><div><br></div><div>For the final aspect of this study, a flow-control actuator was computationally modeled as a sinusoidally varying body-force function. Effects of high-frequency forcing at F⁺ =1.6 on the flowfield corresponding to a backward facing step flow reattaching on to a ramp were examined. Conditionally averaged profile of streamwise velocity fluctuations, based on reattachment shock position, was used for the formulation of spatial distribution of the actuator. The forcing did not change the mean and RMS profiles significantly, but affected the unsteadiness of the interaction significantly. The effects of forcing were localized to the recirculation zone and did not affect the evolution of the shear-layer. The acoustic disturbances propagating through the freestream and recirculation zone drove the motion of the reattachment shock, and did not alter the low-frequency dynamics of the interaction.</div>