Physics of Fluids

Physics of Fluids

Published by AIP Publishing

Online ISSN: 1089-7666

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Print ISSN: 1070-6631

Disciplines: Fluid dynamics; Fluides, Dynamique des; Fluids; Natuurkunde; Vloeistoffen

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Comprehensive information about publications and citations of PINNs. Top left: Citations about PINNs from 2019 to the present; top right: Publications of PINNs from 2019 to the present; bottom left: PINN publication volume by field in 2019 to date; and bottom right: PINN publication volume by affiliation in 2019 to date (cited in Web of Science).
Author co-citation network mapping in PINN research from 2019 to 2024.
Schematic diagram of the article structure hierarchy.
Schematic of the PINN model (as an example of solving the inverse problem of the 2-dimensional Navier–Stokes equation).
(a) Schematic of the data parallel approach and (b) schematic of the model parallel approach, cited in Ref. 59. Shukla et al., J. Comput. Phys. 447, 110683 (2021). Copyright 2021 Elsevier.

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A comprehensive review of advances in physics-informed neural networks and their applications in complex fluid dynamics

October 2024

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895 Reads

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5 Citations

Chi Zhao

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[...]

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Jianyong Yang
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Aims and scope


Physics of Fluids features intriguing original theoretical, computational, and experimental publications to deepen our understanding of the dynamics of gases, liquids, or complex fluids.

Recent articles


Water wave interaction with a submerged porous disc in a two-layer fluid
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February 2025

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44 Reads

Using linear water wave theory, we consider a three-dimensional problem concerning the interaction of waves with a submerged porous disk in a fluid containing two layers of finite depth bounded above and below by a free surface and a rigid surface, respectively. The porous disk is positioned in the upper layer. The solution is based on the domain decomposition method to avoid the complex dispersion equation that often arises while studying porous structures, making it easier for numerical implementation. The velocity potentials are determined by the matched eigenfunction expansion method. The velocity potentials in those regions that contain the porous disk as a boundary have been decomposed into several components. Each component of the velocity potential is then expressed in terms of the eigenfunctions. Matching conditions and the orthogonal properties of eigenfunction assist in determining the velocity potential. The wave-induced forces and the amplitude of the propagating waves have been numerically analyzed. The variation in the wave-induced forces and amplitude of the waves above and below the disk, for different depths of submergence of the disk, density ratio of the fluid, and porous effect parameter of the disk has been analyzed. Sudden amplification and reduction of forces have been observed at certain frequencies. The numerical results show that, for low frequencies, the presence of an interface has a significant effect on the hydrodynamic coefficients. The results provide important insights for applications in offshore engineering, coastal protection, and environmental modeling, specifically in situations where porous materials interact with waves in multi-layered fluid systems.


Artificial neural network analysis of irreversibility in electroosmotic flow of Prandtl–Eyring fluid through an inclined peristaltic channel with ciliated walls

February 2025

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18 Reads

This study investigates the artificial neural network (ANN) analysis of electroosmotically driven flow of a Prandtl–Eyring fluid through a peristaltic inclined channel with ciliated walls, influenced by non-Darcy porous medium and motile microorganisms. The governing nonlinear partial differential equations are reduced into set of ordinary differential equations (ODEs) using lubrication approximations and Debye–Hückel transformations with suitable dimensionless variables. These ODEs are addressed analytically using the homotopy perturbation method, which linearizes them into subproblems and assumes a perturbed series solution for velocity, temperature, concentration, and bioconvection. The symbolic solutions for these subproblems are derived in the MATLAB environment using the dsolve command. Subsequently, expressions for concentration, velocity, bioconvection, and temperature are plotted as function of various parameters, including the Prandtl number, non-Newtonian fluid parameter, and magnetic parameter, to evaluate their effects. Data from these profiles are extracted to construct the ANN model, which is trained in a Python environment using TensorFlow version 2.17.0. The model includes a starting layer, couple of hidden layers having 64 neurons each, and an output layer, utilizing the rectified linear unit activation mechanism and Adam optimization algorithm. The performance of our ANN model is monitored by mean square error, root mean square error, regression (R²), gradients, validation, and error histograms, which demonstrate the model's high accuracy in predicting thermal, velocity, concentration, and bioconvection profiles. The results indicate significant impacts of the non-Darcy porous medium, magnetic field, electroosmotic parameter, and nonlinear fluid parameter on the momentum profile. The potential applications of this study include the development of microfluidic devices for targeted drug transport in biomedical engineering and the optimization of pollutant transport in environmental engineering.


Scattering by a vortex of sound wave from a moving source

February 2025

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15 Reads

This study investigates the interaction between a moving monopole point source and a vortex, with a particular focus on the spatiotemporal and frequency characteristics of the sound field. High-precision numerical simulations are employed to obtain the sound field characteristics for different vortex Mach numbers and source wavelengths. As a stationary source, the vortex disrupts the symmetry of the sound field, creating stable beam structures, with the root mean square of the scattered pressure proportional to the vortex Mach number. However, when the source is in motion, the distribution of these beams evolves over time, with noticeable bending due to interference effects as the source passes through the vortex. Both the source wavelength and the vortex Mach number significantly affect the intensity of the scattered sound, with shorter wavelengths and higher Mach numbers leading to a stronger scattered field. Moreover, the time evolution of the scattered sound can be divided into three stages: short-wave, transitional, and long-wave stages, based on observed changes in frequency and directivity. Wavelet transforms are used to analyze the time–frequency characteristics of the scattered sound pressure signals at various observation points. The frequency components of the scattered pressure exhibit a distinct shift over time and display different features at various observation locations. Finally, the instantaneous scattered sound power follows a characteristic trend of increasing and then decreasing, with the peak occurring just before the source passes through the vortex.


Effect of ventilation on supercavitation dynamics and hydroacoustic characteristics: A numerical comparison with unventilated conditions

This numerical study examines the hydrodynamic and hydroacoustic behavior of an underwater vehicle under supercavitating conditions, both with and without ventilation. A body measuring 2100 mm in length and 128 mm in diameter operates in a 2300 mm-long domain. A water inflow of 10 ms and gas injection of 0.3 kgs create ventilated supercavitation. Without ventilation, the drag coefficient is about 0.7, while strong vortices and flow separations generate intense, low-frequency noise. At 10 m and 90∘, the sound pressure level (SPL) peaks near 110 dB below 50 Hz. At 100 m, this attenuates to 60–80 dB. Ventilation reduces drag to ∼0.3, but increases low-frequency SPL at 10 m and 90∘ up to 135 dB ( 2–50 Hz). Ventilation also broadens the noise spectrum, with the SPL at 100 m still around 80–90 dB below 50 Hz, surpassing the unventilated case. At 1000 m, SPLs for both conditions drop to about 20–40 dB at high frequencies, demonstrating distance-related attenuation. Monopole sources dominate at low frequencies, with up to 110 dB near-field SPL in the unventilated case, while dipole sources significantly influence mid-frequency ranges ( 50–300 Hz). Under ventilation, the monopole remains strong at low frequencies (about 80–90 dB at 100 m), but dipole contributions weaken over distance. Overall, while ventilation reduces drag, it intensifies and broadens the acoustic field at near-field locations, underscoring the complex tradeoffs between drag reduction and noise emission. These findings highlight the importance of careful ventilation strategies to manage noise and performance.


The mass transfer function ΔxALP2t/2tDABP of a two- and three-dimensional inertial active particle (with zero translational noise) normalized by the translational diffusion coefficient of the inertialess ABP.
Inertial correction factors of a free ALP with different moments of inertia ( α=0.75J/MR2) in two and three dimensions: (a) βDDr/νr for the orientational persistence time ( τ̃D=βDτD) and effective diffusion coefficient ( DALP=βDDABP=βDDAOUP); (b) γ2Dr/νr and (c) γ3Dr/νr for the momentum relaxation time ( τ̃m=γDτm).
Time-independent statistical properties of a free active particle in two and three dimensions as a function of the reduced moment of inertia Dr/νr: (a) normalized mean square velocity VALP2D/V02 for α=0.3; (b) ratio of mean square velocities, V3ALP2/V2ALP2, of 3 and 2D ALP; (c) ratio of effective diffusion coefficients, D3ALP/D2ALP, of 3 and 2D ALP.
Active Brownian motion with inertia: The role of dimensionality

Evgeny A. Lisin

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Irina I. Lisina

The joint influence of rotational inertia and dimensionality on the translational motion of a free self-propelled (active) Brownian particle is studied. When the reduced moment of inertia is not large, the three-dimensional particle dynamics is statistically described by the equations for the two-dimensional case only with the doubled rotational diffusion coefficient. However, for large reduced moment of inertia, the three- and two-dimensional dynamics of the particle differ dramatically. It is shown that the time-dependent mean square particle displacement can be described by the active Ornstein–Uhlenbeck particle model, where the orientational persistence and momentum relaxation times are effectively corrected by the particle rotational inertia.


An experimental investigation of wind-induced snow drifting on low-rise flat roofs: A systematic analysis with or without snowfall

Wind-induced snow transport plays a key role in uneven snow drift on rooftops, yet the mechanisms driving this transport remain poorly understood. To investigate the mass transport of snow drifting on rooftops, this study systematically conducted a series of wind tunnel experiments using blowing snow on low-rise flat roofs. High-density silica particles were employed, and various test parameters, including snowfall, wind speed, roof span, and blowing duration, were varied. The results showed that the snow-depth shape on the central axis of a roof can be summarized and simplified into four typical patterns according to different test conditions. The average transport rate on a flat roof decreases exponentially with the duration of blowing snow. A greater wind speed will significantly increase the transport rate on the roof. The saturated mass transport rate can be described by a polynomial of the wind speed and particle threshold wind speed under no-snowfall conditions and can be expressed as the product of snowfall intensity and saturated length for snowfall conditions. When drifting snow is not saturated, the initial transport rate on a roof can be expressed as the product of the saturated transport rate and the power function of a roof span, and the power index value is 0.65 for a no-snowfall condition and 0.75 for a snowfall condition. For saturated length, since snowfall leads to an increase in particle mass flux in the saltation layer and a decrease in particle threshold wind speed, the saturated length with snowfall will be smaller than that without snowfall and will decrease with an increase in snowfall intensity. Finally, the snow distribution pattern and blowing snow transport model derived in this study can provide valuable insights for snow load design in practical engineering applications.


Kinetic energy correction factor model for elliptical engineering pipelines under laminar–turbulent transition flow

In the fields of oil and gas, aerospace, and marine engineering, elliptical pipes are utilized for optimizing space usage, reducing aerodynamic drag, and enhancing structural resilience against bending and torsional forces. Predicting and optimizing fluid dynamics within such configurations remains challenging due to complex velocity distributions impacting kinetic energy calculations. This study explores the interaction between the kinetic energy correction factor and velocity distribution in elliptical pipes by uniquely solving the Navier–Stokes equations in an elliptical coordinate system. We begin by deriving transformation relationships between elliptical and Cartesian coordinates and defining gradient and Laplacian operators to express fundamental fluid dynamics quantities such as velocity vectors and pressure distributions. After analyzing the steady-state Navier–Stokes equations, we establish a set of partial differential equations that describe fluid velocity and pressure. Employing the method of separation of variables and linearizing into an eigenvalue problem, we analytically solve these equations. To confirm the validity of our theoretical models, we utilize computational fluid dynamics with the Wray–Agarwal turbulence model, alongside physical experiments with Preston tubes, which corroborate the predicted velocity distributions in elliptical pipes. Comparative analysis with experimental data using the root mean square error (RMSE) and Bland–Altman methods demonstrates that RMSE values are less than 0.05 and all differences fall within the 95% confidence interval. This level of precision significantly improves the reliability of kinetic energy correction factor predictions and supports the design and study of fluid dynamics in elliptical pipes.


Review of smoothed particle hydrodynamics modeling of fluid flows in porous media with a focus on hydraulic, coastal, and ocean engineering applications

February 2025

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49 Reads

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Xiujia Su

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Ehsan Kazemi

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[...]

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Abbas Khayyer

A comprehensive review is conducted on the application of Lagrangian mesh-free methods for simulating flows in various types of porous media, ranging from fixed structures like coastal breakwaters to deformable and transportable media. Deformable porous media refer to soil structures that may deform under the influence of currents and waves, while transportable media involve processes such as sediment transport and scour around hydraulic, coastal, and ocean structures. This review addresses problem dimensionality, governing equations, domain discretization schemes, interaction mechanisms, and applications. The literature analysis reveals that while various numerical techniques have been employed to model the complex interaction between fluid and solid phases, not all methods are physically or mathematically justifiable. However, some approaches have significantly advanced the modeling process over the past two decades. Based on these findings, a modeling framework is proposed to guide the construction of mesh-free models for simulating flow interactions with natural or engineered porous structures. It highlights two effective approaches: (i) Three-dimensional (3D) pore-scale microscopic modeling of flow through large-sized solid particles using coupled smoothed particle hydrodynamics (SPH) and discrete element method (DEM), and (ii) two-dimensional (2D) macroscopic modeling of flow in small-sized porous media using the mixture theory and SPH. The framework highlights the mixture-theory-based methods as particularly effective for large-scale simulations and the advanced SPH-DEM coupling techniques that enable precise simulations of complex fluid–solid interactions. The framework serves as a guide for researchers developing mesh-free numerical models to simulate fluid flows in porous media for hydraulic, coastal, and ocean engineering applications.


Solitary bubbles rising in quiescent liquids: A critical assessment of experimental data and high-fidelity numerical simulations, and performance evaluation of selected prediction methods

February 2025

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22 Reads

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Mirco Magnini

Bubbles are ubiquitous in industrial applications and in the natural environment. The dynamics of solitary bubbles rising through quiescent liquids, in particular, underpins the physics of two-phase bubbly flows, which are commonplace in industrial, biological, and environmental flows. This review provides a critical assessment of experimental data and high-fidelity numerical simulations concerning the rise of solitary bubbles in quiescent liquids, and an evaluation of selected prediction methods for the rise velocity and the aspect ratio of the bubbles. The assessment of the experimental data is performed by way of a large and diversified bubble rise data bank collected from the literature (7192 data points from 58 literature studies), which is critically analyzed dedicating special attention to various aspects that have not been adequately addressed in previous investigations, including the methodologies employed to generate the bubbles, the techniques adopted to measure their size, shape, and rise velocity, the consequence of the liquid contamination on the bubble dynamics, wall-confinement effects, and the mass transfer between the bubble and the surrounding liquid. The assessment of the computational studies covers direct numerical simulations with interface capturing, interface tracking methods, and linear stability analyses, which are critically analyzed with specific focus on numerical methods, computational mesh, validation vs experimental data, and their main findings. The evaluation of the prediction methods is restricted to selected and widely quoted methodologies, three for the bubble rise velocity and four for the bubble aspect ratio, which have been proposed for final applications and whose performance is assessed against the measured data. The curated bubble rise data bank is provided in full and usable form. Research gaps and topics that necessitate further investigation are identified and discussed.


Comparison of multiple machine learning models for the regression of water hammer with column separation

You Fu

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Shanshan Zhang

This paper seeks to harness the potential of machine learning techniques to substantially enhance both the precision and efficacy of predicting water hammer phenomena, while simultaneously reducing time, safeguarding pipeline, and conserving resources. A novel mathematical model is proposed by integrating the two-fluid model and the interphase relaxation model with an improved Godunov–Harten–Lax–van Leer numerical method. The study conducts a comprehensive evaluation of the performance of four prominent machine learning algorithms—Back Propagation Neural Network (BP neural network), deep forest, Long Short-Term Memory (LSTM), and Extreme Gradient Boosting (XGBoost)—for the regression analysis of water hammer with column separation. In terms of predictive accuracy, the LSTM model achieves an impressive accuracy of 0.981 94. The BP neural network, deep forest, and XGBoost models yield accuracies of 0.975 01, 0.929 83, and 0.928 65, respectively. Regarding computational efficiency, XGBoost shows a clear advantage, with an overall average execution time of 4.13 s. Deep forest is distinguished by its simplicity in parameter configuration. This research provides valuable insights for selecting the optimal model for regression analysis of water hammer with column separation under a variety of conditions. Furthermore, the paper employs data visualization to directly generate visual trend representations of the overall pressure distribution, thereby eliminating the need for cumbersome numerical comparisons typical of traditional methods.


A sudden alteration in the self-propulsion of tandem flapping foils

February 2025

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11 Reads

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Tao Zhou

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Yusheng Liu

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Jie Wu

The self-propulsion of tandem flapping foils, which can self-propel identically and maintain a fixed gap distance, is numerically studied in this paper. It is found that there is a sudden alteration in the self-propulsion of tandem flapping foils, in which the speed of the tandem-foil system dramatically changes from the highest to the lowest. Moreover, the emergence of the sudden alteration is determined by the gap distance and phase difference between tandem foils. This can be described as the equivalent distance G. The critical points at which the sudden alteration occurs are located at G = (2N − 1)/2, where N = 1, 2, 3…. In the interval between two adjacent critical points, the propulsive speed, power consumption, and propulsive efficiency of the tandem-foil system increase monotonically with the rise of G. Additionally, compared with the isolated flapping foil, the tandem-foil system shows performance enhancement at every interval where G = 0.5. Furthermore, the mechanism behind the sudden alteration is analyzed, and it is found that this sudden alteration is associated with the potential landscape. Finally, the hydrodynamics of each foil are discussed in detail. The results obtained here may shed some light on understanding the performance of dual-flipper/wings in nature.


Innovative noise-cancellation strategies for fluid-immersed cylindrical structures using viscous rotational flow and porous functionally graded piezoelectric materials

February 2025

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24 Reads

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H. Zafari

This article presents a novel acoustic analysis of two coaxial cylindrical shells filled with fluid, explicitly considering the effect of fluid viscosity. This factor is crucial for sound-fluid–structure interactions, particularly in systems that experience detrimental vibrations. The cross-sectional architecture consists of a porous functionally graded piezoelectric (PFGP) coating and two coaxial isotropic cylinders separated by a compressible viscous fluid. The entire structure is completely submerged in a uniform inviscid fluid flow, such as water, and the internal acoustic environment is considered a resonant cavity. A power-law relation is employed to characterize the material properties of the PFGP coating in the thickness direction. The motion of viscous fluid substances is modeled with the three-dimensional (3D) Navier–Stokes equations. The governing equations of motion for each layer of the PFGP coating are derived using an orthotropic laminated model based on the exact linear theory of 3D piezoelasticity. In this regard, the classical state-space technique and the transfer matrix mathematical model are used to solve the problem. Guided wave propagation in elastic isotropic cylinders is adapted to Navier's wave equation, allowing for the inclusion of both longitudinal and torsional waves. Helmholtz decomposition is applied to solve these wave equations. To validate the proposed model, the results are compared with findings from other researchers. Overall, the results indicate that fluids with higher viscosity are more effective in reducing noise levels, and the structure oscillates at a lower speed due to enhanced energy dissipation within the rotational flow layer at the solid–fluid interface.


On one-dimensional surrogacy of probability density function of enstrophy in isotropic turbulence

Toshiyuki Gotoh

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P. K. Yeung

One-dimensional surrogates of fully three-dimensional (3D) quantities such as fluctuations of dissipation rate and enstrophy in turbulent flows have played an important role in many experimental and computational studies of intermittency. This paper addresses the connections between the probability density functions (PDFs) of the square of the magnitude of a fluctuating vector and that of a single Cartesian coordinate component under the condition of isotropy. A pair of rigorous relations between the PDFs of 3D enstrophy and its one-dimensional (1D) surrogate is derived mathematically. These relations are general, and independent of the functional form of the PDFs, degree of non-Gaussianity or the Reynolds number. The 1D surrogate is substantially more intermittent than its 3D counterpart. The functional forms of the respective PDFs are also examined using numerical simulation data, especially for regimes of very small and very large amplitudes. In the latter case, stretched exponential fits with different algebraic pre-factors but the same exponents at a given Reynolds number are found to agree very well with the data available.


Shape deformation of a gas bubble forced by a dual frequency time-dependent pressure field

February 2025

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6 Reads

Stephen J. Shaw

The nonlinear volume oscillations and shape deformation of a gas bubble in water driven by a spatially uniform, time-dependent dual frequency acoustic source is considered. Employing a model that includes shape mode interactions to third order, the respective, distinct frequency values of the driving pressure are chosen in order to parametrically excite two different axisymmetric shape modes via the fundamental resonance. It is shown that the shape modes develop on different timescales with their relative growth rates controlling the resultant dynamics. For suitably chosen driving strengths, intermediate steady state shape oscillations are observed. In particular, for cases where the higher order shape mode grows fastest and subsequently saturates first, then steady state shape oscillations dominated by this mode are observed for a finite time. However, as the lower mode grows, the higher mode decays and if the lower mode saturates, the resultant steady state oscillations are dominated by the lower mode, indicating that this mode is a preferential oscillation state. For cases where the shape modes develop on similar timescales, the balance between the driving strengths results in either the lower mode growing unbounded or one of the shape modes suppressing the parametric growth of the other mode.


Time-domain analysis of oblique wave scattering by a forced floating elastic plate over porous bed

Dona Alex

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R. Ashok

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N. Balasubramani

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Harekrushna Behera

This study examines the interaction of waves with a floating elastic plate subjected to a time-harmonic delta function force, taking into account oblique wave incidence over a porous seabed. The boundary value problem is addressed using the eigenfunction matching technique, while Fourier transforms are employed to study the time-dependent deflection. Numerical results are analyzed to understand the influence of three different edge conditions (built-in, free, and simply supported), as well as the properties of the wave, plate, and porous bottom. The analysis shows that for larger angles of incidence region, full reflection occurs with zero transmission. For smaller angles of incidence, however, the frequency of zero reflection and full transmission increases as the porous bottom parameter is increased. Additionally, a free-edge condition results in reduced reflection and increased transmission. The time-dependent deflection of the free surface is significantly influenced by the porous parameter and the angle of incidence, whereas the time-dependent deflection of the plate is notably affected by the Young's modulus of the plate along with the other parameters.


Effect of sinusoidal injection velocity on miscible thermo-viscous fingering in a rectilinear Hele-Shaw cell

Syed Zahid

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Surfarazhussain S. Halkarni

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Pritiparna Das

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[...]

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Deepali Goyal

This study examines the impact of sinusoidal time-dependent injection velocities on miscible thermo-viscous fingering instabilities observed in enhanced oil recovery. Linear stability analysis (LSA) and nonlinear simulations (NLS) are used to investigate fingering dynamics, considering parameters such as thermal mobility ratio ( Rθ), solutal mobility ratio ( Rc), Lewis number (Le), and thermal-lag coefficient ( λ). The LSA employs a quasi-steady state approximation in a transformed self-similar coordinate system, while NLS uses a finite element solver. Two injection scenarios are explored: injection-extraction ( Γ=2) and extraction-injection ( Γ=−2), with fixed periodicity ( T=100). Results show that for unstable solutal and thermal fronts ( Rc>0,Rθ>0), increasing Le with fixed λ≠1 leads to more prominent mixing and interfacial length for Γ=2 compared to constant injection and Γ=−2. While for unstable solutal fronts ( Rc>0) and stable thermal fronts ( Rθ<0), increasing Le results in more prominent mixing and interfacial length for Γ=−2, except during early diffusion. Thus, when porous media are swept using cold fluid, increasing the Lewis number intensifies the level of flow instability for Γ=−2; whereas when hot fluid is used, the instability enhances for Γ=2. Furthermore, it is observed that the high thermal diffusion ( Le≫1) and enhanced thermal redistribution between solid and fluid phases ( λ≪1) effectively mitigate destabilizing effects associated with positive Rθ, reducing overall instability. Overall, in extraction-injection scenarios, the phenomenon of tip-splitting and coalescence is attenuated, and the channeling regime is observed.


Three-dimensional collapse analysis of deep-buried tunnels in weak surrounding rock considering longitudinal collapse width and flexible support

This study performed a comprehensive three-dimensional (3D) analysis on tunnel collapse by incorporating the effects of longitudinal collapse width and flexible support characteristics of tunnel linings. The nonlinear Hoek–Brown criterion was employed for collapse analysis, and an upper limit analysis was conducted on the transverse section of the collapse body. Furthermore, the impact of flexible support systems on longitudinal collapse width was considered to enhance the accuracy of collapse predictions in a tunnel design. Comparisons between numerical simulations and theoretical analyses were performed to verify the feasibility of the proposed analytical approach. The rigid support of the structure led to inevitable active support reactions, and the predicted size of the collapse body obtained through calculation was very conservative, with a significant margin of error compared to the actual size. The collapse zone at the vault gradually extended to the sidewall and interconnected with the broken zone at the sidewall when A was greater than 0.5 or B was less than 0.65. For tunnels with σci less than 5 MPa, supporting the vault with a combination of rock bolts and anchor cables could prevent its collapse. This study offers a theoretical basis for the design of deep tunnels in weak surrounding rocks.


Tailwind turbulence: A bound on the energy available from turbulence for transit, tested in Kraichnan's model

S. A. Bollt

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G. P. Bewley

We investigate the unconstrained minimum energy required for vehicles to move through turbulence. We restrict our study to vehicles that interact with their environment through thrust, weight, and drag forces, such as rotorcraft or submersibles. For such vehicles, theory predicts an optimum ratio between vehicle velocity and a characteristic velocity of the turbulence. The energy required for transit can be substantially smaller than what is required to move through quiescent fluid. We describe a simple picture for how a flight trajectory could preferentially put vehicles in tailwinds rather than headwinds, predicated on the organization of turbulence around vortices. This leads to an analytical parameter-free lower bound on the energy required to traverse a turbulent flow. We test this bound by computationally optimizing trajectories in Kraichnan's model of turbulence and find that the energy required by point-models of vehicles is slightly larger than but close to our bound. Finally, we predict the existence of an optimum level of turbulence for which power is minimized, so that turbulence can be both too strong and too weak to be useful. This work strengthens previous findings that environmental turbulence can always reduce energy use. Thus, favorable trajectories are available to maneuverable vehicles if they have sufficient knowledge of the flow and computational resources for path planning.


Simulation setup consisting of 800 surface molecules (hydroxylated alkanes) assembled into two self-assembled monolayers and solvated by 16 353 water molecules. Each surface molecule consists of an alkyl chain terminated by a modified hydroxyl group with its partial charges scaled by a factor α. Simulation box (black frame) is replicated in all three directions via periodic boundary conditions. The box length for the initial pressure of −30 MPa in the normal direction is Lz0=8 nm.
(a) Schematics of bubble cavitation on a surface. Bubble contact angle φ and water contact angle θ are related by φ=180°−θ. (b) Free energy G2D of a bubble on a surface with a contact angle of θ=97° as a function of the bubble base radius a from Eq. (8) for various negative pressures p. (c) Geometric factor h(θ)=G2D*/G3D* in Eq. (10).
(a) Time-dependent pressure (p, top) and simulation box size ( Lz, bottom) during a pressure ramp simulation with a pressure rate of ṗ=−5 MPa/ns for a system with a surface contact angle of θ=97°. The presented trajectory corresponds to the final 200 ps prior to cavitation, identified as a 50 % increase in Lz relative to its initial value Lz0=8 nm. We find a cavitation pressure of pcav*=−93.9 MPa. Vertical lines mark individual simulation segments at constant pressure. The inset shows consecutive snapshots of the cavitation event. (b) Cavitation configurations with Lz/Lz0=3/2 for different contact angles. We also present trajectory visualizations for θ=45° (upper left panel) and θ=135° (lower right panel). (c) Simulation results for (1/pcav*)2 vs ṗ for different contact angles. The lines are fits of Eq. (1) to the data, where κ2D is the only fitting parameter. (d) Results for κ2D (left scale) and the ratio ξ=κ2D/κ3D (right scale) as a function of contact angle θ. The solid black line is a fit of Eq. (S13) in the supplementary material, section S3. For θ<52°, the fit does not serve as a reliable extrapolation and is denoted as a broken line. Multimedia available online. 10.1063/5.0247610.1 10.1063/5.0247610.2
(a) Cavitation pressure pcav of a water-filled cubic container as a function of the contact angle θ of the defect-free inner walls, for a fixed waiting time of τ=1 s, computed by numerically inverting Eq. (3) for Ndef=0 (solid lines). Different colors represent different cube sizes L. Dotted lines show the 2D cavitation pressure according to Eq. (12), while dashed horizontal lines denote the 3D cavitation pressure based on Eq. (7). (b) Crossover contact angle θ*, where k2D=k3D, as a function of container size L for different waiting times τ, according to Eq. (13).
(a) Illustration of a cavitation bubble on a circular surface defect with radius Rdef and contact angle θdef on a flat surface of contact angle θ. (b) Cavitation pressure of a water-filled container with a single surface defect Ndef=1 as a function of Rdef for different θdef. Solid lines are obtained by numerically solving Eq. (3) for a waiting time of τ=1 s and a container size of L=1 cm (volume of 1 mL). Dotted lines show the limiting pressure for a large defect, given by Eq. (16), whereas the horizontal dashed line shows the bulk cavitation pressure Eq. (7). (c) Crossover defect radius Rdef* as a function of container size L for a fixed waiting time of τ=1 s from Eq. (17). (d) Simulation snapshots for box expansions of Lz/Lz0=3/2 after cavitation in systems with a surface contact angle of 97° and cylindrical hydrophobic pits, from pressure-ramp simulations at a rate of ṗ=−5 MPa/ns. The pits have radii of Rdef≈1 nm (upper panel) and 2 nm (lower panel). Multimedia available online. 10.1063/5.0247610.3 10.1063/5.0247610.4
Water cavitation results from the kinetic competition of bulk, surface, and surface-defect nucleation events

February 2025

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5 Reads

Water at negative pressures can remain in a metastable state for a surprisingly long time before it reaches equilibrium by cavitation, i.e., by the formation of vapor bubbles. The wide spread of experimentally measured cavitation pressures depending on water purity, surface contact angle, and surface quality implicates the relevance of water cavitation in bulk, at surfaces, and at surface defects for different systems. We formulate a kinetic model that includes all three different cavitation pathways and determine the nucleation attempt frequencies in bulk, at surfaces, and at defects from atomistic molecular dynamics simulations. Our model reveals that cavitation occurs in pure bulk water only for defect-free hydrophilic surfaces with wetting contact angles below 50° to 60° and at pressures of the order of −100 MPa, depending only slightly on system size and observation time. Cavitation on defect-free surfaces occurs only for higher contact angles, with the typical cavitation pressure rising to about −30 MPa for very hydrophobic surfaces. Nanoscopic hydrophobic surface defects act as very efficient cavitation nuclei and can dominate the cavitation kinetics in a macroscopic system. In fact, a nanoscopic defect that hosts a preexisting vapor bubble can raise the critical cavitation pressure much further. Our results explain the wide variation of experimentally observed cavitation pressures in synthetic and biological systems and highlight the importance of surface and defect mechanisms for the nucleation of metastable systems.


Morphodynamics of mobile dunes with downward seepage

February 2025

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40 Reads

The experimental study examines the flow dynamics and sediment transport behavior of mobile dune-shaped bedforms induced by downward seepage. The longitudinal velocities in the stream flow direction, Reynolds shear stresses (RSS), energy budget, and transitional probabilities of turbulence bursting events were analyzed without and with downward seepage. Application of downward seepage discharge significantly altered flow patterns, increasing streamwise velocities and magnitude of RSS on the gradually rising face and reducing them at the crest and trailing section of the bedform. Downward seepage intensifies turbulence dissipation and diffusion at the steep slip side of the dune due to enhanced circulation, which encourages scour hole formation. However, in the proximity of the bed at the initial region on the gradually rising bed surface and leeward sections of the mobile bed features, turbulent production surges substantially with seepage. With seepage, the anisotropy invariant map shows a shift in patterns of turbulence anisotropy from two-dimensional (2D) to one-dimensional at the initial and middle sections, while at the crest and leeward side sections, 2D anisotropy. Enhanced transition probabilities of outward interaction and sweep events at the initial sections on the gradually rising bed surface and leeward side intensify under seepage conditions, increasing vortex strength and promoting erosion and sediment mobilization under seepage conditions. Scour depth on the leeward side section of the dune intensifies over time both under no-seepage and seepage, with greater scour observed under seepage conditions. Sediment transport rates were also significantly higher under seepage than under no seepage conditions.


High-to-low flow dynamics learning with deep convolutional encoder–decoder networks for randomly packed pebble-bed geometry

February 2025

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10 Reads

David Lanade

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Yang Liu

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Yassin Hassan

Randomly packed pebble-bed reactors are integral components in various engineering applications, in nuclear reactors where they offer inherent safety advantages through the use of tristructural isotropic coated fuel particles embedded in a graphite matrix. Predicting coolant flow and heat transfer within these packed beds presents significant challenges due to the complex, non-uniform arrangement of pebbles, resulting in intricate flow patterns and thermal fields. High-fidelity simulations like large Eddy simulation (LES) provide detailed insight but are computationally expensive, necessitating efficient alternatives for practical applications. This study introduces a machine learning-based approach for high-to-low flow field learning using deep convolutional encoder–decoder networks applied to randomly packed pebble-bed geometry. An end-to-end field-to-field regression framework is employed, utilizing a fully convolutional encoder–decoder architecture with DenseNet feature extraction. The model is trained on velocity fields derived from both coarse and fine mesh simulations across multiple Reynolds numbers. The proposed method significantly reduces computational cost while maintaining high accuracy in predicting detailed velocity flow fields. The model's performance is validated across different Reynolds numbers and flow configurations, demonstrating a strong ability to capture dominant flow structures and localized turbulence, especially near pebble surfaces. The results confirm that this deep learning model can effectively upscale coarse mesh flow fields to high-resolution outputs, offering a promising solution for efficient and accurate simulation of packed bed reactors in thermal-hydraulic applications. Furthermore, the model's robustness is validated through tests on different pebble bed configurations, ensuring its generalizability and potential for real-world applications.


Anomalous stability behaviors in two-sided wavy collapsible channels

February 2025

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17 Reads

Stents have been extensively used to handle the severe stenosis of arteries. The properties of the stented arteries have not been carefully studied. This study investigates the dynamic behaviors of two-sided wavy collapsible channels conveying a pulsatile flow by using the immersed boundary-lattice Boltzmann method. A pulsatile flow representing heartbeats and a simplified wavy wall modeling the stent geometry are incorporated, along with two configurations: wall movement with and without a symmetric constraint. The fluid–structure interaction system is solved by a hybrid method of the immersed boundary-lattice Boltzmann and the generalized interpolation material point methods. Several key parameters are analyzed: Reynolds number (Re), non-dimensional frequency, external pressure, mass ratio of the wall, and the constraint of flexible walls. It is found that the chaotic paths of systems with and without the symmetric constraint are opposite within the ranges of the parameters considered here, which may be due to the energy input associated with the constraint. Specifically, for channels without the constraint, the flow goes from periodic to quasiperiodic and then chaotic when Re, and the pressure ratio decrease; while the system with the constraint experiences such changes when Re, and the pressure ratio increase. Moreover, increasing the frequency of the pulsatile flow shows a transition from quasiperiodic to chaotic behavior for both systems with and without constraint, which is due to the shift of the phase between the flow pressure and the wall movement from almost in phase for the quasiperiodic cases to anti phase for the chaotic cases. The results obtained in this work can be used to plan and evaluate the stent insertion. The two-dimensional simulation is considered due to its low computational cost and its ability to reveal the major mechanisms. It is beneficial to study the three-dimensional cases with contact models between the stent and the artery in the future.


Finger properties in bounded double diffusive finger convection

A. Rosenthal

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A. Tilgner

We analyze experimental data on double diffusive convection in an electrochemical cell in the finger regime. All fingers in the experiments are bounded on at least one end by a solid wall. The properties of these fingers are compared with those of fingers in other experiments which are surrounded by fluid on all sides. The compositional boundary layers are found to be thinner than the finger width. The finger thickness agrees well with half the wavelength of the fastest growing mode obtained in linear stability analysis. The ion transport through the boundary layers is reduced by two orders of magnitude compared with unbounded fingers. The overturning layers in staircases contribute negligibly to salinity mixing because of efficient transport between finger layers and convection rolls.


Schematic of a viscous fluid slab bounded by a rigid wall on the top ( y=−h) and by an unstable interface with a semi-infinite ideal fluid on the bottom ( y=0).
Growth rate given by the numerical solution of Eq. (26) (dash-dotted lines) and by the present model [Eq. (37)] (full lines) for three layer thicknesses ( α=100,2,1) and for (a) AT=1; (b) AT=0.5; and (c) AT=0.1.
Growth rate given by the numerical solution of Eq. (26) (dash-dotted lines) and by the Mikaelian's model [Eq. (36)] (full lines) for three layer thicknesses ( α=100,2,1) and for (a) AT=1; (b) AT=0.5; and (c) AT=0.1.
Growth rate given by the Mikaelian's numerical solution (circles and triangles) and model²¹ (dashed-cross and dashed-plus) and by the present model, Eq. (42) (full and dashed-dot lines) for two layer thicknesses ( α1=α2=4,2), and for (a) AT=0.9; (b) AT=0.5; and (c) AT=0.1.
The Rayleigh–Taylor instability in viscous fluids: The finite thickness effect revisited

February 2025

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5 Reads

A quasi-irrotational approximation is found for the problem of the Rayleigh–Taylor instability at the interface between a viscous fluid layer attached to a rigid wall and a semi-infinite ideal fluid. It takes into account the first order effects of the vorticity, and this turns out to be sufficient to produce a very accurate dispersion relation in a close and explicit analytical form. The resulting asymptotic growth rate reduces to the one obtained in the limit of pure irrotational flow for very thick layers, which is known to be accurate within a 10 %. For arbitrary thickness, the accuracy progressively improves for thinner layers retrieving the well-known exact results for very thin layers. For the more general case of two superposed layers of viscous fluids bounded, respectively, at the top and at the bottom by rigid walls, an interpolation formula is proposed for the dispersion relation on the basis of the problem symmetry, which, although it introduces a further approximation, still improves considerably the existing results.


Evaporation of aerosol droplets from contaminated cooling tower water

The evaporation dynamics of water-based aerosol droplets carrying pathogens, such as Legionella from cooling towers, is critical for assessing the risks of airborne transmission. Yet, the evaporation of contaminated aerosol droplets remains poorly understood and is often overlooked by current risk assessment models. Changes in water properties, such as viscosity and surface tension, induced by the presence of nonvolatile solids or contaminants, affect the evaporation time, the droplet nuclei size, and the time resolved size evolution. The effect of these parameters was experimentally and analytically studied. Surfactants lowering surface tension introduced non-linearity in droplet size evolution, extending evaporation time by up to 14% and halting it at high concentrations. Increased viscosity delayed evaporation onset without affecting nuclei size, which remained around 8–9 μm compared to 0.5 μm for reference water droplets. High concentration of solids, covering over 60% of the droplet surface, nearly doubled the evaporation time and increased nuclei size to 20 μm. Existing evaporation models do not fully account for temporal size changes and the variability in nuclei size due to solids concentration. Improving evaporation models and incorporating them into microbial contamination risk assessments are critical to develop effective mitigation strategies, such as using efficient drift eliminators for cooling towers.


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