Model reduction for supersonic cavity flow using proper orthogonal decomposition (POD) and Galerkin projection

Zhang, Chao; Wan, Zhen-Hua; Sun, Daoyuan

doi:10.1007/s10483-017-2195-9

Cited by 11 publications

(7 citation statements)

References 16 publications

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“…Further simpler improvements can be carried out. The inner product in the POD analysis and the governing equations employed in the Galerkin projection can be modified, see for instance Zhang et al [37] where a POD ROM was constructed involving primitive variables of the fully compressible Navier-Stokes equations. Concerning the chirp actuation law, used for extracting the actuation mode and defining the generalized POD modes, its influence should be evaluated as well.…”

Section: Resultsmentioning

confidence: 99%

Open-loop control of cavity noise using Proper Orthogonal Decomposition reduced-order model

et al. 2018

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a b s t r a c tFlow over open cavities is mainly governed by a feedback mechanism due to the interaction of shear layer instabilities and acoustic forcing propagating upstream in the cavity. This phenomenon is known to lead to resonant tones that can reach 180 dB in the far-field and may cause structural fatigue issues and annoying noise emission. This paper concerns the use of optimal control theory for reducing the noise level emitted by the cavity. Boundary control is introduced at the cavity upstream corner as a normal velocity component. Model-based optimal control of cavity noise involves multiple simulations of the compressible Navier-Stokes equations and its adjoint, which makes it a computationally expensive optimization approach. To reduce the computational costs, we propose to use a reduced-order model (ROM) based on Proper Orthogonal Decomposition (POD) as a surrogate model of the forward simulation. For that, a control input separation method is first used to introduce explicitly the control effect in the model. Then, an accurate and robust POD ROM is derived by using an optimization-based identification procedure and generalized POD modes, respectively. Since the POD modes describe only velocities and speed of sound, we minimize a noise-related cost functional characteristic of the total enthalpy unsteadiness. After optimizing the control function with the reduced-order model, we verify the optimality of the solution using the original, high-fidelity model. A maximum noise reduction of 4.7 dB is reached in the cavity and up to 16 dB at the far-field. .in (K.K. Nagarajan). roof of cars, etc. These flows are largely characterized by the presence of a global instability, that dominates the flow, and belong to the oscillators' category as defined by Huerre and Rossi [21] . Reducing the cavity noise is then of extreme importance for the development of quieter transport means. It is now well-known that the control of instabilities for oscillator flows is feasible with a model-based approach relying on linear control tools [35] . In this paper, the objective is to reduce the level of noise emitted by the cavity with an optimal control approach based on a nonlinear model of the dynamics. High-fidelity numerical simulations, like Direct Numerical Simulation (DNS) of Navier-Stokes equations (NSE), are too expensive for flow control applications. This observation is particularly true when iterative optimization methods are used as in the case of optimal control [19] . It is then necessary to derive surrogate models for reducing the computational costs related to optimal control of high-dimensional nonlinear systems. Starting from an experimental or computational database, the objective is to derive Reduced-Order Models (ROMs) which mine the relevant information content in terms of dynamics.

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Section: Resultsmentioning

confidence: 99%

Open-loop control of cavity noise using Proper Orthogonal Decomposition reduced-order model

et al. 2018

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“…Their work involves reduced order modelling for supersonic flow over a cavity using POD and Galerkin projection, whereas the present research focuses on the study of the hydrodynamic and acoustic modes due to the convection of discrete vortices along the shear layer. To be precise the major philosophical difference between our study and that of the study of by Zhang et al [27] lies in the fact that they propose a new norm for the reduced order modelling of the supersonic flow. However, in the present investigation, we are only interested in the modal decomposition and not the reduced order modelling, by this we mean that these decomposition tools are utilized to characterize the structures generated due to the hydrodynamic and acoustic interactions leading to the self-sustained oscillation.…”

Section: Introductionmentioning

confidence: 85%

“…To the authors' best knowledge POD and DMD analysis of a supersonic cavity flow has not been reported widely except recent work by Zhang et al [27]. Their work involves reduced order modelling for supersonic flow over a cavity using POD and Galerkin projection, whereas the present research focuses on the study of the hydrodynamic and acoustic modes due to the convection of discrete vortices along the shear layer.…”

Section: Introductionmentioning

confidence: 95%

“…The SGS stresses 𝜏 𝑖𝑗 = 𝑢 𝑖 𝑢 𝑗 ̅̅̅̅̅ − 𝑢 𝑖 ̅ 𝑢 𝑗 ̅ are related to the resolved turbulent stresses 𝐿 𝑖𝑗 = 𝑢 𝑖 ̅ 𝑢 𝑗 ̅ ̂− 𝑢 𝑖 ̅ ̂𝑢𝑗 ̅ ̂ and the subtest stresses 𝑇 𝑖𝑗 = 𝑢 𝑖 𝑢 𝑗 ̅̅̅̅̅ ̂− 𝑢 𝑖 ̅ ̂𝑢𝑗 ̅ ̂ via Germano identity [28]. A dynamic procedure was applied by Moin et al [27] for the two constant model proposed by…”

Section: Numerical Detailsmentioning

confidence: 99%

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Modal decomposition of turbulent supersonic cavity

Soni

Arya

2018

Shock Waves

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Self-sustained oscillation in Mach 3 supersonic cavity with a length-to-depth ratio of 3 is investigated using wall modeled Large Eddy Simulation (LES) methodology for ReD = 3.39×10 5 . The unsteady data obtained through computation is utilized to investigate the spatial and temporal evolution of the flow field, especially second invariant of velocity tensor; while the phase averaged data is analyzed over a feedback cycle to study the spatial structures. This analysis is accompanied by the Proper Orthogonal Decomposition (POD) data, which reveals the presence of discrete vortices along the shear layer. The POD analysis is performed in both the spanwise and streamwise planes to extract the coherence in flow structures. Finally, Dynamic Mode Decomposition (DMD) is performed on the data sequence to get the dynamic information and deeper insight into the self-sustained mechanism.

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“…POD looks for spatial base functions that capture the most energetic components of a dynamical system [22] . Suppose that N snapshots of the three-dimensional velocity field u(x, t) are recorded during the numerical simulation, and POD decomposes the fluctuating velocity u (x, t) into a set of spatial modes ψ i (x) with temporal coefficients a i (t), by separating the independent variables x and t. In this work, the snapshot POD approach of Sirovich was adopted [23][24] . The mode amplitude a i (t) is obtained from the eigenvectors of the auto-correlation matrix…”

Section: Pod Modesmentioning

confidence: 99%

Proper orthogonal decomposition analysis of coherent motions in a turbulent annular jet

Zhang

Vanierschot

2021

Appl. Math. Mech.-Engl. Ed.

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A three-dimensional incompressible annular jet is simulated by the large eddy simulation (LES) method at a Reynolds number Re = 8 500. The time-averaged velocity field shows an asymmetric wake behind the central bluff-body although the flow geometry is symmetric. The proper orthogonal decomposition (POD) analysis of the velocity fluctuation vectors is conducted to study the flow dynamics of the wake flow. The distribution of turbulent kinetic energy across the three-dimensional POD modes shows that the first four eigenmodes each capture more than 1% of the turbulent kinetic energy, and hence their impact on the wake dynamics is studied. The results demonstrate that the asymmetric mean flow in the near-field of the annular jet is related to the first two POD modes which correspond to a radial shift of the stagnation point. The modes 3 and 4 involve the stretching or squeezing effects of the recirculation region in the radial direction. In addition, the spatial structure of these four POD eigenmodes also shows the counter-rotating vortices in the streamwise direction downstream of the flow reversal region.

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Model reduction for supersonic cavity flow using proper orthogonal decomposition (POD) and Galerkin projection

Cited by 11 publications

References 16 publications

Open-loop control of cavity noise using Proper Orthogonal Decomposition reduced-order model

Open-loop control of cavity noise using Proper Orthogonal Decomposition reduced-order model

Modal decomposition of turbulent supersonic cavity

Proper orthogonal decomposition analysis of coherent motions in a turbulent annular jet

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