Dynamic Mode Decomposition Technique Research Articles

Numerical investigation of the effect of the non-uniform intake flow on the unsteady flow and the excitation of the pump in a water-jet propulsion

Abstract Water-jet propulsions are widely used in high-performance ships. This study conducts numerical study on the unsteady flow of a complete water-jet propulsion. The internal flow field of the propulsion pump under the conditions of no installation of the shaft sleeve (and installation of the shaft sleeve. Spectrum analysis is used to compare the time-varying external characteristic and excitation characteristic under different conditions. Then, Dynamic Mode Decomposition technique is used to extract the high energy flow structures and corresponding frequencies. The results indicated that a large-scale vortex roll up above the driving shaft under the condition of rotational shaft, a pair of anti-rotation vortices appear behind the driving shaft under the condition of stationary shaft. These shaft induced vortices develop into unstable flow structures in the impeller region which moves relative to the impeller blades at rotational frequency. They further affect the unsteady flow in the guide vane region. The shedding vortices induced by the rotor-stator interaction are strengthened, while the passage vortices are weakened. Moreover, the dominant frequency of the passage vortex has decreased from 1.68 times the rotational frequency to 1.50 times the rotational frequency.

Estimation of Carleman operator from a univariate time series.

Reconstructing a nonlinear dynamical system from empirical time series is a fundamental task in data-driven analysis. One of the main challenges is the existence of hidden variables; we only have records for some variables, and those for hidden variables are unavailable. In this work, the techniques for Carleman linearization, phase-space embedding, and dynamic mode decomposition are integrated to rebuild an optimal dynamical system from time series for one specific variable. Using the Takens theorem, the embedding dimension is determined, which is adopted as the dynamical system's dimension. The Carleman linearization is then used to transform this finite nonlinear system into an infinite linear system, which is further truncated into a finite linear system using the dynamic mode decomposition technique. We illustrate the performance of this integrated technique using data generated by the well-known Lorenz model, the Duffing oscillator, and empirical records of electrocardiogram, electroencephalogram, and measles outbreaks. The results show that this solution accurately estimates the operators of the nonlinear dynamical systems. This work provides a new data-driven method to estimate the Carleman operator of nonlinear dynamical systems.

A data-driven approach for rapid detection of aeroelastic modes from flutter flight test based on limited sensor measurements

Flutter flight test involves the evaluation of the airframe’s aeroelastic stability by applying artificial excitation on the aircraft lifting surfaces. The subsequent responses are captured and analyzed to extract the frequencies and damping characteristics of the system. However, noise contamination, turbulence, non-optimal excitation of modes, and sensor malfunction in one or more sensors make it time-consuming and corrupt the extraction process. In order to expedite the process of identifying and analyzing aeroelastic modes, this study implements a time-delay embedded Dynamic Mode Decomposition technique. This approach is complemented by Robust Principal Component Analysis methodology, and a sparsity promoting criterion which enables the automatic and optimal selection of sparse modes. The anonymized flutter flight test data, provided by the fifth author of this research paper, is utilized in this implementation. The methodology assumes no knowledge of the input excitation, only deals with the responses captured by accelerometer channels, and rapidly identifies the aeroelastic modes. By incorporating a compressed sensing algorithm, the methodology gains the ability to identify aeroelastic modes, even when the number of available sensors is limited. This augmentation greatly enhances the methodology’s robustness and effectiveness, making it an excellent choice for real-time implementation during flutter test campaigns.

On the aeroacoustic simulation and far-field noise modeling of a cylinder turbulent wake at the Reynolds number of 3900

The turbulent wake flows of circular cylinders have been under extensive study due to their strong fluctuating forces and noise levels, yet the relationship between them has rarely been examined. In this study, a high-fidelity numerical simulation is performed for a cylinder wake flow at the Reynolds number of 3900, aimed at far-field noise modeling based on the investigation of noise source characteristics. Despite irregular multi-scale turbulent wake eddies, the primary vortex shedding that resembles the Karman vortex shedding is observed, and the modes extracted by the dynamic mode decomposition technique at the primary shedding frequency and its higher harmonics appear as nearly two-dimensional spanwise structures. A non-permeable Ffowcs Williams and Hawkings (FW-H) approach is used to formulate the far-field noise spectra as the surface integral of unsteady flow samples on the cylinder surface and the volume integral of unsteady stress in the turbulent wake. The former can be modeled as the dipole sound of unsteady lift and drag, and the latter can be modeled as the tonal noise of discrete two-dimensional (i.e., spanwise-averaged) vortex modes. The results show that the vortex sound is extremely weak. Thus, the far-field noise can be modeled almost entirely by the aerodynamic forces, and the quantitative relationship between them is established by the convective FW-H solutions.

Coexistence of different mechanisms underlying the dynamics of supersonic turbulent flow over a compression ramp

Supersonic turbulent flow over a compression ramp is studied using wall-resolved large eddy simulation with a freestream Mach number of 2.95 and a Reynolds number [based on δ0: the thickness of incoming turbulent boundary layer (TBL)] of 63 560. The unsteady dynamics of the present shock wave/turbulent boundary layer interaction (STBLI) flow are investigated by using dynamic mode decomposition techniques, linear and nonlinear disambiguation optimization, local stability analysis (LSA), and global stability analysis (GSA). By analyzing the dynamic system for the STBLI flow, three dynamically important modes with characteristic spanwise wavelengths of 2δ0, 3δ0, and 6δ0 are captured. The 2δ0 mode approximates the spanwise scale of the Görtler-like vortices and Görtler mode of LSA, suggesting the presence of Görtler instability, which is believed to be related to the unsteady motion of streaks downstream of reattachment in the flow. The features of the 3δ0 mode are also observed in large-scale motions of the incoming TBL, implying the existence of a convective mechanism that is excited and maintained by such motions. Additionally, the GSA results show the most unstable mode features a spanwise wavelength of around 6δ0, indicating the existence of global instability that is believed to be related to the oscillating motion of separation shock. The coexistence of these three mechanisms is confirmed. Discussions on the above findings provide an interpretation for low-frequency unsteadiness that the unsteadiness of surface streaks results from the combined effects of the Görtler instability near flow reattachment and the convection of large-scale motions in the incoming boundary layer, while the low-frequency shock motion may be related to a global mode driven by upstream disturbances.

Experimental investigation of impact force variations during high-speed liquid impingement erosion

High-speed liquid impingement erosion occurs in many industrial settings. The erosion transition, which occurs after the incubation period of liquid impingement erosion, significantly changes the erosion behavior, such as the material erosion rate and surface roughness; however, when and how the transition occurs remains elusive. The study focused on the impact force exerted on a material by a liquid jet impact during the transition in high-speed liquid impingement erosion. To this end, the force acting on an aluminum specimen attached to a force sensor during liquid impingement erosion was examined experimentally. The critical condition, which indicates the beginning of the accumulation stage of erosion, was detected through mass-loss measurements and visual observation of the target material. The results demonstrated a distinctive transition in the impact force with respect to the exposed flow volume. Additionally, a dynamic mode decomposition technique was employed to analyze variations in the impact force. Finally, the mechanism underlying the long-term variation in the impact force was discussed, and the correlation between the impact forces and erosion depths during high-speed liquid impingement erosion was presented.

Stochastic Real-Time Second-Order Green's Function Theory for Neutral Excitations in Molecules and Nanostructures.

We present a real-time second-order Green's function (GF) method for computing excited states in molecules and nanostructures, with a computational scaling of O(Ne3), where Ne is the number of electrons. The cubic scaling is achieved by adopting the stochastic resolution of the identity to decouple the 4-index electron repulsion integrals. To improve the time propagation and the spectral resolution, we adopt the dynamic mode decomposition technique and assess the accuracy and efficiency of the combined approach for a chain of hydrogen dimer molecules of different lengths. We find that the stochastic implementation accurately reproduces the deterministic results for the electronic dynamics and excitation energies. Furthermore, we provide a detailed analysis of the statistical errors, bias, and long-time extrapolation. Overall, the approach offers an efficient route to investigate excited states in extended systems with open or closed boundary conditions.

Surrogate modeling of time-domain electromagnetic wave propagation via dynamic mode decomposition and radial basis function

This work introduces an ‘equation-free’ non-intrusive model order reduction (NIMOR) method for surrogate modeling of time-domain electromagnetic wave propagation. The nested proper orthogonal decomposition (POD) method, as a prior dimensionality reduction technique, is employed to extract the time- and parameter-independent reduced basis (RB) functions from a collection of high-fidelity (HF) solutions (or snapshots) on a properly chosen training parameter set. A dynamic mode decomposition (DMD) method, resulting in a further dimension reduction of the NIMOR method, is then used to predict the reduced-order coefficient vectors for future time instants on the previous training parameter set. The radial basis function (RBF) is employed for approximating the reduced-order coefficient vectors at a given untrained parameter in the future time instants, leading to the applicability of DMD method to parameterized problems. A main advantage of the proposed method is the use of a multi-step procedure consisting of the POD, DMD and RBF techniques to accurately and quickly recover field solutions from a few large-scale simulations. Numerical experiments for the scattering of a plane wave by a dielectric disk, by a multi-layer disk, and by a 3-D dielectric sphere nicely illustrate the performance of the NIMOR method.

Analysis of the dispersive Fourier transform dataset using dynamic mode decomposition: evidence of multiple vibrational modes and their interplay in a three-soliton molecule.

We demonstrate that the dynamic mode decomposition technique can effectively reduce the amount of noise in the dispersive Fourier transform dataset and allow for finer quantitative analysis of the experimental data. We therefore show that the oscillation pattern of a soliton molecule actually results from the interplay of several elementary vibration modes.

On erosion transition from the incubation stage to the accumulation stage in liquid impingement erosion

The evolution of surface profiles during erosion caused by the continuous impact of a liquid jet was studied using a water-jet apparatus. In this study, we focused on the erosion transition from the incubation stage to the accumulation stage during liquid impingement erosion, which is important for water-jet cleaning and aging management for nuclear power plants. By computing the local erosion rate distribution and surface roughness parameters, the formations of isolated pits and asperities were investigated. The structure of erosion caused by liquid impingement was extracted by using a dynamic mode decomposition technique. The surface profile changes were primarily caused by the formation of isolated pits and asperities during the incubation stage. The roughness parameters remained unchanged during the incubation stage, with barely measurable erosion depth, whereas the skewness of the surface profile began to increase during this stage. The initial erosion with a small-scale roughness gradually evolved into a large-scale crater. Dynamic mode decomposition analysis showed the presence of a short-wavelength (mode A) surface depression during the incubation stage, followed by a long-wavelength (mode B) erosion crater caused by the merging of mode A surface depressions during the accumulation stage.

Low-frequency unsteadiness of recompression shock structures in the diffuser of supersonic ejectors

Supersonic ejectors are passive gasdynamic devices that compress a low-pressure fluid by utilizing the kinetic energy of a high-pressure fluid in a variable area duct. The ejector consists of a primary supersonic nozzle in a mixing duct where the secondary flow is entrained and mixed. The mixed flow can undergo a series of recompression shocks resulting in a subsonic flow in the diverging portion to aid pressure recovery. Recompression shocks usually lead to unsteady shock boundary layer interactions. The performance of the ejector is influenced by shear layers, shock and expansion waves, and their mutual interactions. While existing literature has extensively dealt with mixing of the primary and secondary flows, the unsteadiness in flow resulting from recompression shocks has been seldom investigated. Fluctuations in pressure due to the unsteadiness of the shock often lead structural fatigue issues. This paper reports a detailed investigation on low-frequency unsteadiness of recompression shock using high-speed schlieren images and dynamic pressure measurements. Modal analyses using proper orthogonal decomposition and dynamic mode decomposition techniques are used to determine the dominant spatial modes and associated frequencies. Multimodal frequencies ranging between 80 and 300 Hz are observed. These findings are further corroborated by Fourier and wavelet transformations of the experimentally measured wall static pressure signals. Subsequently, scaling parameter is established for the dominant frequencies based on flow velocities upstream of the shock and the distance between two consecutive shocks. This results in a unique scaling frequency of 4.58% ± 18%, for the recompression shock independent of operating conditions.

Transonic Shock Buffet Flowfield Assessment Using Various Dynamic Mode Decomposition Techniques

Dynamic mode decomposition (DMD) is a powerful data-driven modal decomposition technique that extracts spatiotemporal coherent structures: a useful process in flow diagnostics and future state estimation of complex nonlinear flow phenomena. Transonic shock buffet is a complicated phenomenon, and modal decomposition techniques such as DMD provide significant insight into its complicated flow physics; but, often, flowfield data are corrupted because of various sources of noise due to the presence of outliers or the absence of critical data components. Therefore, noise corruption renders the modal decomposition inaccurate, and thereby not useful. In this paper, two sources of noise have been considered: simple white noise, and complex salt-and-pepper-type spurious noise. Various DMD techniques including standard DMD, forward–backward DMD, total-least-squares DMD, higher-order DMD, and robust DMD have been implemented. Their effectiveness and limitations in countering noise corruption have been investigated systematically. In the case of white noise corruption, forward–backward DMD, total-least-squares DMD, and higher-order DMD capture the buffet frequency and growth rate with sufficient accuracy, whereas the latter outperforms the other two when the noise variance level is above 5%. In the case of spurious noise, robust DMD handles noise corruption efficiently, with surprisingly high values of pixel corruption of up to 30%.

Strong effect of fluid rheology on electrokinetic instability and subsequent mixing phenomena in a microfluidic T-junction

When two fluids of different electrical conductivities are transported under the influence of an electric field, the electrokinetic instability (EKI) phenomenon often triggers in a microfluidic device once the electric field strength and conductivity gradient exceed some critical values. This study presents a detailed numerical investigation of how the rheological behavior of a fluid obeyed by the non-Newtonian power-law constitutive relation could influence this EKI phenomenon in a microfluidic T-junction. We find that as the fluid rheological behavior changes from shear-thickening (n >1) to shear-thinning (n <1), the EKI phenomenon is significantly influenced under the same conditions. In particular, the intensity of this EKI phenomenon is found to be significantly higher in shear-thinning fluids than in Newtonian and shear-thickening fluids. Also, the critical value of the applied electric field strength for the inception of this EKI phenomenon gradually increases as the fluid rheological behavior progressively moves from shear-thinning to shear-thickening. The corresponding mixing phenomenon, often achieved using this EKI phenomenon, is also notably higher in shear-thinning fluids compared to Newtonian and shear-thickening fluids. A detailed analysis of both the flow dynamics and mixing phenomena inside the microdevice is presented and discussed in this study. To perform so, we also employ the data-driven dynamic mode decomposition technique, considered one of the widely used reduced-order models to analyze a dynamical system. This analysis facilitates a better understanding of the EKI-induced chaotic convection and mixing phenomena inside the microdevice. We observe that the spatial expanse and intensity of the coherent flow structures differ significantly as the power-law index changes, thereby providing valuable insight into certain aspects of the underlying flow dynamics that, otherwise, are not apparent from other analyses.

Application of Hankel Dynamic Mode Decomposition for Wide Area Monitoring of Subsynchronous Resonance

In recent years, subsynchronous resonance (SSR) has frequently occurred in DFIG-connected series-compensated systems. For the analysis and prevention, it is of great importance to achieve wide area monitoring of the incident. This paper presents a Hankel dynamic mode decomposition (DMD) method to identify SSR parameters using synchrophasor data. The basic idea is to employ the DMD technique to explore the subspace of Hankel matrices constructed by synchrophasors. It is analytically demonstrated that the subspace of these Hankel matrices is a combination of fundamental and SSR modes. Therefore, the SSR parameters can be calculated once the modal parameter is extracted. Compared with the existing method, the presented work has better dynamic performances as it requires much less data. Thus, it is more suitable for practical cases in which the SSR characteristics are time-varying. The effectiveness and superiority of the proposed method have been verified by both simulations and field data.

Parametric dynamic mode decomposition for reduced order modeling

Dynamic Mode Decomposition (DMD) is a model-order reduction approach, whereby spatial modes of fixed temporal frequencies are extracted from numerical or experimental data sets. The DMD low-rank or reduced operator is typically obtained by singular value decomposition of the temporal data sets. For parameter-dependent models, as found in many multi-query applications such as uncertainty quantification or design optimization, the only parametric DMD technique developed was a stacked approach, with data sets at multiple parameter values were aggregated together, increasing the computational work needed to devise low-rank dynamical reduced-order models. In this paper, we present two novel approach to carry out parametric DMD: one based on the interpolation of the reduced-order DMD eigen-pair and the other based on the interpolation of the reduced DMD (Koopman) operator. Numerical results are presented for diffusion-dominated nonlinear dynamical problems, including a multiphysics radiative transfer example. All three parametric DMD approaches are compared.

Data-driven global stability of vertical planar liquid jets by dynamic mode decomposition on random perturbations

A data-driven approach to estimate the global spectrum of gravitational planar liquid jets (sheet or curtain flows) is presented in this work. The investigation is carried out by means of two-dimensional numerical simulations performed through the solver BASILISK, based on the one-fluid formulation and the volume-of-fluid approach. The dynamic mode decomposition technique is applied to extract the underlying linear operator, considering random perturbations of the base flow. The effectiveness of this procedure is first evaluated comparing results with those of a simplified one-dimensional curtain model in terms of spectrum and eigenfunctions. The methodology is then applied to a two-dimensional configuration obtaining the BiGlobal spectra for both supercritical (Weber number We > 1) and subcritical (We < 1) regimes. Results highlight that in supercritical regime, the spectrum presents three branches: the upper and lower ones exhibit a purely sinuous behavior with frequencies quite close to those predicted by the one-dimensional model; the middle branch presents a predominant varicose component, increasing with the frequency. The subcritical spectrum, instead, shows that the first two less stable eigenvalues, sorted by increasing frequency, exhibit, respectively, a sinuous and a varicose behavior, while their growth rate is almost the same. As expected, the subcritical regime does not reveal the slow branch. The effect of the density ratio, rρ, between the two phases is investigated, revealing that the flow system is unstable for rρ>0.05. Topological inspections of the leading modes in this unstable configuration show that the predominance of a varicose behavior is related to the rupture of the curtain.

Dynamic mode decomposition for subcriticality measurement using measured data at single location

Dynamic mode decomposition (DMD) is an effective approach for extracting a fundamental mode eigenvalue in subcriticality measurements. According to several previous studies, data for DMD must be obtained at a sufficient number of locations. However, the number of measurement locations is typically limited owing to experimental constraints. In this study, a time-shifting augmentation technique for DMD is employed, where an augmented data matrix is constructed by stacking multiple time-shifted copies of time-series data at a single location. The proposed DMD technique is applied to numerical simulations of subcriticality measurements, such as those involving the pulsed neutron method and Rossi-α method. The fundamental mode eigenvalues of these measurements are accurately extracted via DMD using the augmented data matrix for a single location without introducing the masking time technique.

A dynamic mode decomposition technique for the analysis of non–uniformly sampled flow data

A novel Dynamic Mode Decomposition (DMD) technique capable of handling non–uniformly sampled data is proposed. As it is usual in DMD analysis, a linear relationship between consecutive snapshots is made. The performance of the new method, which we term θ-DMD, is assessed on three different, increasingly complex datasets: a synthetic flow field, a ReD=60 flow around a cylinder cross section, and a Reτ=200 turbulent channel flow. For the three datasets considered, whenever the dataset is uniformly sampled, the θ-DMD method provides comparable results to the original DMD method. Additionally, the θ-DMD is still capable of recovering relevant flow features from non–uniformly sampled databases, whereas DMD cannot. The proposed tool opens the way to conduct DMD analyses for non–uniformly sampled data, and can be useful e.g., when confronted with experimental datasets with missing data, or when facing numerical datasets generated using adaptive time-integration schemes.

A Data-Driven Algorithm for Enabling Delay Tolerance in Resilient Microgrid Controls Using Dynamic Mode Decomposition

The increased implementation of smart grid technologies in the power distribution grid presents unique opportunities that enable resiliency, but also brings challenges motivating needs for novel solutions and mitigation techniques. The bi-directional power and data flow allow for the grid to operate with increased resiliency, which is the ability to avoid discontinuity of service to end-use loads during extreme events. However, in applications where control of the distribution grid or microgrid relies on communication networks, the degradation of communication systems in the form of loss or high latency can cause maloperation and result in loss of end-use loads. This paper presents a novel framework to enable delay tolerance of centralized microgrid control schemes to mitigate communication system latency impacts and guarantee successful control action. We demonstrate the delay tolerance on a control scheme that operates a battery energy storage system (BESS) to offset the sudden loss of generation and maintain system frequency. During periods of severely degraded communication system performance, the proposed delay-tolerant algorithm compensates for the latency by utilizing a data-driven model generated at the device level using dynamic mode decomposition (DMD) to determine the performance of the communications. The DMD technique predicts the system’s frequency using device-level terminal measurements and provides updated control signals. The HELICS cosimulation platform evaluates the cyber-physical interaction of the power system model in GridLAB-D, the centralized control agent in Python, and the discrete network model in NS-3. The framework is tested and validated on the IEEE-123 node system modified to represent a networked remote microgrid model, and the results show an improvement in the dynamic performance of the control scheme when subject to communication delays.

A fast method based on Dynamic Mode Decomposition for radiative heat transfer in participating media

The radiative transfer equation (RTE) is an integro-differential equation and solving it is time-consuming except in a few specific cases. A fast method based on dynamic mode decomposition (DMD) is introduced for solving the RTE in an absorbing-emitting and scattering medium. First, some parameters are considered as independent variables. The RTE is solved for different values of these parameters (known input vectors) using the discrete ordinates method (S6 approximation), and the system responses generate the snapshot matrix. Then using the DMD technique, the dynamic modes are constructed, so the degree of freedom of the system is decreased. The reduced-order model (ROM), called DMD-RBF, is generated by combining the DMD and the radial basis functions. Two cases, radiative equilibrium and medium with known temperature (isothermal and non-isothermal), are considered. The accuracy of the model is investigated using random input vectors. The results show that the DMD-RBF has a good agreement with the numerical solutions. Comparison between the ROM and numerical CPU times shows the high efficiency of the ROM. The results also show that the problem complexity does not affect the computational cost. For all cases, the CPU time of the ROM is of the order of 0.01 seconds.