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Large-scale circulation of the atmosphere in the Earth's extratropics is dominated by eddies, eastward (westerly) zonal winds, and their interaction. Eddies not only bring about weather variabilities but also help maintain the average state of climate. In recent years, our understanding of how large-scale eddies and mean flows interact in the extratropical atmosphere has advanced significantly due to new dynamical constraints on finite-amplitude eddies and the related eddy-free reference state. This article reviews the theoretical foundations for finite-amplitude Rossby wave activity and related concepts. Theory is then applied to atmospheric data to elucidate how angular momentum is redistributed by the generation, transmission, and dissipation of Rossby waves and to reveal how an anomalously large wave event such as atmospheric blocking may arise from regional eddy-mean flow interaction.
Stephen H. Davis (1939–2021) was an applied mathematician, fluid dynamicist, and materials scientist who lead the field in his contributions to interfacial dynamics, thermal convection, thin films, and solidification for over 50 years. Here, we briefly review his personal and professional life and some of his most significant contributions to the field.
Airtanker firefighting is the most spectacular tool used to fight wildland fires. However, it employs a rudimentary large-scale spraying technology operating at a high speed and a long distance from the target. This review gives an overview of the fluid dynamics processes that govern this practice, which are characterized by rich and varied physical phenomena. The liquid column penetration in the air, its large-scale fragmentation, and an intense surface atomization give shape to the rainfall produced by the airtanker and the deposition of the final product on the ground. The cloud dynamics is controlled by droplet breakup, evaporation, and wind dispersion. The process of liquid deposition onto the forest canopy is full of open questions of great interest for rainfall retention in vegetation. Of major importance, but still requiring investigation, is the role of the complex non-Newtonian viscoelastic and shear-thinning behavior of the retardant dropped to stop the fire propagation. The review describes the need for future research devoted to the subject.
This review highlights major developments and milestones during the early days of numerical simulation of turbulent flows and its use to increase our understanding of turbulence phenomena. The period covered starts with the first simulations of decaying homogeneous isotropic turbulence in 1971–1972 and ends about 25 years later. Some earlier history of the progress in weather prediction is included if relevant. Only direct simulation, in which all scales of turbulence are accounted for explicitly, and large-eddy simulation, in which the effect of the smaller scales is modeled, are discussed. The method by which all scales are modeled, Reynolds-averaged Navier–Stokes, is not covered.
Understanding and predicting turbulent flow phenomena remain a challenge for both theory and applications. The nonlinear and nonlocal character of small-scale turbulence can be comprehensively described in terms of the velocity gradients, which determine fundamental quantities like dissipation, enstrophy, and the small-scale topology of turbulence. The dynamical equation for the velocity gradient succinctly encapsulates the nonlinear physics of turbulence; it offers an intuitive description of a host of turbulence phenomena and enables establishing connections between turbulent dynamics, statistics, and flow structure. The consideration of filtered velocity gradients enriches this view to express the multiscale aspects of nonlinearity and flow structure in a formulation directly applicable to large-eddy simulations. Driven by theoretical advances together with growing computational and experimental capabilities, recent activities in this area have elucidated key aspects of turbulence physics and advanced modeling capabilities.
Rotating-disk flows were first considered by von Kármán in a seminal paper in 1921, where boundary layers in general were discussed and, in two of the nine sections, results for the laminar and turbulent boundary layers over a rotating disk were presented. It was not until in 1955 that flow visualization discovered the existence of stationary cross-flow vortices on the disk prior to the transition to turbulence. The rotating disk can be seen as a special case of rotating cones, and recent research has shown that broad cones behave similarly to disks, whereas sharp cones are susceptible to a different type of instability. Here, we provide a review of the major developments since von Kármán's work from 100 years ago, regarding instability, transition, and turbulence in the boundary layers, and we include some analysis not previously published.
Bubble plumes are ubiquitous in nature. Instances in the natural world include the release of methane and carbon dioxide from the seabed or the bottom of a lake and from a subsea oil well blowout. This review describes the dynamics of bubble plumes and their various spreading patterns in the surrounding environment. We explore how the motion of the plume is affected by the density stratification in the external environment, as well as by internal processes of dissolution of the bubbles and chemical reaction. We discuss several examples, such as natural disasters, global warming, and fishing techniques used by some whales and dolphins.
We review some fundamentals of turbulent drag reduction and the turbulent drag reduction techniques using streamwise traveling waves of blowing/suction from the wall and wall deformation. For both types of streamwise traveling wave controls, their significant drag reduction capabilities have been well confirmed by direct numerical simulation at relatively low Reynolds numbers. The drag reduction mechanisms by these streamwise traveling waves are considered to be the combination of direct effects due to pumping and indirect effects of the attenuation of velocity fluctuations due to reduced receptivity. Prediction of their drag reduction capabilities at higher Reynolds numbers and attempts at experimental validation are also intensively ongoing toward their practical implementation.
Ventilation is central to human civilization. Without it, the indoor environment rapidly becomes uncomfortable or dangerous, but too much ventilation can be expensive. We spend much of our time indoors, where we are exposed to pollutants and can be infected by airborne diseases. Ventilation removes pollution and bioaerosols from indoor sources but also brings in pollution from outdoors. To determine an appropriate level of ventilation and an appropriate way of providing it, one must understand that the needs for ventilation extend beyond simple thermal comfort; the quality of indoor air is at least as important. An effective ventilation system will remove unwanted contaminants, whether generated within the space by activities or by the simple act of breathing, and ensure that the ventilation system does not itself introduce or spread contaminants from elsewhere. This review explores how ventilation flows in buildings influence personal exposure to indoor pollutants and the spread of airborne diseases.
In the last ten years, advances in experimental techniques have enabled remarkable discoveries of how the dynamics of thin gas films can profoundly influence the behavior of liquid droplets. Drops impacting onto solids can skate on a film of air so that they bounce off solids. For drop–drop collisions, this effect, which prevents coalescence, has been long recognized. Notably, the precise physical mechanisms governing these phenomena have been a topic of intense debate, leading to a synergistic interplay of experimental, theoretical, and computational approaches. This review attempts to synthesize our knowledge of when and how drops bounce, with a focus on (a) the unconventional microscale and nanoscale physics required to predict transitions to/from merging and (b) the development of computational models. This naturally leads to the exploration of an array of other topics, such as the Leidenfrost effect and dynamic wetting, in which gas films also play a prominent role.
Publication date: Available online 25 May 2024
Source: Computers & Fluids
Author(s): Judith Angel, Jörn Behrens, Sebastian Götschel, Marten Hollm, Daniel Ruprecht, Robert Seifried
Publication date: Available online 25 May 2024
Source: Computers & Fluids
Author(s): Niccolò Tonicello, Andrea Lario, Gianluigi Rozza, Gianmarco Mengaldo
Publication date: Available online 26 May 2024
Source: Computers & Fluids
Author(s): J. Tieber, H. Steiner, P. Maurerlehner, S. Schoder, K. Schäfer, A. Ennemoser, M. Kaltenbacher, G. Brenn
Publication date: Available online 28 May 2024
Source: Computers & Fluids
Author(s): Junhong Jo, Wanho Lee, Do Wan Kim
Publication date: 15 June 2024
Source: Computers & Fluids, Volume 277
Author(s): Lianxia Li, Michael Stoellinger, Maysam Mousaviraad
Publication date: 15 June 2024
Source: Computers & Fluids, Volume 277
Author(s):
Publication date: Available online 23 May 2024
Source: Computers & Fluids
Author(s): Jaehee Chang, Kiyoung Kim, Haecheon Choi
Publication date: Available online 23 May 2024
Source: Computers & Fluids
Author(s): Shengsheng Xia, Yingjie Wei, Cong Wang
Publication date: Available online 21 May 2024
Source: Computers & Fluids
Author(s): Yong-Dong Liang, Xin-Yu Jiang, Zhi-Hui Li
Publication date: Available online 16 May 2024
Source: Computers & Fluids
Author(s): Anass Serhani, Victor Xing, Dorian Dupuy, Corentin Lapeyre, Gabriel Staffelbach
I propose a new framework of Lagrangian schemes to unify the SGH and CCH methods in one dimension. The scheme neither contains empirical parameters often contained in the SGH method nor solves Riemann problems frequently presented in the CCH method, which is a big difference from existing SGH/CCH methods and more general. The scheme is a new way to build the connection between SGH and CCH methods.
This paper focuses on a general computational framework to unify both Lagrangian staggered-grid hydrodynamic (SGH) and cell-centered hydrodynamic (CCH) methods. One challenge is that artificial viscosity has contained empirical parameters in the SGH method for seven decades. To address this challenge, a new relationship between pressure and velocity is constructed using specific volume as a medium. Another challenge is that entropy is increasing in isentropic flows for the CCH method. To overcome this second challenge, the forces acting on a target cell are split into linear and quadratic terms in the CCH method. The numerical results of the two methods are almost identical. The scheme is more general than both existing SGH and CCH methods.
A directionally-split volume-of-fluid (VOF) technique is proposed to study the evolution of interfaces under self-generated curvature-dependent velocity. A topological volume conservation penalty is incorporated in the geometric VOF methodology by altering the advection equation using variational principles. Parallel implementation of the approach is validated with canonical level set (LS) evolution problems involving interface motion in the normal direction. Constrained curvature flow of different geometries is demonstrated with emphasis on the required numerical components for an accurate and stable solution.
A directionally-split volume-of-fluid (VOF) methodology for evolving interfaces under curvature-dependent speed is devised. The interface is reconstructed geometrically and the volume fraction is advected with a technique to incorporate a topological volume conservation constraint. The proposed approach uses the idea that the role of curvature in a speed function V$$ \mathbf{V} $$ is analogous to the role of viscosity in the corresponding hyperbolic conservation law to propagate complex interfaces where singularities may exist. The approach has the advantage of simple implementation and straightforward extension to more complex multiphase systems by formulating the interface evolution problem using energy functionals to derive an expression for the interface-advecting velocity. The numerical details of the volume-of-fluid based formulation are discussed with emphasis on the importance of curvature estimation. Finally, canonical curves and surfaces traditionally investigated by the level set (LS) method are tested with the devised approach and the results are compared with existing work in LS.
Box method is a piecewise linear Petrov–Galerkin formulation on the Voronoi dual mesh of a Delaunay triangulation. Rhie–Chow interpolation is a technique widely adopted in finite volumes to stabilize the Stokes problem. This stabilization satisfies continuity, consistency, coercivity and inf-sup stability in a variational framework and the well posedness and the convergence of the Box method can be proved both theoretically and numerically.
The finite volume method (FVM) is widely adopted in many different applications because of its built-in conservation properties, its ability to deal with arbitrary mesh and its computational efficiency. In this work, we consider the Rhie–Chow stabilized Box method (RCBM) for the approximation of the Stokes problem. The Box method (BM) is a piecewise linear Petrov–Galerkin formulation on the Voronoi dual mesh of a Delaunay triangulation, whereas the Rhie–Chow (RC) stabilization is a well known stabilization technique for FVM. The first part of the article provides a variational formulation of the RC stabilization and discusses the validity of crucial properties relevant for the well-posedness and convergence of RCBM. Moreover, a numerical exploration of the convergence properties of the method on 2D and 3D test cases is presented. The last part of the article considers the theoretically justification of the well-posedness of RCBM and the experimentally observed convergence rates. This latter justification hinges upon suitable assumptions, whose validity is numerically explored.
A parallel grad-div stabilized finite element algorithm based on fully overlapping domain decomposition is proposed for the Navier–Stokes equations with damping. The algorithm calculates a local solution in a subdomain on a global composite mesh that is locally refined around the subdomain, making it simple to carry out on the basis of available sequential solvers. Effectiveness of the algorithm is verified by theoretical analysis and numerical experiments.
In this work, we propose a parallel grad-div stabilized finite element algorithm for the Navier–Stokes equations attached with a nonlinear damping term, using a fully overlapping domain decomposition approach. In the proposed algorithm, we calculate a local solution in a defined subdomain on a global composite mesh which is fine around the defined subdomain and coarse in other regions. The algorithm is simple to carry out on the basis of available sequential solvers. By a local a priori estimate of the finite element solution, we deduce error bounds of the approximations from our presented algorithm. We perform also some numerical experiments to verify the effectiveness of the proposed algorithm.
Large eddy simulation (LES) coupled with Lagrangian particle simulation (LPS) is performed for high-speed turbulent planar jets with a chemical reaction. The molecular diffusion is modeled by a mixing volume model for notional particles, which is extended for compressible reacting flows. The LES/LPS accurately predicts the progress of mixing and reaction in both subsonic and supersonic jets.
Large eddy simulation (LES) coupled with Lagrangian particle simulation (LPS) is applied to investigate high-speed turbulent reacting flows. Here, LES solves a velocity field while LPS solves scalar transport equations with notional particles. Although LPS does not require sub-grid scale models for chemical source terms, molecular diffusion has to be modeled by a so-called mixing model, for which a mixing volume model (MVM), that is originally proposed for an inert scalar in incompressible flow, is extended to reactive scalars in compressible flows. The extended model is based on a relaxation process toward the average of nearby notional particles and assumes a common mixing timescale for all species. LES/LPS with the MVM is applied to a temporally-evolving compressible turbulent planar jet with an isothermal reaction and is tested by comparing the results with direct numerical simulation (DNS). The results show that LES/LPS well predicts the statistics of mass fractions. As the jet Mach number increases, the reaction progress delays due to the delayed jet development. This Mach number dependence is also well reproduced in LES/LPS. The mean molecular diffusion term of the product calculated as a function of its mass fraction also agrees well between LES/LPS and DNS. An important parameter for the MVM is the distance among particles, for which the requirement for accurate prediction is presented for the present test case. LES/LPS with the MVM is expected to be a promising method for investigating compressible turbulent reactive flows at a moderate computational cost.
This study presents a stabilized PFEM formulation to simulate an incompressible fluid with free-surface flow. Comparisons results demonstrate the strong ability of the proposed stabilized PFEM to solve incompressible free-surface flow with high accuracy and promising application prospects.
In simulations using the particle finite element method (PFEM) with node-based strain smoothing technique (NS-PFEM) to simulate the incompressible flow, spatial and temporal instabilities have been identified as crucial problems. Accordingly, this study presents a stabilized NS-PFEM-FIC formulation to simulate an incompressible fluid with free-surface flow. In the proposed approach, (1) stabilization is achieved by implementing the gradient strain field in place of the constant strain field over the smoothing domains, handling spatial and temporal instabilities in direct nodal integration; (2) the finite increment calculus (FIC) stabilization terms are added using nodal integration, and a three-step fractional step method is adopted to update pressures and velocities; and (3) a novel slip boundary with the predictor–corrector algorithm is developed to deal with the interaction between the free-surface flow with rigid walls, avoiding the pressure concentration induced by standard no-slip condition. The proposed stabilized NS-PFEM-FIC is validated via several classical numerical cases (hydrostatic test, water jet impinging, water dam break, and water dam break on a rigid obstacle). Comparisons of all simulations to the experimental results and other numerical solutions reveal good agreement, demonstrating the strong ability of the proposed stabilized NS-PFEM-FIC to solve incompressible free-surface flow with high accuracy and promising application prospects.
This paper presents two new improved WENO schemes: WENO-MZ, which uses a mapping function to increase the ratio of less smooth sub-stencils to smooth ones; WENO-MD, which includes a modifier function. Both schemes demonstrate higher shock capture capabilities and better resolution than existing WENO schemes. In addition, they require less computational time than WENO-M and WENO-AIM. This has been confirmed by both theoretical and numerical experiments.
This paper presents a new WENO-Z scheme (WENO-MZ) that incorporates a mapping function to enhance the weights of the less smooth sub-stencils. The mapping function uses an innovative approach to modify the weight ratio of the less smooth sub-stencil to the smooth stencil. In addition, we present the WENO-MD scheme, which is a further development of the WENO-MZ scheme that incorporates a modifier function. The WENO-MD scheme shows improvements over the WENO-MZ scheme by achieving an improved optimal order at critical points in higher orders and by increasing the proportion of less smooth sub-stencils. Theoretical and numerical experiments have shown that the newly developed methods have improved shock capture capabilities and resolution compared to WENO-JS, WENO-Z, WENO-M, WENO-D, and WENO-AIM, and also lead to significant computational time savings compared to WENO-M and WENO-AIM.
We simulate aerosol transmission in an aircraft cabin and compare simulated particle counts with measurements. Simulations were done using MESHFREE, a meshfree Lagrangian method for computational fluid dynamics. Measurements were performed at the Fraunhofer Flight Test Facility.
We investigate the transmission of aerosol particles in an airplane cabin with a joint approach using experiments and simulation. Experiments were conducted in a realistic aircraft cabin with heated dummies acting as passengers. A Sheffield head with an aerosol generator was used to emulate an infected passenger and particle numbers were measured at different locations throughout the cabin to quantify the exposure of other passengers. The same setting was simulated with a computational fluid dynamics model consisting of a Lagrange continuous phase for capturing the air flow, coupled with a Lagrange suspended discrete phase to represent the aerosols. Virtual measurements were derived from the simulation and compared with the experiments. Our main results are: the experimental setup provides good measurements well suited for model validation, the simulation does correctly reproduce the fundamental mechanisms of aerosol dispersion and simulations can help to improve the understanding of aerosol transmission for example by visualizing particle distributions. Furthermore, with findings from the simulation it was possible to crucially improve the experimental setup, proving that feedback between the numerical and the hardware world is indeed beneficial.
Publication date: 1 August 2024
Source: Journal of Computational Physics, Volume 510
Author(s): Katherine Asztalos, René Steijl, Romit Maulik
Publication date: 1 August 2024
Source: Journal of Computational Physics, Volume 510
Author(s): Jianhua Xian, Ziqi Wang
Publication date: 1 August 2024
Source: Journal of Computational Physics, Volume 510
Author(s): Zhongqin Xue, Shuying Zhai, Xuan Zhao
Publication date: 1 August 2024
Source: Journal of Computational Physics, Volume 510
Author(s): Yigong Qin, Stephen DeWitt, Balasubramaniam Radhakrishnan, George Biros
Publication date: 1 August 2024
Source: Journal of Computational Physics, Volume 510
Author(s): Shuaihao Zhang, Sérgio D.N. Lourenço, Dong Wu, Chi Zhang, Xiangyu Hu
Publication date: 1 August 2024
Source: Journal of Computational Physics, Volume 510
Author(s): Mohammad Zandsalimy, Carl Ollivier-Gooch
Publication date: 1 August 2024
Source: Journal of Computational Physics, Volume 510
Author(s): Zhao Zhang, Piyang Liu, Ying Liu, Tianyu Zeng, Menghan Li
Publication date: 1 August 2024
Source: Journal of Computational Physics, Volume 510
Author(s): Hang Su, Eric E. Keaveny
Publication date: 1 August 2024
Source: Journal of Computational Physics, Volume 510
Author(s): Aekta Aggarwal, G.D. Veerappa Gowda, K. Sudarshan Kumar
Publication date: 1 August 2024
Source: Journal of Computational Physics, Volume 510
Author(s): L. Boittin, F. Bouchut, M.-O. Bristeau, A. Mangeney, J. Sainte-Marie, F. Souillé
Spreading time, the time that an impacting droplet attains the maximum wetting area on a solid surface, plays a critical role in many engineering applications particularly where heat transfer or chemical reactions are involved. Although the impact dynamics of a droplet significantly differ across the different spreading regimes depending on various collision parameters, it still remains unclear how the spreading time changes for each spreading regime. In the present study, the spreading time during droplet impact on a large spherical target is systematically studied at the three different spreading regimes for a wide range of impact parameters (Weber number, equilibrium contact angle, and Ohnesorge number). The changes of spreading time depending on the impact parameters and underlying physical mechanisms are analyzed in detail at the level of three different spreading regimes. Our results show that the spreading time, proper time scales, dominant impact parameters and associated physical behaviors all significantly and non-linearly change across the three spreading regimes. An improved prediction model for the spreading time is also proposed for each regime, which is now based on only the controllable variables and has an explicit form. Finally, a data-driven prediction model is proposed to represent the complicated and non-linear nature of the spreading time broadly across the three spreading regimes.
We perform a resolvent analysis of a compressible turbulent jet, where the optimisation domain of the response modes is located in the acoustic field, excluding the hydrodynamic region, in order to promote acoustically efficient modes. We examine the properties of the acoustic resolvent and assess its potential for jet-noise modelling, focusing on the subsonic regime. Resolvent forcing modes, consistent with previous studies, are found to contain supersonic waves associated with Mach wave radiation in the response modes. This differs from the standard resolvent in which hydrodynamic instabilities dominate. We compare resolvent modes with SPOD modes educed from LES data. Acoustic resolvent response modes generally have better alignment with acoustic SPOD modes than standard resolvent response modes. For the optimal mode, the angle of the acoustic beam is close to that found in SPOD modes for moderate frequencies. However, there is no significant separation between the singular values of the leading and sub-optimal modes. Some suboptimal modes are furthermore shown to contain irrelevant structure for jet noise. Thus, even though it contains essential acoustic features absent from the standard resolvent approach, the SVD of the acoustic resolvent alone is insufficient to educe a low-rank model for jet noise. But because it identifies the prevailing mechanisms of jet noise, it provides valuable guidelines in the search of a forcing model (Karban et al. in J Fluid Mech 965:18, 2023).
This work presents a methodology to extract coherent structures from high-speed schlieren images of turbulent twin jets which are more physically interpretable than those obtained with currently existing techniques. Recently, Prasad and Gaitonde (J Fluid Mech 940:1–11, 2022) introduced an approach which employs the momentum potential theory of Doak (J Sound Vib 131(1):67–90, 1989) to compute potential (acoustic and thermal) energy fluctuations from the schlieren images by solving a Poisson equation, and combines it with spectral proper orthogonal decomposition (SPOD) to educe coherent structures from the momentum potential field instead of the original schlieren field. While the latter field is dominated by a broad range of vortical fluctuations in the turbulent mixing region of unheated high-speed jets, the momentum potential field is governed by fluctuations which are intimately related to acoustic emission, and its spatial structure in the frequency domain is very organized. The proposed methodology in this paper improves the technique of Prasad and Gaitonde (J Fluid Mech 940:1–11, 2022) in three new ways. First, the solution of the Poisson equation is carried out in the frequency-wavenumber domain instead of the time-space domain, which simplifies and integrates the solution of the Poisson equation within the SPOD framework based on momentum potential fluctuations. Second, the issue of solving the Poisson equation on a finite domain with ad hoc boundary conditions is explicitly addressed, identifying and removing those unphysical harmonic components introduced in the solution process. Third, the solution of the SPOD problem in terms of momentum potential fluctuations is used to reconstruct schlieren SPOD fields associated with each mode, allowing the visualization of the obtained coherent structures also in terms of the density gradient. The method is applied here to schlieren images of a twin-jet configuration with a small jet separation at two supersonic operation conditions: a perfectly-expanded and an overexpanded one. The SPOD modes based on momentum potential fluctuations retain the wavepacket structure including the direct Mach-wave radiation, together with upstream- and downstream-traveling acoustic waves, similar to SPOD modes based on the schlieren images. However, for the same dataset, they result in a lower-rank decomposition than schlieren-based SPOD and provide an effective separation of twin-jet fluctuations into independent toroidal and flapping oscillations that are recovered as different SPOD modes. These coherent structures are more consistent with twin-jet wavepacket models available in the literature than those originally obtained with direct schlieren-based SPOD, facilitating their interpretation and comparison against theoretical analyses.
We present an extension of the RSVD- \(\Delta t\) algorithm initially developed for resolvent analysis of statistically stationary flows to handle harmonic resolvent analysis of time-periodic flows. The harmonic resolvent operator, as proposed by Padovan et al. (J Fluid Mech 900, 2020), characterizes the linearized dynamics of time-periodic flows in the frequency domain, and its singular value decomposition reveals forcing and response modes with optimal energetic gain. However, computing harmonic resolvent modes poses challenges due to (i) the coupling of all \(N_{\omega }\) retained frequencies into a single harmonic resolvent operator and (ii) the singularity or near-singularity of the operator, making harmonic resolvent analysis considerably more computationally expensive than a standard resolvent analysis. To overcome these challenges, the RSVD- \(\Delta t\) algorithm leverages time stepping of the underlying time-periodic linearized Navier–Stokes operator, which is \(N_{\omega }\) times smaller than the harmonic resolvent operator, to compute the action of the harmonic resolvent operator. We develop strategies to minimize the algorithm’s CPU and memory consumption, and our results demonstrate that these costs scale linearly with the problem dimension. We validate the RSVD- \(\Delta t\) algorithm by computing modes for a periodically varying Ginzburg–Landau equation and demonstrate its performance using the flow over an airfoil.
This paper presents simulations of dam-break flows of Herschel–Bulkley viscoplastic fluids over complex topographies using the shallow water equations (SWE). In particular, this study aims to assess the effects of rheological parameters: power-law index (n), consistency index (K), and yield stress ( \(\tau _{c}\) ), on flow height and velocity over different topographies. Three practical examples of dam-break flow cases are considered: a dam-break on an inclined flat surface, a dam-break over a non-flat topography, and a dam-break over a wet bed (downstream containing an initial fluid level). The effects of bed slope and depth ratios (the ratio between upstream and downstream fluid levels) on flow behaviour are also analyzed. The numerical results are compared with experimental data from the literature and are found to be in good agreement. Results show that for both dry and wet bed conditions, the fluid front position, peak height, and mean velocity decrease when any of the three rheological parameters are increased. However, based on a parametric sensitivity analysis, the power-law index appears to be the dominant factor in dictating fluid behaviour. Moreover, by increasing the bed slope and/or depth ratio, the wave-frontal position moves further downstream. Furthermore, the presence of an obstacle is observed to cause the formation of an upsurge that moves in the upstream direction, which increases by increasing any of the three rheological parameters. This study is useful for an in-depth understanding of the effects of rheology on catastrophic gravity-driven flows of non-Newtonian fluids (like lava or mud flows) for risk assessment and mitigation.
We numerically investigate the fluidic pinball under symmetric forcing and find seven flow regimes under different rotation speeds. The fluidic pinball consists of three rotatable cylinders placed at the vertices of an equilateral triangle pointing upstream in a uniform oncoming flow. The starting point is the unforced asymmetric periodic vortex shedding at Reynolds number Re = 100 based on the cylinder diameter. The flow is symmetrically actuated by rotating the two rear cylinders at constant speed |b| up to three times the oncoming velocity in both directions. Counterclockwise (b > 0) and clockwise (b < 0) rotation of the bottom cylinder correspond to boat tailing and base bleeding, respectively. A total of seven distinct flow regimes are observed, including a steady flow, three symmetric/asymmetric periodic types of shedding, two symmetric/asymmetric quasi-periodic behaviors, and a chaotic dynamics. The vortex shedding features multiple coupled oscillator modes, including in-phase, anti-phase, and out-of-phase synchronization and non-synchronization. These shedding regimes are analyzed employing the temporal evolution of the aerodynamic forces and a dynamical mode decomposition of the wake flow. The kaleidoscope of unforced and forced dynamics promotes the fluidic pinball as a challenging modeling and control benchmark.
Shear-induced droplet formation is important in many industrial applications, primarily focusing on droplet sizes and pinch-off frequency. We propose a one-dimensional mathematical model that describes the effect of shear forces on the droplet interface evolution. The aim of this paper is to simulate paraffin wax droplets in a co-flowing fluid using the proposed model to estimate the droplet volume rate for different flow velocities. Thus, the study focuses only on the dripping regime. This one-dimensional model has a single parameter that arises from the force balance on the interface. This parameter is related to the shear layer thickness and hence influenced by the change in quantities like velocity, viscosity, and surface tension. The correlation describing the dependence of the parameter on these quantities using non-dimensional numbers is presented. The model is then cross-validated with the previous computational and experimental data. We use PETSc, an open-source solver toolkit, to implement our model using a mixed finite element discretization. We present the simulation results for liquid paraffin wax under fast-moving airflow with a range of velocities.
Employing direct numerical simulations, we investigate water and water-glycerol (85 wt%) droplets ( \(\sim \) 25 µL) moving on smooth surfaces, with contact angles of around 90 \(^{\circ }\) , at varying inclinations. Our focus is on elucidating the relative contribution of local viscous forces in the wedge and bulk regions in droplets to the total viscous force. We observe that, for fast-moving droplets, both regions contribute comparably, while the contribution of the wedge region dominates in slow-moving cases. Comparisons with existing estimates reveal the inadequacy of previous predictions in capturing the contributions of wedge and bulk viscous forces in fast-moving droplets. Furthermore, we demonstrate that droplets with identical velocities can exhibit disparate viscous forces due to variations in internal fluid dynamics.
We study generalised quasilinear (GQL) approximations applied to turbulent plane Couette flow. The GQL framework is explored in conjunction with a Galerkin reduced-order model (ROM) recently developed by Cavalieri and Nogueira (Phys Rev Fluids 7:102601, 2022), which considers controllability modes of the linearised Navier–Stokes system as basis functions, representing coherent structures in the flow. The velocity field is decomposed into two groups: one composed by high-controllability modes and the other by low-controllability modes. The former group is solved with the full nonlinear equations, whereas the equations for the latter are linearised. We also consider a new GQL framework wherein the linearised equations for the low-controllability modes are driven by nonlinear interactions of modes in the first group, which are characterised by large-scale coherent structures. It is shown that GQL-ROMs successfully recover the statistics of the full model with relatively high controllability thresholds and sparser nonlinear operators. Driven GQL-ROMs were found to converge more rapidly than standard GQL approximations, providing accurate description of the statistics with a larger number of linearised modes. This indicates that the forcing of linearised flow structures by large-scale coherent structures is an important feature of turbulence dynamics that should be considered in GQL models. The results presented here reveal that further model reductions are attainable with GQL-ROMs, which can be valuable to extend these models to larger Reynolds numbers.
This study presents a physics-based, low-order model for the trailing edge (TE) noise generated by an airfoil at low angle of attack. The approach employs incompressible resolvent analysis of the mean flow to extract relevant spanwise-coherent structures in the transitional boundary layer and near wake. These structures are integrated into Curle’s solution to Lighthill’s acoustic analogy to obtain the scattered acoustic field. The model has the advantage of predicting surface pressure fluctuations from first principles, avoiding reliance on empirical models, but with a free amplitude set by simulation data. The model is evaluated for the transitional flow ( \(\text {Re} = 5e4\) ) around a NACA0012 airfoil at 3 deg angle of attack, which features TE noise with multiple tones. The mean flow is obtained from a compressible large eddy simulation, and spectral proper orthogonal decomposition (SPOD) is employed to extract the main hydrodynamic and acoustic features of the flow. Comparisons between resolvent and SPOD demonstrate that the physics-based model accurately captures the leading coherent structures at the main tones’ frequencies, resulting in a good agreement of the reconstructed acoustic power with that of the SPOD (within 4 dB). Discrepancies are observed at high frequencies, likely linked to nonlinearities that are not considered in the resolvent analysis. The model’s directivity aligns well with the data at low Helmholtz numbers, but it fails at high frequencies where the back-scattered pressure plays a significant role in directivity. This modeling approach opens the way for efficient optimization of airfoil shapes in combination with low-fidelity mean flow solvers to reduce TE noise.