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The problem of the geodynamo is simple to formulate (Why does the Earth possess a magnetic field?), yet it proves surprisingly hard to address. As with most geophysical flows, the fluid flow of molten iron in the Earth's core is strongly influenced by the Coriolis effect. Because the liquid is electrically conducting, it is also strongly influenced by the Lorentz force. The balance is unusual in that, whereas each of these effects considered separately tends to impede the flow, the magnetic field in the Earth's core relaxes the effect of the rapid rotation and allows the development of a large-scale flow in the core that in turn regenerates the field. This review covers some recent developments regarding the interplay between rotation and magnetic fields and how it affects the flow in the Earth's core.
Chemical gradients, the spatial variations in chemical concentrations and components, are omnipresent in environments ranging from biological and environmental systems to industrial processes. These thermodynamic forces often play a central role in driving transport processes taking place in such systems. This review focuses on diffusiophoresis, a phoretic transport phenomenon driven by chemical gradients. We begin by revisiting the fundamental physicochemical hydrodynamics governing the transport. Then we discuss diffusiophoresis arising in flow systems found in natural and artificial settings. By exploring various scenarios where chemical gradients are encountered and exploited, we aim to demonstrate the significance of diffusiophoresis and its state-of-the-art development in technological applications.
Raye Jean Montague (1935–2018) was a computer programmer and self-taught engineer who was at the forefront of modernizing naval architecture and naval engineering through the use of computer-aided design. In this biographical review, she is referred to as Montague, the surname she had for much of her professional life. Since she was a working engineer rather than a scholar, she did not create a publication record by which her achievements can be easily tracked, but her name appears in committee memberships, conference and working group proceedings, and other such interstices of computer-aided ship design. This key contributor to computer-aided design and manufacturing and to naval engineering is well worth getting to know.
The environmental setting of the Dead Sea combines several aspects whose interplay creates flow phenomena and transport processes that cannot be observed anywhere else on Earth. As a terminal lake with a rapidly declining surface level, the Dead Sea has a salinity that is close to saturation, so that the buoyancy-driven flows common in lakes are coupled to precipitation and dissolution, and large amounts of salt are being deposited year-round. The Dead Sea is the only hypersaline lake deep enough to form a thermohaline stratification during the summer, which gives rise to descending supersaturated dissolved-salt fingers that precipitate halite particles. In contrast, during the winter the entire supersaturated, well-mixed water column produces halite. The rapid lake level decline of O(1 m/year) exposes vast areas of newly formed beach every year, which exhibit deep incisions from streams. Taken together, these phenomena provide insight into the enigmatic salt giants observed in the Earth's geological record and offer lessons regarding the stability, erosion, and protection of arid coastlines under sea level change.
Thermoacoustic instability is a flow instability that arises due to a two-way coupling between acoustic waves and unsteady heat release rate. It can cause damaging, large-amplitude oscillations in the combustors of gas turbines, aeroengines, rocket engines, etc., and the transition to decarbonized fuels is likely to introduce new thermoacoustic instability problems. With a focus on practical thermoacoustic instability problems, especially in gas turbine combustors, this review presents the common types of combustor and burner geometry used. It discusses the relevant flow physics underpinning their acoustic and unsteady flame behaviors, including how these differ across combustor and burner types. Computational tools for predicting thermoacoustic instability can be categorized into direct computational approaches, in which a single flow simulation resolves all of the most important length scales and timescales, and coupled/hybrid approaches, which couple separate computational treatments for the acoustic waves and flame, exploiting the large disparity in length scales associated with these. Examples of successful computational prediction of thermoacoustic instability in realistic combustors are given, along with outlooks for future research in this area.
Many flows that are expected to be symmetric are actually observed to be asymmetric. The appearance of asymmetry in the face of no particular cause is a widespread although underappreciated occurrence. This rather puzzling and sometimes frustrating phenomenon can occur in wide-angle diffusers, over the forebody of axisymmetric bodies at high angles of attack, in the wake downstream of streamlined as well as bluff bodies, and in the flow over three-dimensional bumps and ramps. We review some notable examples and highlight the extreme sensitivity of many such flows to small disturbances in the body geometry or the incoming flow. Some flows appear to be permanently asymmetric, while others are bistable on timescales that are orders of magnitude longer than any convective timescale. Convective or global instabilities can occur, bistability is common, and mode interactions become important when multiple similar but distinct timescales and length scales are present. Our understanding of these phenomena is still very limited, and further research is urgently required; asymmetries in otherwise symmetric flows can have serious real-world consequences on vehicle control and performance.
Our understanding of respiratory flow phenomena has been consolidated over decades with the exploration of in vitro and in silico canonical models that underscore the multiscale fluid mechanics spanning the vast airway complex. In recent years, there has been growing recognition of the significant intersubject variability characterizing the human lung morphometry that modulates underlying canonical flows across subjects. Despite outstanding challenges in modeling and validation approaches, exemplified foremost in capturing chronic respiratory diseases, the field is swiftly moving toward hybrid in silico whole-lung simulations that combine various model classes to resolve airflow and aerosol transport spanning the entire respiratory tract over cumulative breathing cycles. In the years to come, the prospect of accessible, community-curated datasets, in conjunction with the use of machine learning tools, could pave the way for in silico population-based studies to uncover unrecognized trends at the population level and deliver new respiratory diagnostic and pulmonary drug delivery endpoints.
The merging of two fluid drops is one of the fundamental topological transitions occurring in free surface flow. Its description has many applications, for example, in the chemical industry (emulsions, sprays, etc.), in natural flows driving our climate, and for the sintering of materials. After the reconnection of two drops, strongly localized surface tension forces drive a singular flow, characterized by a connecting liquid bridge that grows according to scaling laws. We review theory, experiment, and simulation of the coalescence of two spherical drops for different parameters and in the presence of an outer fluid. We then generalize to other geometries, such as drops spreading on a substrate and in Hele–Shaw flow, and we discuss other types of mass transport, apart from viscous flow. Our focus is on times immediately after reconnection and on the limit of initially undeformed drops at rest relative to one another.
By imploding fuel of hydrogen isotopes, inertial confinement fusion (ICF) aims to create conditions that mimic those in the Sun's core. This is fluid dynamics in an extreme regime, with the ultimate goal of making nuclear fusion a viable clean energy source. The fuel must be reliably and symmetrically compressed to temperatures exceeding 100 million degrees Celsius. After the best part of a century of research, the foremost fusion milestone was reached in 2021, when ICF became the first technology to achieve an igniting fusion fuel (thermonuclear instability), and then in 2022 scientific energy breakeven was attained. A key trade-off of the ICF platform is that greater fuel compression leads to higher burn efficiency, but at the expense of amplified Rayleigh–Taylor and Richtmyer–Meshkov instabilities and kinetic-energy-wasting asymmetries. In extreme cases, these three-dimensional instabilities can completely break up the implosion. Even in the highest-yielding 2022 scientific breakeven experiment, high-atomic-number (high-Z) contaminants were unintentionally injected into the fuel. Here we review the pivotal role that fluid dynamics plays in the construction of a stable implosion and the decades of improved understanding and isolated experiments that have contributed to fusion ignition.
Publication date: 15 March 2025
Source: Computers & Fluids, Volume 289
Author(s): Weiheng Pan, Zhicong Kang, Liang Xie
Publication date: 15 March 2025
Source: Computers & Fluids, Volume 289
Author(s): Johannes Blühdorn, Pedro Gomes, Max Aehle, Nicolas R. Gauger
Publication date: 15 March 2025
Source: Computers & Fluids, Volume 289
Author(s): Goncalo Silva
Publication date: 15 March 2025
Source: Computers & Fluids, Volume 289
Author(s): Ashwani Punia, Rajendra K. Ray
Publication date: 15 March 2025
Source: Computers & Fluids, Volume 289
Author(s): Yuzhe Zhang, Qizhen Hong, Xiaoyong Wang, Chao Yang, Quanhua Sun
Publication date: 15 March 2025
Source: Computers & Fluids, Volume 289
Author(s): Pardeep Kumar, Benjamin Sanderse, Patricio I. Rosen Esquivel, R.A.W.M. Henkes
Publication date: Available online 19 December 2024
Source: Computers & Fluids
Author(s): Krishnan Swaminathan Gopalan, Arnaud Borner, Kelly A. Stephani
Publication date: 15 March 2025
Source: Computers & Fluids, Volume 289
Author(s): Atin Kumar Dolai, Vinod Pandey, Gautam Biswas, Suman Chakraborty
Publication date: 15 March 2025
Source: Computers & Fluids, Volume 289
Author(s): Ondřej Kincl, Ilya Peshkov, Walter Boscheri
Publication date: 15 March 2025
Source: Computers & Fluids, Volume 289
Author(s): Abdallah ElSherbiny, Sébastien Leclaire
UNet++ Networks: Utilized for predicting RANS solutions. Symbolic Distance Function (SDF): Used for geometry and flow condition representation. Parameterization: Based on UIUC airfoil data sets. Performance Evaluation: Assesses trained networks' accuracy in pressure and velocity predictions. Optimal Model: Achieves mean relative errors < 1.72% for unseen wing shapes and with a computational speedup factor of up to 1,000× in certain scenarios. Significance: Demonstrates deep learning's potential in aerodynamic design and optimization
This paper investigates the accuracy of U-Net++ networks in predicting Reynolds-Averaged Navier-Stokes (RANS) solutions. The study employs the symbolic distance function (SDF) to represent geometry and flow conditions, utilizing parameterized airfoil data from the UIUC (University of Illinois at Urbana-Champaign) airfoil datasets. The research assesses the performance of multiple trained neural networks in predicting pressure and velocity distributions. Specifically, the study examines the influence of varying network weights on solution accuracy. Through the optimization of the model, the research demonstrates that the mean relative error is below 1.72% for a range of previously unseen wing shapes, with a computational speedup factor of up to 1,000× in certain scenarios. The accuracy achieved by this model underscores the significant potential of deep learning-based approaches as reliable tools for aerodynamic design and optimization.
In situations where a wide range of flow scales are involved, the non-linear scheme should be capable of both shock capturing and low-dissipation. Most of the existing Weighted Compact Non-linear Schemes (WCNS) are too dissipative and incapable of achieving fourth-order for the two smooth stencils located on the same side of a discontinuity due to the weight deviations and the defect of the weighting strategy. In this paper, a novel filtered embedded WCNS is introduced for complex flow simulations involving both shock and small-scale structures. To overcome the above deficiency of existing WCNS, a pre-discrete mapping function is proposed to filter the weight deviation out and amend the inappropriate weights to ideal weights in smooth regions. Meanwhile, the embedded process is also implemented by this function, which is utilized to improve the resolution of shock capturing in certain discontinuity distributions. The pre-discrete mapping function is also extended to the WENO framework. The approximate-dispersion-relation analysis indicates that the scheme with the mapping function has lower dispersion and dissipation error than the WCNS-JS, WCNS-Z, and WCNS-T schemes. Numerical results show that WCNS with the new non-linear weights captures discontinuities sharply without obvious oscillation, has a higher resolution than other non-linear schemes, and has an obvious advantage in capturing small-scale structures.
We introduce a finite element (FE) method for computing the damping rate and frequency of an oscillating fluid with a free surface in the limit of small viscosity and high surface tension. The method is orders of magnitude (minutes compared to days) faster than CFD simulations that struggle to accurately predict meniscus damping in this regime. We reproduce the results of an analytical benchmark problem and demonstrate convergence of the FE method on examples with axisymmetric geometry.
The computation of damping rates of an oscillating fluid with a free surface in which viscosity is small and surface tension high is numerically challenging. A typical application requiring such computation is drop-on-demand (DoD) microfluidic devices that eject liquid metal droplets, where accurate knowledge of the damping rates for the least-damped oscillation modes following droplet ejection is paramount for assessing jetting stability at higher jetting frequencies, as ejection from a nonquiescent meniscus can result in deviations from nominal droplet properties. Computational fluid dynamics (CFD) simulations often struggle to accurately predict meniscus damping unless very fine discretizations are adopted, so calculations are slow and computationally expensive. The faster alternative we adopt here is to compute the damping rate directly from the eigenvalues of the linearized problem. The presence of a surface tension term in Stokes or sloshing problems requires approximation of the meniscus displacements as well, which introduces additional complexity in their numerical solution. In this paper, we consider the combined effects of viscosity and surface tension, approximate the meniscus displacements, and construct a finite element method to compute the fluid's oscillation modes. We prove that if the finite element spaces satisfy a typical inf-sup condition, and the space of the meniscus displacements is a subset of the set of normal traces of the space of velocities, then the method is free of spurious modes with zero or positive damping rates. To construct numerical examples, we implement the method with Taylor-Hood elements for the velocity and pressure fields, and with continuous piecewise quadratic elements for the displacement of the meniscus. We verify the numerical convergence of the method by reproducing the solution to an analytical benchmark problem and two more complex examples with axisymmetric geometry. Remarkably, the spatial shape and temporal evolution (angular frequency and damping rate) of the set of least-damped oscillation modes are obtained in a matter of minutes, compared to days for a CFD simulation. The method's ability to quickly generate accurate estimates of fluid oscillation damping rates makes it suitable for integration into design loops for prototyping microfluidic nozzles.
Direct numerical simulation and implicit large eddy simulation of shock train in a channel flow is performed using a high-order optimized TENO scheme. The DNS results are compared and are found to be better compared to those obtained using bandwidth-optimized WENO scheme. The TENO scheme is found to be suitable for performing implicit LES of this flow.
Direct numerical simulation (DNS) and implicit large-eddy simulation (LES) of turbulent channel flows with isothermal walls, with and without shock trains, are performed using a recently proposed high-order optimized targeted essentially non-oscillatory (TENO) scheme. Mean flow and turbulence statistics are presented and compared with those previously obtained from DNS using a bandwidth-optimized weighted essentially non-oscillatory (WENO) scheme with limiter. It is observed that the TENO scheme performs better than the WENO scheme in predicting the mean flow and Reynolds stresses in these flows. The optimized TENO scheme used here is found to be very suitable for performing implicit LES on a relatively coarse grid.
The suggested practical approach for time-varying inflow simulations is to obtain time-series wind data with a time interval of 1 min or less, and the linearly molded line would be critical; for larger time intervals, reasonable molded lines would be required. The required time series of inflow wind velocity could be collected on a varying curve of the moving averaged measured data.
Based on large eddy simulations, intermittent airflow within an urban street canyon was simulated. The practice of time-varying inflow conditions (TVIC) required a time series of inflow wind velocity, which could be collected on a varying curve of the moving averaged measured data. The influences of the time interval of the wind series and the varying trend (or molded line) between adjacent data on airflow within the street canyon were analyzed. The results showed that TVIC would result in larger average wind velocity and turbulence intensity than that simulated under steady inflow conditions (SIC). The simulated total vertical air exchanges under TVIC would be one order of magnitude higher than that simulated under SIC. Airflow characteristics within street canyons were influenced by the varying trends and the time intervals of the time-series inflow wind. Average vertical wind velocity and turbulent kinetic energy (TKE) simulated under the stepped varying trend was higher than that under the jagged varying trend. The shorter the time interval, the larger the TKE within the street canyon. Vertical air exchanges induced by turbulence (ACH′) at the roof level simulated under the stepped molded lines were twice that of the jagged molded line. Under the time interval of 30 s, the ACH′ was significantly increased, which was 2.558 times that simulated with a time interval of 1 min. Thus, the suggested practical approach for time-varying inflow simulations is to obtain time-series wind data with a time interval of 1 min or less, and the linearly molded line would be critical; for larger time intervals, reasonable molded lines would be required.
In this paper, Shallow Water Equations involving dry areas and a moving shoreline are solved using the Runge–Kutta Discontinuous Galerkin approach. Problems with dry areas are considered. Hence, three drying treatments based on Slope Modification, p-adaptation, extended Finite Element methods, and mesh adaptation are compared and tested with numerical and experimental benchmarks.
This work is devoted to the numerical simulation of Shallow Water Equations involving dry areas, a moving shoreline and in the context of mesh adaptation. The space and time discretization using the Runge–Kutta Discontinuous Galerkin approach is applied to nonlinear hyperbolic Shallow Water Equations. Problems with dry areas are challenging for such methods. To counter this issue, special treatment is applied around the shoreline. This work compares three treatments, one based on Slope Modification, one based on p-adaptation and the last one based on eXtended Finite Element methods and mesh adaptation.
We follow the proposition of the original AWENO Finite Difference (FD) scheme and construct the new AMDCD FD scheme, which can perform better both in dispersion and dissipation. Then, the proposed AMDCD FD scheme is further combined with the original AWENO FD scheme using a hybrid interpolation scheme to solve compressible flows with discontinuities. Various test problems of compressible flow manifest the accuracy, superior resolution, as well as the robustness of the resulting hybrid AWENO-AMDCD FD scheme in solving compressible flows with discontinuities.
Following the proposition of the original AWENO (Alternative Formulation of Weighted Essentially Non-Oscillatory) FD (Finite Difference) scheme, we construct the new AMDCD FD scheme, an Alternative formulation of the linear FD scheme with Minimized Dispersion and Controllable Dissipation, in this article. Spectral analysis shows that the proposed AMDCD FD scheme can be more efficient in resolving smooth solutions due to the flexibility in controlling dissipation. To efficiently solve compressible flows with discontinuities, we further combined the proposed AMDCD FD scheme with the original AWENO FD scheme using a hybrid interpolation scheme, in which the optimized linear MDCD (Minimized Dispersion and Controllable Dissipation) interpolation scheme would be switched to the nonlinear WENO (Weighted Essentially Non-Oscillatory) type interpolation scheme gradually as the flow structures are in transition from smooth region towards the vicinity of discontinuities. Therefore, the resulting hybrid AWENO-AMDCD FD scheme is suitable for solving compressible flows with broad-scale flow structures and/or shock waves. A series of one-, two-, and three-dimensional compressible flow problems are numerically tested to demonstrate the accuracy, superior resolution, as well as the robustness of the proposed hybrid AWENO-AMDCD FD scheme.
We develop a novel viscosity shuffling Lattice–Boltzmann method to enable the simulation of shear thinning viscoelastic fluids with high viscosity ratios.
The simulation of viscoelastic liquids using the Lattice–Boltzmann method (LBM) in full three dimensions remains a formidable numerical challenge. In particular the simulation of strongly shear-thinning fluids, where the ratio between the high-shear and low-shear viscosities is large, is often prevented by stability problems. Here we present a novel approach to overcome this issue. The central idea is to artificially increase the solvent viscosity which allows the method to benefit from the very good stability properties of the LBM. To compensate for this additional viscous stress, the polymer stress is reduced by the same amount. We apply this novel method to simulate two realistic cell carrier fluids, methyl cellulose and alginate solutions, of which the latter exhibits a viscosity ratio exceeding 10,000.
A robust and accurate discontinuous Galerkin method is developed for the nonequilibrium multi-material system on tetrahedral meshes. A robust limiting strategy that is crucial for calculations of complex multi-material interactions is presented. A consistency reinstating projection and a shock detector underpin this limiting strategy. Several problems with multi-material interface and shock interactions, like the shock-slug interaction shown here, demonstrate the robustness of the DG method.
A high-order discontinuous Galerkin (DG) method is presented for nonequilibrium multi-material (m≥2$$ m\ge 2 $$) flow with sharp interfaces. Material interfaces are reconstructed using the algebraic THINC approach, resulting in a sharp interface resolution. The system assumes stiff velocity relaxation and pressure nonequilibrium. The presented DG method uses Dubiner's orthogonal basis functions on tetrahedral elements. This results in a unique combination of sharp multimaterial interfaces and high-order accurate solutions in smooth single-material regions. A novel shock indicator based on the interface conservation condition is introduced to mark regions with discontinuities. Slope limiting techniques are applied only in these regions so that nonphysical oscillations are eliminated while maintaining high-order accuracy in smooth regions. A local projection is applied on the limited solution to ensure discrete closure law preservation. The effectiveness of this novel limiting strategy is demonstrated for complex three-dimensional multi-material problems, where robustness of the method is critical. The presented numerical problems demonstrate that more accurate and efficient multi-material solutions can be obtained by the DG method, as compared to second-order finite volume methods.
Publication date: 1 March 2025
Source: Journal of Computational Physics, Volume 524
Author(s): Xuehan Zhang, Lijian Jiang
Publication date: 1 March 2025
Source: Journal of Computational Physics, Volume 524
Author(s): Nathan Gaby, Xiaojing Ye
Publication date: 1 March 2025
Source: Journal of Computational Physics, Volume 524
Author(s): Wenxuan Xie, Zihan Wang, Junseok Kim, Xing Sun, Yibao Li
Publication date: 1 March 2025
Source: Journal of Computational Physics, Volume 524
Author(s): Qing Cheng, Qianqian Liu, Wenbin Chen, Jie Shen
Publication date: 1 March 2025
Source: Journal of Computational Physics, Volume 524
Author(s): Wenbin Zhang, Thomas Paula, Alexander Bußmann, Stefan Adami, Nikolaus A. Adams
Publication date: 1 March 2025
Source: Journal of Computational Physics, Volume 524
Author(s): Zhe Li
Publication date: 1 March 2025
Source: Journal of Computational Physics, Volume 524
Author(s): Fang Zhu, Keyue Sun, Guangtao Zhang, Junxiang Yang
Publication date: 1 March 2025
Source: Journal of Computational Physics, Volume 524
Author(s): Yijie Jin, Shu Liu, Hao Wu, Xiaojing Ye, Haomin Zhou
Publication date: 1 March 2025
Source: Journal of Computational Physics, Volume 524
Author(s): Jordi Poblador-Ibanez, Nicolás Valle, Bendiks Jan Boersma
Publication date: 1 March 2025
Source: Journal of Computational Physics, Volume 524
Author(s): N. Anders Petersson, Stefanie Günther, Seung Whan Chung
The spread of machine learning techniques coupled with the availability of high-quality experimental and numerical data has significantly advanced numerous applications in fluid mechanics. Notable among these are the development of data assimilation and closure models for unsteady and turbulent flows employing neural networks (NN). Despite their widespread use, these methods often suffer from overfitting and typically require extensive datasets, particularly when not incorporating physical constraints. This becomes compelling in the context of numerical simulations, where, given the high computational costs, it is crucial to establish learning procedures that are effective even with a limited dataset. Here, we tackle those limitations by developing NN models capable of generalizing over unseen data in low-data limit by: (i) incorporating invariances into the NN model using a Graph Neural Networks (GNNs) architecture; and (ii) devising an adaptive strategy for the selection of the data utilized in the learning process. GNNs are particularly well-suited for numerical simulations involving unstructured domain discretization and we demonstrate their use by interfacing them with a Finite Elements (FEM) solver for the supervised learning of Reynolds-averaged Navier–Stokes equations. We consider as a test-case the data-assimilation of meanflows past generic bluff bodies, at different Reynolds numbers \(50 \le Re \le 150\) , characterized by an unsteady dynamics. We show that the GNN models successfully predict the closure term; remarkably, these performances are achieved using a very limited dataset selected through an active learning process ensuring the generalization properties of the RANS closure term. The results suggest that GNN models trained through active learning procedures are a valid alternative to less flexible techniques such as convolutional NN.
Normal shock trains are a flow phenomenon of significance to ramjet engines, but it remains unclear what its structure is decided by and how it evolves with the incoming Mach number. To seek a theoretical explanation, the minimum entropy production principle is generalized to the quasi-steady behavior of normal shock trains in two-dimensional straight channels with uniform incoming flow. Numerical simulations are also performed to validate the model together with the data collected from public literature. The analysis suggests that the flow parameters of a normal shock train depend on the inviscid shock-shock interactions rather than the local boundary-layer separations, though the angles of two incident shocks should still be equal as similar to the case that complies with the free-interaction theory. The shock feet’s positions, meanwhile, are allowed to be coincident or not, free from the entropy restriction. This freedom of position explains why both symmetric and partially asymmetric normal shock trains could be found previously. Further theoretical calculations reveal the inclinations of two incident shocks increase first and then decrease with the incoming Mach number, peaking at 48.570 degrees when the Mach number reaches 1.753. It is also indicated that the Mach number range allowing for a normal shock train is 1.652 to 2.254, giving evidence for past observations.
A numerical approach is proposed for the study of instabilities in helical vortex systems as found in the near-wake of turbines or propellers. The methodology has a high degree of generality, yet the present paper focusses on the case of one unique helical vortex. First, a method based on helical symmetry aimed at computing a three-dimensional base flow with prescribed parameters—helical pitch, helical radius, vortex circulation, core size and inner jet component—is presented. Second, the linear instability of this base flow is examined by reducing the three-dimensional instability problem to two-dimensional simulations with wavenumbers prescribed along the helix axis. Each simulation converges towards an exponentially growing or decaying complex state from which eigenfunctions, growth rate and frequency are extracted. This procedure is validated against a standard method based on direct three-dimensional numerical simulations of the Navier–Stokes equations linearized in the vicinity of the same helical base flows. Three illustrative base flows are presented with or without inner jet component, the instability of which is dominated, at the prescribed axial wavenumber, by unstable modes of three different types: long-wave instability, short-wave elliptic and curvature instabilities. Results from the new procedure and from the fully three-dimensional one are found in excellent agreement, which validates the new methodology. The gain in computational time is typically the one that is achieved while going from three-dimensional to two-dimensional simulations.
This study presents new analytical solutions for the dynamics and dispersion of particles laden in two-dimensional Taylor–Green vortex flows. Explicit solutions are found for the temporal evolution of free and forced particles under the viscous decaying vortical flow for low Stokes numbers. When placed in the vicinity of the vortex structure, forced particles may either trap within or escape the vortex cell, for which an explicit criterion is proposed. Using the same methodology, the trajectories of charged particles in a vortex flow in the presence of a magnetic field are solved. All cases are compared to numerical simulations demonstrating the validity of the proposed theoretical solutions. The explicit analytical solutions derived here provide fundamental insights into the complex phenomena of particle-vortex interactions and may be used to predict and control particle dispersion in various engineering and natural systems .
The dynamic characteristics of mode behavior in a low-speed, single-stage axial compressor are crucial for studying linear stall inception. An input–output analysis framework has been established, enabling the introduction of forcing into the compressor system and identifying the most energetic mode. Both standard and compressed input–output analysis are conducted to explore sensitive forcing positions and flow variables, with opposition control employed to suppress energy gain. As throttling progresses, a shift in high energy gain distribution from high-order to first-order circumferential modes is observed, with two distinct branches emerging across the domain of circumferential mode numbers and forcing frequencies. Compressed input–output analysis shows that limiting the forcing range to the shroud, from the inlet to the rotor blade section, is sufficient to excite the energetic mode in the current cases. Subsequently, opposition control is applied at the shroud to suppress energy amplification and modulate stall propensity within these two distinct branches. The results reveal that axial velocity control reduces energy amplification and suppresses perturbation modes related to stall inception. A comprehensive assessment of componentwise energy amplification is conducted, considering various variable forcing. The predicted results indicate that velocity perturbations are the predominant factors influencing the resolvent mode distribution pattern. Moreover, opposition control significantly impacts the critical branch associated with stall inception.
Fully-convolutional neural networks (FCN) were proven to be effective for predicting the instantaneous state of a fully-developed turbulent flow at different wall-normal locations using quantities measured at the wall. In Guastoni et al. (J Fluid Mech 928:A27, 2021. https://doi.org/10.1017/jfm.2021.812), we focused on wall-shear-stress distributions as input, which are difficult to measure in experiments. In order to overcome this limitation, we introduce a model that can take as input the heat-flux field at the wall from a passive scalar. Four different Prandtl numbers \(Pr = \nu /\alpha = (1,2,4,6)\) are considered (where \(\nu \) is the kinematic viscosity and \(\alpha \) is the thermal diffusivity of the scalar quantity). A turbulent boundary layer is simulated since accurate heat-flux measurements can be performed in experimental settings: first we train the network on aptly-modified DNS data and then we fine-tune it on the experimental data. Finally, we test our network on experimental data sampled in a water tunnel. These predictions represent the first application of transfer learning on experimental data of neural networks trained on simulations. This paves the way for the implementation of a non-intrusive sensing approach for the flow in practical applications.
We study the pressure-driven steady gas flow, imposed by temperature or density gradients, over a backward-facing step in a two-dimensional microchannel. Focusing on the near-free-molecular regime of high Knudsen ( \(\textrm{Kn}\) ) numbers, the problem is analyzed asymptotically based on the Bhatnagar, Gross and Krook kinetic model, and supported by numerical Discrete Velocity Method and Direct Simulation Monte Carlo calculations. The wall conditions are formulated using the Maxwell model, superposing specular and diffuse surface conditions. The asymptotic solution contains the leading-order free-molecular description and a first-order integral representation of the near-free-molecular correction. Our results indicate that flow separation at the step can occur at arbitrarily large (yet finite) Knudsen numbers in channels with specular surfaces (i.e., having an accommodation coefficient of \(\alpha = 0\) ), driven by temperature differences between the inlet and outlet reservoirs. It is then shown that detachment is significantly suppressed by density variations between reservoirs and partially diffuse surfaces (with \(\alpha \gtrsim 0.3\) ). While the mass flow rate in a specular channel decreases with decreasing \(\mathrm {Kn\gg 1}\) in a density-driven setup (in line with the Knudsen Paradox), it increases in a temperature-driven flow. The results are obtained for arbitrary differences between the inlet and outlet reservoir equilibrium properties, and are rationalized using the linearized problem formulation.
A methodology to numerically assess wall-curvature effects in boundary layers is introduced. Wall curvature, which directly induces streamline curvature, is associated with several changes in boundary-layer flow. By necessity, a local radial pressure gradient emerges to balance mean flow turning. Moreover, a streamwise (wall-tangential) pressure gradient can appear for configurations with non-constant wall curvature or a particular freestream condition; zero pressure gradient is a special case. In laminar concave flow, the Görtler instability and the associated Taylor-Görtler vortices destabilize the flow and promote laminar-turbulent transition, whereas in the fully turbulent regime, unsteady coherent structures formed by the centrifugal instability mechanism dramatically redistribute turbulent shear stress. One difficulty of assessing centrifugal effects on boundary layers is that they often appear simultaneously with other phenomena, such as a streamwise pressure gradient, making their individual evaluation often ambiguous. For numerical studies of transitional and turbulent boundary layers, it is therefore beneficial to understand the interactive nature of such coupled effects for generic configurations. A methodology to do so is presented, and is verified using the case of a subsonic, compressible turbulent boundary layer. Four direct numerical simulations have been computed, forming a \(2{\times }2\) matrix of turbulent boundary-layer states; namely with and without concave wall curvature, each having a zero and a non-zero streamwise-pressure-gradient realization. The setup and accompanying procedures to determine appropriate boundary conditions are discussed, and the methodology is evaluated through analysis of the mean flow fields. Differences in mean flow properties such as wall shear stress and boundary-layer thickness due to either streamwise pressure gradient or wall curvature are shown to be remarkably independent of one another.
We investigate scenarios, where only sparse wall shear stress measurements are available, while accurate wall shear stress and velocity profiles are sought. Applying discrete adjoint-based data assimilation, with only near-wall measurements, accurate wall shear stress profiles are achieved at the expense of unrealistic velocity profiles. We therefore add and employ internal reference data generated by performing a relatively cheap hybrid simulation. We modified the dual-mesh hybrid LES/RANS framework recently proposed by Xiao and Jenny (J Comput Phys 231(4):1848–1865, 2012, https://doi.org/10.1016/j.jcp.2011.11.009) by loosely coupling under-resolved LES in the interior with steady RANS near the walls. The framework was developed in OpenFOAM and tested for flow over periodic hills with Re = 10,595. Results show that the devised framework outperforms conventional dual-mesh hybrid LES/RANS and standalone sparse wall-data assimilated RANS models. Graphical abstract Horizontal mean velocity component \(U_{1}\) (top plot) and wall shear stress (friction coefficient \(C_{f}\) ) profiles at the lower wall (bottom plot) obtained with S-RANS and assimilation of sparse wall shear stress data
Dynamics of a multiphase flow phenomenon involving water (at top), molten metal (at bottom), and vapor (between them), was numerically studied using volume of fluid method. Multiphase flow systems like this are present in a wide range of industrial applications and natural phenomena and are extensively investigated because of their potential to produce energy. This work pays special attention to the interface shape because of its influence on heat transfer rate. An approach, new for systems larger than drop scale, which consists in the construction of an interface shape diagram based on Reynolds (Re) and Bond (Bo) dimensionless numbers is proposed. The presented model demonstrated good capability to discern the governing forces such as viscous, inertial, and surface tension. The most favorable interface shapes for efficient premixing of phases involved were identified. The premixing significance lies in its determining role in steam explosion generation. Moreover, the effect of density ratio and triggering pressure is examined. In addition, Kelvin–Helmholtz and Rayleigh–Taylor fragmentation mechanisms were observed, and their preponderance was analyzed. The results obtained were validated with previous experimental data available in the literature finding good agreement. This proposal aims to provide useful information to enhance our understanding of this phenomenon from a fundamental perspective, applicable to further numerical and experimental studies in different research areas.
