Experimental and Numerical Analysis of a Compressor Stage under Flow Distortion

Pulsed high-intensity focused ultrasound (pHIFU) can induce sparse de novo inertial cavitation without the introduction of exogenous contrast agents, promoting mild mechanical disruption in targeted tissue. Because the bubbles are small and rapidly dissolve after each HIFU pulse, mapping transient bubbles and obtaining real-time quantitative metrics correlated to tissue damage are challenging. Prior work introduced Bubble Doppler, an ultrafast power Doppler imaging method as a sensitive means to map cavitation bubbles. The main limitation of that method was its reliance on conventional wall filters used in Doppler imaging and optimized for imaging blood flow rather than transient scatterers. This study explores Bubble Doppler enhancement using dynamic mode decomposition (DMD) of a matrix created from a Doppler ensemble for mapping and extracting the characteristics of transient cavitation bubbles. DMD was first tested in silico with a numerical dataset mimicking the spatiotemporal characteristics of backscattered signal from tissue and bubbles. The performance of DMD filter was compared to other widely used Doppler wall filters - singular value decomposition (SVD) and infinite impulse response (IIR) highpass filter. DMD was then applied to an ex vivo tissue dataset where each HIFU pulse was immediately followed by a plane wave Doppler ensemble. In silico DMD outperformed SVD and IIR high pass filter and ex vivo provided physically interpretable images of the modes associated with bubbles and their corresponding temporal decay rates. These DMD modes can be trackable over the duration of pHIFU treatment using k-means clustering method, resulting in quantitative indicators of treatment progression.

A parallel and streaming Dynamic Mode Decomposition algorithm with finite precision error analysis for large data

Dynamic mode decomposition (DMD) is a popular technique for modal decomposition, flow analysis, and reduced-order modeling. In situations where a system is time varying, one would like to update the system's description online as time evolves. This work provides an efficient method for computing DMD in real time, updating the approximation of a system's dynamics as new data becomes available. The algorithm does not require storage of past data and computes the exact DMD matrix using rank-1 updates. A weighting factor that places less weight on older data can be incorporated in a straightforward manner, making the method particularly well suited to time-varying systems. A variant of the method may also be applied to online computation of “windowed DMD,” in which only the most recent data are used. The efficiency of the method is compared against several existing DMD algorithms: for problems in which the state dimension is less than about 200, the proposed algorithm is the most efficient for real-time computation, and it can be orders of magnitude more efficient than the standard DMD algorithm. The method is demonstrated on several examples, including a time-varying linear system and a more complex example using data from a wind tunnel experiment. In particular, we show that the method is effective at capturing the dynamics of surface pressure measurements in the flow over a flat plate with an unsteady separation bubble.

Dynamic mode decomposition (DMD) is essentially a hybrid algorithm based on mode decomposition and singular value decomposition, and it inevitably inherits the drawbacks of these two algorithms, including the selection strategy of truncated rank order and wanted mode components. A novel denoising and feature extraction algorithm for multi-component coupled noisy mechanical signals is proposed based on the standard DMD algorithm, which provides a new method solving the two intractable problems above. Firstly, a sparse optimization method of non-convex penalty function is adopted to determine the optimal dimensionality reduction space in the process of DMD, obtaining a series of optimal DMD modes. Then, multiscale permutation entropy calculation is performed to calculate the complexity of each DMD mode. Modes corresponding to the noise components are discarded by threshold technology, and we reconstruct the modes whose entropies are smaller than a threshold to recover the signal. By applying the algorithm to rolling bearing simulation signals and comparing with the result of wavelet transform, the effectiveness of the proposed method can be verified. Finally, the proposed method is applied to the experimental rolling bearing signals. Results demonstrated that the proposed approach has a good application prospect in noise reduction and fault feature extraction.

We establish the convergence of a class of numerical algorithms, known as dynamic mode decomposition (DMD), for computation of the eigenvalues and eigenfunctions of the infinite-dimensional Koopman operator. The algorithms act on data coming from observables on a state space, arranged in Hankel-type matrices. The proofs utilize the assumption that the underlying dynamical system is ergodic. This includes the classical measure-preserving systems, as well as systems whose attractors support a physical measure. Our approach relies on the observation that vector projections in DMD can be used to approximate the function projections by the virtue of Birkhoff's ergodic theorem. Using this fact, we show that applying DMD to Hankel data matrices in the limit of infinite-time observations yields the true Koopman eigenfunctions and eigenvalues. We also show that the singular value decomposition, which is the central part of most DMD algorithms, converges to the proper orthogonal decomposition of observables. We use this result to obtain a representation of the dynamics of systems with continuous spectrum based on the lifting of the coordinates to the space of observables. The numerical application of these methods is demonstrated using well-known dynamical systems and examples from computational fluid dynamics.

Lagrangian dynamic mode decomposition for construction of reduced-order models of advection-dominated phenomena

Oscillation of the vocal folds makes a sound source of the human voiced sound. Understanding of the oscillation mechanism, which is a complex flow-structure interaction problem in the airway, is crucial for considering clinical diagnosis of voice disorders. However, details of the oscillation mechanism are still unclear partly because, from a fluid mechanical viewpoint, the effect of oscillation of the vocal fold wall during the phonation on airflow behaviors remains elusive. In the present study, flow characteristics in a sinusoidally-oscillating constriction mimicking the vocal fold were investigated by numerical and experimental approaches. The numerical analyses focused in particular on the effect of constriction oscillation on flow separation demonstrated that the flow separation point moves continuously and periodically in a frequency-dependent manner. In the experimental study, an apparatus was newly designed, with a view to detect the oscillation-induced movement of the flow separation point, to enable detailed measurement of pressure distribution along the constriction with an interval of 2 mm that is synchronized with measurement of constriction displacement. Although movement of the separation point as seen in the numerical analyses was not detected by this limiting resolution of the apparatus, we obtained pressure-width relations that is partly contrary to the numerical results but is presumably dependent on the inlet boundary condition. These findings indicate that appropriate evaluations of separation point and inlet boundary conditions are key factors to characterize the flow in oscillating constriction, which is crucial for better understanding of the vocal fold mechanics.

To address the issue of low accuracy in the dynamic modal decomposition (DMD) method used for operational modal analysis (OMA) under noise conditions of aerospace structures, an enhanced identification approach is proposed in this paper, which integrates subspace orthogonal projection with DMD to better determine the modal properties of linear mechanical systems with noisy observations. Subspace orthogonal projection applied to the Hankelized matrix is utilized for denoising observation signals. Compact singular value decomposition (SVD) is employed on the projection matrix in order to acquire the optimal realization of system matrix. Subsequently, DMD is introduced to reduce the dimensionality of the system matrix and extract the dominant modal features. The effectiveness and practicality of the proposed method are confirmed through numerical and experimental examples. The proposed method demonstrates marginally improved identification accuracy in modal frequency and enhanced performance in damping ratios when compared to representative OMA methods under different white noise conditions.

When using CFD for the designing of fluid equipment, turbulence model is frequently used. However the accuracy of analysis is not sufficient in some cases when complicated flow separation is occurred. Therefore, it is important to select appropriate turbulence model and consider boundary layer development. In this study, we conducted numerical analyses for turbulent flow in a square sectioned U-bend duct in which flow separation is occurred due to strong curvature and tested two turbulence models and two inlet boundary conditions. Then we compared computations and measurements and it was revealed that separation region tended to be overpredicted under uniform inlet flow conditions regardless of turbulence model.

Air-flow distortion and wave interactions on research vessels: An experimental and numerical comparison

In fluid mechanics, modal decomposition, deeply intertwined with the concept of symmetry, is an essential data analysis method. It facilitates the segmentation of parameters such as flow, velocity, and pressure fields into distinct modes, each exhibiting symmetrical or asymmetrical characteristics in terms of amplitudes, frequencies, and phases. This technique, emphasizing the role of symmetry, is pivotal in both theoretical research and practical engineering applications. This paper delves into two dominant modal decomposition methods, infused with symmetry considerations: Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD). POD excels in dissecting flow fields with clear periodic structures, often showcasing symmetrical patterns. It utilizes basis functions and time coefficients to delineate spatial modes and their evolution, highlighting symmetrical or asymmetrical transitions. In contrast, DMD effectively analyzes more complex, often asymmetrical structures like turbulent flows. By performing iterative analyses on the flow field, DMD discerns symmetrical or asymmetrical statistical structures, assembling modal functions and coefficients for decomposition. This method is adapted to extracting symmetrical patterns in vibration frequencies, growth rates, and intermodal coupling. The integration of modal decomposition with symmetry concepts in fluid mechanics enables the effective extraction of fluid flow features, such as symmetrically or asymmetrically arranged vortex configurations and trace evolutions. It enhances the post-processing analysis of numerical simulations and machine learning approaches in flow field simulations. In engineering, understanding the symmetrical aspects of complex flow dynamics is crucial. The dynamics assist in flow control, noise suppression, and optimization measures, thus improving the symmetry in system efficiency and energy consumption. Overall, modal decomposition methods, especially POD and DMD, provide significant insights into the symmetrical and asymmetrical analysis of fluid flow. These techniques underpin the study of fluid mechanics, offering crucial tools for fluid flow control, optimization, and the investigation of nonlinear phenomena and propagation modes in fluid dynamics, all through the lens of symmetry.

The objectives of this work are to analyze and investigate the turbulence structures in a channel flow and in a mixing jet using Dynamic Mode Decomposition (DMD) and Snapshot Proper Orthogonal Decomposition (SPOD). The analyzed data have been generated by Direct Numerical Simulation at high Reynolds numbers. In the channel flow, the occurrence of turbulent superstructures is mainly examined. The jet case is employed to investigate mixing in a turbulent jet flow. In both cases, DMD and SPOD analysis are compared to test their performance concerning the analysis of complex flows and to highlight the complementarity between these two approaches.

Unstable movement of the unstart shock may pose a threat to the safety of a scramjet. The perturbation induced by the unstable movement can also influence the shock structure and the downstream flow, possibly causing a dynamic load on the wall or affecting downstream combustion. Without a thorough analysis of the isolator flow or by ignoring its properties, it is not possible to understand some of the phenomena prevalent in downstream combustion. In this study, two types of instabilities were observed in the unstart shock system. It is shown that if the flow distortion is not severe, the instability in the streamwise direction plays a dominant role. Sequential displacement of the downstream shock was observed in this mode. The time delay between sequential shock motions indicates their response to the movement of the first separation shock. With a highly distorted flow, a flapping mode that resulted in instability in the vertical direction with an asymmetrical effect on the pressures at the walls was observed. In this situation, the shock structure is successively attached to the wall from the head to the tail. By conducting a dynamic mode decomposition analysis, several oscillatory modes, characterized by low-frequency periodicity in the streamwise and vertical directions, were revealed in the shock system. Subsequently, the feasibility of considering the periodical deflection of the incoming flow induced by the significantly unequal amplitudes of shock movements at the two walls as the underlying mechanism for the flapping mode is explored.

This paper presents a new technique for norm-convergent dynamic mode decomposition of deterministic systems. The developed method utilizes recent results on singular dynamic mode decomposition where it is shown that by appropriate selection of domain and range Hilbert spaces, the Liouville operator (also known as the Koopman generator) can be made to be compact. In this paper, it is shown that by selecting appropriate collections of finite basis functions in the domain and the range, a novel finite-rank representation of the Liouville operator may be obtained. It is also shown that the model resulting from dynamic mode decomposition of the finite-rank representation is closely related to regularized regression using the so-called occupation kernels as basis functions.

Numerical investigations of the flow around a wall-mounted square structure have been carried out by using three-dimensional Spalart-Allmaras Delayed Detached Eddy Simulations (SADDES). The Reynolds number based on the free-stream velocity and the height of the structure is 1.19×105. The instantaneous hydrodynamic quantities are analyzed. The time-averaged results of the velocities, the Reynolds-averaged statistics and the vortical structures are presented and discussed. Dynamic Mode Decomposition (DMD) is applied to study the flow in the wake region behind the square structure. The dynamically important modes are extracted by further using a sparsity-promoted algorithm. The temporal information of the modes is compared with the results of the frequency analysis. The reduced order model of the flow field is constructed by the modes and shows good agreement with the numerical simulation results.