Fluid Mechanical Systems Research Articles

Lagrangian gradient regression for the detection of coherent structures from sparse trajectory data.

Complex flows are often characterized using the theory of Lagrangian coherent structures (LCS), which leverages the motion of flow-embedded tracers to highlight features of interest. LCS are commonly employed to study fluid mechanical systems where flow tracers are readily observed, but they are broadly applicable to dynamical systems in general. A prevailing class of LCS analyses depends on reliable computation of flow gradients. The finite-time Lyapunov exponent (FTLE), for example, is derived from the Jacobian of the flow map, and the Lagrangian-averaged vorticity deviation (LAVD) relies on velocity gradients. Observational tracer data, however, are typically sparse (e.g. drifters in the ocean), making accurate computation of gradients difficult. While a variety of methods have been developed to address tracer sparsity, they do not provide the same information about the flow as gradient-based approaches. This work proposes a purely Lagrangian method, based on the data-driven machinery of regression, for computing instantaneous and finite-time flow gradients from sparse trajectories. The tool is demonstrated on a common analytical benchmark to provide intuition and demonstrate performance. The method is seen to effectively estimate gradients using data with sparsity representative of observable systems.

Fluid Mechanics of Gas-Liquid Systems

The study of gas-liquid systems in fluid mechanics is essential for understanding multiphase flows, particularly in industries such as oil and gas field development. This research explores the key parameters that govern the behavior of such systems, including volume flow, velocity, area, dynamic viscosity, and diameter. Volume flow represents the quantity of fluid moving through a system per unit time, while velocity determines the rate at which the fluid particles travel. The cross-sectional area of the conduit directly influences the flow regime, and the dynamic viscosity defines the fluid's internal resistance to flow, significantly impacting pressure drops and flow patterns. The pipe diameter plays a critical role in determining flow characteristics such as Reynolds number and transition between laminar and turbulent flow. By analyzing these factors, this study provides insights into optimizing gas-liquid systems for improved performance and efficiency in industrial applications.

Extreme statistics and extreme events in dynamical models of turbulence.

We present a study of the intermittent properties of a shell model of turbulence with statistics of ∼10^{7} eddy turn over time, achieved thanks to an implementation on a large-scale parallel GPU factory. This allows us to quantify the inertial range anomalous scaling properties of the velocity fluctuations up to the 24th-order moment. Through a careful assessment of the statistical and systematic uncertainties, we show that none of the phenomenological and theoretical models previously proposed in the literature to predict the anomalous power-law exponents in the inertial range are in agreement with our high-precision numerical measurements. We find that at asymptotically high-order moments, the anomalous exponents tend toward a linear scaling, suggesting that extreme turbulent events are dominated by one leading singularity. We found that systematic corrections to scaling induced by the infrared and ultraviolet (viscous) cutoffs are the main limitations to precision for low-order moments, while high orders are mainly affected by the finite statistical samples.. The high-fidelity numerical results reported in this work offer an ideal benchmark for the development of future theoretical models of intermittency in dynamical systems for either extreme events (high-order moments) or typical fluctuations (low-order moments). For the latter, we show that we achieve a precision in the determination of the inertial range scaling exponents of the order of one part over ten thousand (fifth significant digit), which may be considered a record for out-of-equilibrium fluid-mechanics systems and models.

Physics-Informed Neural Networks for Solving High-Index Differential-Algebraic Equation Systems Based on Radau Methods

As is well known, differential algebraic equations (DAEs), which are able to describe dynamic changes and underlying constraints, have been widely applied in engineering fields such as fluid dynamics, multi-body dynamics, mechanical systems, and control theory. In practical physical modeling within these domains, the systems often generate high-index DAEs. Classical implicit numerical methods typically result in varying order reduction of numerical accuracy when solving high-index systems. Recently, the physics-informed neural networks (PINNs) have gained attention for solving DAE systems. However, it faces challenges like the inability to directly solve high-index systems, lower predictive accuracy, and weaker generalization capabilities. In this paper, we propose a PINN computational framework, combined Radau IIA numerical method with an improved fully connected neural network structure, to directly solve high-index DAEs. Furthermore, we employ a domain decomposition strategy to enhance solution accuracy. We conduct numerical experiments with two classical high-index systems as illustrative examples, investigating how different orders and time-step sizes of the Radau IIA method affect the accuracy of neural network solutions. For different time-step sizes, the experimental results indicate that utilizing a 5th-order Radau IIA method in the PINN achieves a high level of system accuracy and stability. Specifically, the absolute errors for all differential variables remain as low as 10−6, and the absolute errors for algebraic variables are maintained at 10−5. Therefore, our method exhibits excellent computational accuracy and strong generalization capabilities, providing a feasible approach for the high-precision solution of larger-scale DAEs with higher indices or challenging high-dimensional partial differential algebraic equation systems.

Universality of oscillatory instabilities in fluid mechanical systems

Oscillatory instability emerges amidst turbulent states in experiments in various turbulent fluid and thermo-fluid systems such as aero-acoustic, thermoacoustic and aeroelastic systems. For the time series of the relevant dynamic variable at the onset of the oscillatory instability, universal scaling behaviors have been discovered in experiments via the Hurst exponent and certain spectral measures. By means of a center manifold reduction, the spatiotemporal dynamics of these real systems can be mapped to a complex Ginzburg–Landau equation with a linear global coupling. In this work, we show that this model is able to capture the universal behaviors of the route to oscillatory instability, elucidating it as a transition from defect to phase turbulence mediated by the global coupling.

Numerical Investigation of Fluid In 2D and 3D Lid-Driven Cavity at Different Reynolds Numbers

The lid-driven cavity is an important fluid mechanical system that serves as a benchmark for testing numerical methods and for studying fundamental aspects of incompressible flow in a confined volume. This paper is concerned with the numerical calculation of the LDC on the 2-D and 3-D model. The commercial software ANSYS Fluent was used for the simulation. In these models of the simulated cases, the lid moves in the x-direction. The 2-D solutions for the driven cavity are calculated for 10 ≤ Re ≤ 35,000 with a 501 × 501 and 601 × 601 grid. The driven 3-D cavity is calculated with a 75 × 75 × 75 grid. The steady flow inside the cavity consists of the velocity distributions at different Reynolds numbers. The present numerical results agree well with the literature analytical solutions.

매개변수를 도입한 축류형 송풍기 최적설계 및 데이터 분석 프로세스 구축

Axial fans are important rotating machines in various fluid mechanical systems. Recently, the requirements of axial fans have become more stringent due to the sophisticated demands of fluid mechanical systems. If the boundary dimensions of an axial fan were changed to satisfy a set of requirements, the entire fluid mechanical system would be redesigned and would likely be costly. Accordingly, the development of axial fans that fulfill requirements without any change to their boundary dimensions has increased. However, depending on the expertise of the engineer and through the process of trial and error, adequate designs were made that met target requirements. Therefore, in this study, an optimal design was performed for an axial fan with variable blades. To shorten the design time, the analysis software FanDAS and PIDO software PIAnO were connected to automate the analysis procedure, and the optimization technique was used to perform the optimal design and analyze the design problem. Total Efficiency was selected as the objective function, and 11 constraints related to total pressure, number of rotor/stator blades, variable blades, and solidity were applied. hub to tip ratio, rotor chord length, number of rotor blades, rotor setting angle, rotor camber angle, stator chord length, and number of stator blades were selected as design variables. In particular, in the case of setting angle and camber angle, parameters were introduced so that the value decreases from the Hub position to the Tip position. Optimization results revealed that the objective function was improved while satisfying all design constraints.

A Computational Investigation of the Lid-Driven Cavity Flow

The lid-driven cavity is an important fluid mechanical system that serves as a benchmark for testing numerical methods and for studying fundamental aspects of incompressible flows in confined volumes. These flows are driven by the tangential motion of a bounding wall. The lid-driven cavity serves as a benchmark for testing numerical methods and for studying fundamental aspects of incompressible flows in confined volumes. This article presents a complete study of lid-driven cavity flows, with the primary focus being placed on the development of the flow when the Reynolds number was increased. In order to fully comprehend the physics of flow, it is necessary to take into consideration not only pure two-dimensional flows but also flows that are periodic in one space direction and the whole three-dimensional flow.

The Brinkman-Fourier system with ideal gas equilibrium

<p style='text-indent:20px;'>In this work, we will introduce a general framework to derive the thermodynamics of a fluid mechanical system, which guarantees the consistence between the energetic variational approaches with the laws of thermodynamics. In particular, we will focus on the coupling between the thermal and mechanical forces. We follow the framework for a classical gas with ideal gas equilibrium and present the existences of weak solutions to this thermodynamic system coupled with the Brinkman-type equation to govern the velocity field.</p>

On the existence of positive solutions for a nonlinear elliptic class of equations in R2 and R3

We study the existence of positive solutions for an elliptic equation in RN for N = 2, 3 which is related with the existence of standing (localized) waves and the existence of the ground state solutions for some physical model or systems in fluid mechanics to describe the evolution of weakly nonlinear water waves. We use a variational approach and the well-known principle of concentration-compactness due to P. Lions to obtain the existence of this type of solutions, even in the case that the nonlinear term g is a non-homogeneous function or an operator defined in H1(RN) with values in R.

Ensemble machine learning predicts displacement of cantilevered fibers impacted by falling drops

In this study, we consider a simple system of water drops impacting cantilevered, circular fibers with velocity 1.0–2.4m∕s. The dynamics of the system are complicated because the motion of the drop and deflecting fiber at impact are highly coupled and the outcome is influenced by several continuous variables. The unpredictable dynamics of the system call for the use of computational tools that can reveal relationships between variables and make predictions about the physical outcomes for parameter values for which there is no experimental data. This study considers three fibers of contrasting properties, with hydrophilic and hydrophobic wetting conditions, exposed to a range of falling drop diameters and velocities. We predict maximal fiber deflection due to the impacting drop using an ensemble machine learning algorithm combining three base algorithms: a random forest regressor, a gradient boosting regressor, and a multi-layer perceptron. We train and test our algorithm with experimental datasets comprising 405 total trials using three different fibers and five input variables per fiber. The approach allows the determination of relative dominance of the input features in the prediction, reveals shortcomings of traditional scaling approaches for momentum transfer, and shows that drop momentum plays only a minor role in fiber deflection. Finally, our approach provides another example for the application of machine learning to characterize complex and coupled systems in fluid mechanics.

Universality in spectral condensation

Self-organization is the spontaneous formation of spatial, temporal, or spatiotemporal patterns in complex systems far from equilibrium. During such self-organization, energy distributed in a broadband of frequencies gets condensed into a dominant mode, analogous to a condensation phenomenon. We call this phenomenon spectral condensation and study its occurrence in fluid mechanical, optical and electronic systems. We define a set of spectral measures to quantify this condensation spanning several dynamical systems. Further, we uncover an inverse power law behaviour of spectral measures with the power corresponding to the dominant peak in the power spectrum in all the aforementioned systems.

What can bouncing oil droplets tell us about quantum mechanics?

A recent series of experiments have demonstrated that a classical fluid mechanical system, constituted by an oil droplet bouncing on a vibrating fluid surface, can be induced to display a number of behaviours previously considered to be distinctly quantum. To explain this correspondence it has been suggested that the fluid mechanical system provides a single-particle classical model of de Broglie’s idiosyncratic ‘double solution’ pilot wave theory of quantum mechanics. In this paper we assess the epistemic function of the bouncing oil droplet experiments in relation to quantum mechanics. We find that the bouncing oil droplets are best conceived as an analogue illustration of quantum phenomena, rather than an analogue simulation, and, furthermore, that their epistemic value should be understood in terms of how-possibly explanation, rather than confirmation. Analogue illustration, unlike analogue simulation, is not a form of ‘material surrogacy’, in which source empirical phenomena in a system of one kind can be understood as ‘standing in for’ target phenomena in a system of another kind. Rather, analogue illustration leverages a correspondence between certain empirical phenomena displayed by a source system and aspects of the ontology of a target system. On the one hand, this limits the potential inferential power of analogue illustrations, but, on the other, it widens their potential inferential scope. In particular, through analogue illustration we can learn, in the sense of gaining how-possibly understanding, about the putative ontology of a target system via an experiment. As such, the potential scientific value of these extraordinary experiments is undoubtedly a significant one.

Solitons in fluctuating hydrodynamics of diffusive processes.

We demonstrate that fluid mechanical systems arising from large fluctuations of one-dimensional statistical processes generically exhibit solitons and nonlinear waves. We derive the explicit form of these solutions and examine their properties for the specific cases of the Kipnis-Marchioro-Presutti model (KMP) and the symmetric exclusion process (SEP). We show that the two fluid systems are related by a nonlinear transformation but still have markedly different properties. In particular, the KMP fluid has a nontrivial sound wave spectrum exhibiting birefringence, whereas sound waves for the SEP fluid are essentially trivial. The appearance of sound waves and soliton configurations in the KMP model is related to the onset of instabilities.

Universality in the emergence of oscillatory instabilities in turbulent flows

Self-organization driven by feedback between subsystems is ubiquitous in turbulent fluid mechanical systems. This self-organization manifests as emergence of oscillatory instabilities and is often studied in different system-specific frameworks. We uncover the existence of a universal scaling behaviour during self-organization in turbulent flows leading to oscillatory instability. Our experiments show that the spectral amplitude of the dominant mode of oscillations scales with the Hurst exponent of a fluctuating state variable following an inverse power law relation. Interestingly, we observe the same power law behaviour with a constant exponent near –2 across various turbulent systems such as aeroacoustic, thermoacoustic and aeroelastic systems.

Analysis and classification of droplet characteristics from atomizers using multifractal analysis

Atomizers find applications in diverse fields such as agriculture, pharmaceutics and combustion. Among the most commonly found atomizer classes of designs are pressure swirl, airblast and ultrasonic atomizers. However, it has thus far not been possible to identify the class of an atomizer from spray characteristics. We perform multifractal detrended fluctuation analysis on the droplet inter-arrival times, diameters and axial velocities of pressure swirl, airblast and ultrasonic nebulizer sprays to quantify the differences in complexity in the respective signals. We show that the width of the multifractal spectrum of the signals of droplet diameters and the inter-arrival times, measured at the edge of the spray are robust atomizer identifiers. Further, we show the presence of correlations among the droplet diameters which are otherwise considered as random or derived from a log-normal distribution. This study can be further generalized to classify fluid mechanical systems or biological sprays using an appropriately chosen single point measurement in the flow field.

Matrix logarithmic wave equation and multi-channel systems in fluid mechanics

We formulate the mapping between a large class of nonlinear wave equations and flow equations for barotropic fluid with internal surface tension and capillary effects. Motivated by statistical mechanics and multi-channel physics arguments, we focus on wave equations with logarithmic nonlinearity, and further generalize them to matrix equations. We map the resulting equation to flow equations of multi-channel or multi-component Korteweg-type materials. For some special cases, we analytically derive Gaussian-type matrix solutions and study them in the context of fluid mechanics.

Real-Time Reservoir Balancing and Leak-Free Nonaqueous Cell Design for Flow Batteries

Benchtop-scale testing of redox flow batteries presents numerous operational challenges related to electrolyte imbalance, leakage, and chemical compatibility. Electrolyte imbalance creates a capacity-limiting reservoir and necessitates manual or automatic transfer of electrolyte between reservoirs to rebalance. Leakage of electrolyte in the cell, often at tubing connections or interfaces between the graphite plates, gaskets, and membrane, also reduces capacity and experimental repeatability. The testing of increasingly common nonaqueous electrolytes requires not only strict wetted material compatibility across a range of solvents but also greater resistance to leaks – the lower surface tensions of many organic solvents (vs. water) makes them more prone to leakage. The above issues are more easily dealt with in large-scale, permanent installations that do not have the benchtop-scale requirements of manual assembly/disassembly, modularity, and configurational simplicity. Additionally, benchtop flow batteries often use peristaltic pumps, a type of positive displacement pump which create large pressure and flowrate pulsations compared to the continuous output of centrifugal pumps commonly used in large scale systems. The use of individual peristaltic pumps for each side of the flow battery can create an electrolyte imbalance when an asymmetric pressure drop occurs across the cell, causing a Darcy flow of electrolyte through the membrane separator. Other aspects of the flow battery can exacerbate this imbalance, such as using porous separators which are more permissive to electrolyte crossover, or more viscous electrolytes which create higher pressure differentials in the hydraulic circuit at a given flowrate. A new pump control strategy for flow batteries is designed and implemented which controls the speed and flowrate of the pumps in real time in response to the reservoir levels, as shown in Figure 1. This control scheme maintains balanced electrolyte reservoirs by minimizing the average differential pressure across the membrane. Minimal pressure drops are achieved by effectively matching the pressures in each half-cell of the battery by adjusting each pump’s speed and flowrate independently, so that both pumps are operating at the same pressure on their respective fluid mechanical system curves. Additionally, a more leak-resistant cell gasket design shown in Figure 2 is developed, while maintaining chemical compatibility for nonaqueous systems. These two developments are employed in a long-term cycling experiment using a nonaqueous disproportionation electrolyte. Figure 1

Nonconservative hyperbolic systems in fluid mechanics

This paper is devoted to the numerical approximation of nonconservative hyperbolic systems. More precisely, we consider the bitemperature Euler system and we propose two methods of discretization. The first one is a kinetic approach based on an underlying kinetic model. The second one deals with a Suliciu approach when magnetic fields are taken into account.

No-Go Theorems Face Background-Based Theories for Quantum Mechanics

Recent experiments have shown that certain fluid-mechanical systems, namely oil droplets bouncing on oil films, can mimic a wide range of quantum phenomena, including double-slit interference, quantization of angular momentum and Zeeman splitting. Here I investigate what can be learned from these systems concerning no-go theorems as those of Bell and Kochen-Specker. In particular, a model for the Bell experiment is proposed that includes variables describing a 'background' field or medium. This field mimics the surface wave that accompanies the droplets in the fluid-mechanical experiments. It appears that quite generally such a model can violate the Bell inequality and reproduce the quantum statistics, even if it is based on local dynamics only. The reason is that measurement independence is not valid in such models. This opens the door for local 'background-based' theories, describing the interaction of particles and analyzers with a background field, to complete quantum mechanics. Experiments to test these ideas are also proposed.