# Aeroacoustic modal analysis of underexpanded pipe jets with and without an upstream cavity

Abstract: The investigation of the aeroacoustics of an underexpanded pipe-cavity jet is carried out experimentally. Two different aspect ratios of the cavity are tested for a wide range of nozzle pressure ratios. Both internal and externally radiated pipe-cavity acoustics are studied. Linear and higher-order spectral analyses are implemented on the unsteady cavity pressure to comprehend the nature of the cavity acoustics and nonlinear interactions of different acoustic modes of the pipe–cavity system. Results show that an increase in depth leads to an enhancement in the nonlinear interactions. Furthermore, the power spectral and overall sound pressure level analyses of pipe and pipe-cavity jet noise radiation are carried out. High-speed schlieren imaging techniques are used to understand jet dynamics. Highly unsteady motion of the jet initial shear layer is observed due to an upstream disturbance of the cavity. In addition, proper orthogonal and dynamic mode decomposition methods are used to extract the spatial and dynamic modes of the jet structure. These methods are used to segregate the cavity associated jet dynamics and screech dynamics.

Topics: Jet noise (63%), Jet (fluid) (62%), Aeroacoustics (56%), Dynamic mode decomposition (52%), Sound pressure (52%)

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Abstract: The impinging shock of varying strengths on the free shear layer in a confined supersonic cavity flow is studied numerically using the detached-eddy simulation. The resulting spatiotemporal variations are analyzed between the different cases using unsteady statistics, $x-t$ diagrams, spectral analysis, and modal decomposition. A cavity of length to depth ratio $[L/D]=2$ at a freestream Mach number of $M_\infty = 1.71$ is considered to be in a confined passage. Impinging shock strength is controlled by changing the ramp angle ($\theta$) on the top-wall. The static pressure ratio across the impinging shock ($p_2/p_1$) is used to quantify the impinging shock strength. Five different impinging shock strengths are studied by changing the pressure ratio: $1.0,1.2,1.5,1.7$ and $2.0$. As the pressure ratio increases from 1.0 to 2.0, the cavity wall experiences a maximum pressure of 25% due to shock loading. At [$p_2/p_1]=1.5$, fundamental fluidic mode or Rossiter's frequency corresponding to $n=1$ mode vanishes whereas frequencies correspond to higher modes ($n=2$ and $4$) resonate. Wavefronts interaction from the longitudinal reflections inside the cavity with the transverse disturbances from the shock-shear layer interactions is identified to drive the strong resonant behavior. Due to Mach-reflections inside the confined passage at $[p_2/p_1]=2.0$, shock-cavity resonance is lost. Based on the present findings, an idea to use a shock-laden confined cavity flow in an enclosed supersonic wall-jet configuration as passive flow control or a fluidic device is also demonstrated.

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Abstract: The impinging shock of varying strengths on the free shear layer in a confined supersonic cavity flow is studied numerically using the detached eddy simulation. The resulting spatiotemporal variations are analyzed between the different cases using unsteady statistics, x–t diagrams, spectral analysis, and modal decomposition. A cavity of length to depth ratio [ L / D ] = 2 at a freestream Mach number of M ∞ = 1.71 is considered to be in a confined passage. Impinging shock strength is controlled by changing the ramp angle (θ) on the top wall. The static-pressure ratio across the impinging shock ( p 2 / p 1) is used to quantify the impinging shock strength. Five different impinging shock strengths are studied by changing the pressure ratio: 1.0 , 1.2 , 1.5 , 1.7, and 2.0. As the pressure ratio increases from 1.0 to 2.0, the cavity wall experiences a maximum pressure of 25% due to shock loading. At [ p 2 / p 1 ] = 1.5, fundamental fluidic mode or Rossiter's frequency corresponding to n = 1 mode vanishes whereas frequencies correspond to higher modes (n = 2 and 4) resonate. Wavefronts interaction from the longitudinal reflections inside the cavity with the transverse disturbances from the shock-shear layer interactions is identified to drive the strong resonant behavior. Due to Mach reflections inside the confined passage at [ p 2 / p 1 ] = 2.0, shock-cavity resonance is lost. Based on the present findings, an idea to use a shock-laden confined cavity flow in an enclosed supersonic wall-jet configuration as passive flow control or a fluidic device is also demonstrated.

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4,730 citations

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Abstract: The description of coherent features of fluid flow is essential to our understanding of fluid-dynamical and transport processes. A method is introduced that is able to extract dynamic information from flow fields that are either generated by a (direct) numerical simulation or visualized/measured in a physical experiment. The extracted dynamic modes, which can be interpreted as a generalization of global stability modes, can be used to describe the underlying physical mechanisms captured in the data sequence or to project large-scale problems onto a dynamical system of significantly fewer degrees of freedom. The concentration on subdomains of the flow field where relevant dynamics is expected allows the dissection of a complex flow into regions of localized instability phenomena and further illustrates the flexibility of the method, as does the description of the dynamics within a spatial framework. Demonstrations of the method are presented consisting of a plane channel flow, flow over a two-dimensional cavity, wake flow behind a flexible membrane and a jet passing between two cylinders.

2,909 citations

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838 citations

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Abstract: Dynamic mode decomposition (DMD) represents an effective means for capturing the essential features of numerically or experimentally generated flow fields. In order to achieve a desirable tradeoff between the quality of approximation and the number of modes that are used to approximate the given fields, we develop a sparsity-promoting variant of the standard DMD algorithm. Sparsity is induced by regularizing the least-squares deviation between the matrix of snapshots and the linear combination of DMD modes with an additional term that penalizes the l1-norm of the vector of DMD amplitudes. The globally optimal solution of the resulting regularized convex optimization problem is computed using the alternating direction method of multipliers, an algorithm well-suited for large problems. Several examples of flow fields resulting from numerical simulations and physical experiments are used to illustrate the effectiveness of the developed method.

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