arXiv subjects

Zengshun Chen

Publications and source records attributed to Zengshun Chen.

6 recordsLinked to original sources

arXiv2022

The Linear-Time-Invariance Notion of the Koopman Analysis-Part 2: Physical Interpretations of Invariant Koopman Modes and Phenomenological Revelations

This serial work presents a Linear-Time-Invariance (LTI) notion to the Koopman analysis, finding consistent and physically meaningful Koopman modes and addressing a long-standing problem of fluid-structure interactions: deterministically relating the fluid and structure. Part 1 (Li et al., 2022) developed the Koopman-LTI architecture and applied it to a pedagogical prism wake. By the systematic procedure, the LTI generated a sampling-independent Koopman linearization that captured all the recurring dynamics, finding six corresponding, orthogonal, and in-synch fluid excitation-structure response mechanisms. This Part 2 analyzes the six modal duplets' to underpin their physical interpretations, providing a phenomenological revelation of the subcritical prism wake. By the dynamical mode shape, results show that two mechanisms at St1=0.1242 and St5=0.0497 describe shear layer dynamics, the associated Bérnard-Kármán shedding, and turbulence production, which together overwhelm the upstream and crosswind walls by instigating a reattachment-type of response. The on-wind walls' dynamical similarity renders them a spectrally unified fluid-structure interface. Another four harmonic counterparts, namely the subharmonic at St7=0.0683, the second harmonic at St3=0.2422, and two ultra-harmonics at St7 =0.1739 and St13=0.1935, govern the downstream wall. The 2P wake mode is also observed as an embedded harmonic of the bluff-body wake. Finally, this work discovered the vortex breathing phenomenon, describing the constant energy exchange in wake's circulation-entrainment-deposition processes. With the Koopman-LTI, one may pinpoint the exact excitations responsible for a specific structural response, or vice versa.

physics.flu-dyn↗

arXiv2022

The Linear-Time-Invariance Notion of the Koopman Analysis-Part 1: The Architecture, Practical Rendering on the Prism Wake, and Fluid-Structure Association

This work proposes a Linear-Time-Invariance (LTI) notion to the Koopman analysis, finding an invariant subspace on which Koopman modes are consistent and physically meaningful. It also develops the Koopman-LTI architecture -- a systematic procedure to associate fluid excitation and structure surface pressure by matching Koopman eigen tuples, solving a longstanding problem for fluid-structure interactions. The architecture is data-driven and modular, accommodating all types of data and Koopman algorithms. Through a pedagogical demonstration on a prism wake and the rudimentary Dynamic Mode Decomposition algorithm, results show a near-exact linearization of nonlinear turbulence, with mean and rms errors of O-12 and O-9, respectively. The DMD also approximated the Koopman modes with O-8 error. The LTI reduced the subcritical prism wake during shear layer transition II into only six dominant excitation-response Koopman modal duplets. The upstream and crosswind walls constitute a dynamically unified interface dominated by only two mechanisms. The downstream wall remains a distinct interface and is dominated by four other mechanisms. The complete revelation of the prism wake essentially comes down to understanding the six mechanisms, which Part 2 (Li et al., 2022) will address by investigating the physical interpretations of the duplets' in-synch, phenomenological features. Finally, the current analysis also revealed w's trivial role in this convection-dominated free-shear flow, Reynolds stresses' spectral description of cascading eddies, vortices' sensitivity to dilation and indifference to distortion, and structure responses' origin in vortex activities.

physics.flu-dyn↗

arXiv2022

The Effects of Transverse Inclination on Aeroelastic Cantilever Prisms: Phenomenology, Unsteady Force, and the Base Intensification Phenomenon

The transverse inclination is a probable scenario when inclined structures experience an inflow of altered attack angles. This work investigates the effects of transverse inclination on an aeroelastic prism through forced-vibration wind tunnel experiments. The aerodynamic characteristics are tri-parametrically evaluated under different wind speeds, inclination angles, and oscillation amplitudes. Results show that transverse inclination fundamentally changes the wake phenomenology by impinging the fix-end horseshoe vortex and breaking the separation symmetry. The aftermath is a bi-polar, once-for-all change in the aerodynamics near the prism base. The suppression of the horseshoe vortex unleashes the Karman vortex, which significantly increases the unsteady crosswind force. After the initial morphology switch, the aerodynamics become independent of inclination angle and oscillation amplitude and depend solely on wind speed. The structure's upper portion does not feel the effect, so this phenomenon is called Base Intensification. The phenomenon only projects notable impacts on the low-speed and VIV regime and is indifferent in the high-speed, quasi-steady Galloping regime. In practice, Base Intensification will disrupt the pedestrian-level wind environment from the unleashed Bernard-Karman vortex shedding, making it erratic and gusty. Moreover, it increases the aerodynamic load at a structure base by as much as 4.3 times. Since fix-end stiffness prevents elastic dissipation, the load translates to massive stress, making detection trickier and failures, if they are to occur, more sudden, extreme, and without any warnings. The 4.3-time amplification also surpasses the safety factor of many standard designs, so transverse inclination deserves engineering attention.

physics.flu-dyn↗

arXiv2021

A Parametric and Feasibility Study for Data Sampling of the Dynamic Mode Decomposition: Spectral Insights and Further Explorations

This work continues the parametric investigation on the sampling nuances of the Dynamic Mode Decomposition (DMD) under the Koopman analysis. Through turbulent wakes, the investigation corroborated the generality of the universal convergence states for all DMD implementations. It discovered the implications of sampling range and resolution -- the determinants of the spectral discretisation by discrete frequency bins and the highest resolved frequency, respectively. The work reaffirmed the necessity of the Convergence state for sampling independence, too. Results also suggested that the observables derived from the same flow may contain dynamically distinct information, thus altering the DMD output. The static pressure and vortex identification criteria are optimal variables for characterising structural response and fluid excitation. The pressure, velocity magnitude, and turbulence kinetic energy fields also suffice for general applications, but the Reynolds stresses and velocity components shall be avoided. Mean-subtraction is recommended for best approximations of the Koopman eigen tuples. Furthermore, the parametric investigation on truncation discovered some low-energy states that dictate a system's temporal integrity. The best practice for order reduction is to avoid truncation and employ dominant mode selection on a full-state subspace, though large-degree truncation supports fair data reconstruction with low computational cost. Finally, this work demonstrated the synthetic noise resulting from pre-decomposition interpolation. In unavoidable interpolations to increase the spatial dimension n, high-order schemes are recommended for better retention of the original dynamics. Finally, the observations herein, derived from inhomogeneous anisotropic turbulence, offer constructive references for DMD on fluid systems, if not also others beyond fluid mechanics.

physics.flu-dyn↗

arXiv2021

Establishing Direct Phenomenological Connections between Fluid and Structure by the Koopman-Linearly-Time-Invariant Analysis

In this work, we introduce a novel data-driven formulation, the Koopman-Linearly-Time-Invariant (Koopman-LTI) analysis, for analyzing Fluid-Structure Interactions (FSI). An implementation of the Koopman-LTI on a subcritical free-shear flow over a prism at Re=22,000 corroborated a configuration-wise universal Koopman system, which approximated the configuration's nonlinear dynamics with stellar accuracy. The Koopman-LTI also successfully decomposed the entwined morphologies of raw measurement into a linear superposition of frequency-based constituents. Most importantly, with random and anisotropic turbulence, the Koopman-LTI yielded frequency-wise identical modes for structure response and fluid excitation, thus establishing direct constitutive relations between the phenomenology of fluid and structure.

physics.flu-dyn↗

arXiv2021

A Parametric and Feasibility Study for Data Sampling of the Dynamic Mode Decomposition--Range, Resolution, and Universal Convergence States

Scientific research and engineering practice often require the modeling and decomposition of nonlinear systems. The Dynamic Mode Decomposition (DMD) is a novel Koopman-based technique that effectively dissects high-dimensional nonlinear systems into periodically distinct constituents on reduced-order subspaces. As a novel mathematical hatchling, the DMD bears vast potentials yet an equal degree of unknown. This serial effort investigates the nuances of DMD sampling with an engineering-oriented emphasis. This Part I aimed at elucidating how sampling range and resolution affect the convergence of DMD modes. We employed the most classical nonlinear system in fluid mechanics as the test subject--the turbulent free-shear flow over a prism--for optimal pertinency. We numerically simulated the flow by the dynamic-stress Large-Eddies Simulation with Near-Wall Resolution. With the large-quantity, high-fidelity data, we parametrized and identified four global convergence states: Initialization, Transition, Stabilization, and Divergence with increasing sampling range. Results showed that the Stabilization is the optimal state for modal convergence, in which DMD output becomes independent of the sampling range. The Initialization state also yields sufficient accuracy for most system reconstruction tasks. Moreover, defying popular beliefs, over-sampling causes algorithmic instability: as the temporal dimension, n, approaches and transcends the spatial dimension, m (i.e., m < n), the output diverges and becomes meaningless. Additionally, the convergence of the sampling resolution depends on the mode-specific dynamics, such that the resolution of 15 frames per cycle for target activities is suggested for most engineering implementations. Finally, a bi-parametric study revealed that the convergence of the sampling range and resolution are mutually independent.

physics.flu-dyn↗