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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: 30 May 2024
Source: Computers & Fluids, Volume 276
Author(s): Peng Hu, Mobassir Azam, Wei Li, Linwei Dai, Hongyang Zhao
Publication date: 30 May 2024
Source: Computers & Fluids, Volume 276
Author(s): Ruijie Zhao, Yuanhang Zhang, Xuzhen Zhang, Xikun Wang
Publication date: 30 May 2024
Source: Computers & Fluids, Volume 276
Author(s): Zhixin Huo, Zupeng Jia
Publication date: 30 May 2024
Source: Computers & Fluids, Volume 276
Author(s): V.K. Suman, P. Sundaram, Soumyo Sengupta, Tapan K. Sengupta
Publication date: Available online 25 April 2024
Source: Computers & Fluids
Author(s): Hamid Hassan Khan, Pankaj Jagad, Matteo Parsani
Publication date: Available online 26 April 2024
Source: Computers & Fluids
Author(s): Lianxia Li, Michael Stoellinger, Maysam Mousaviraad
Publication date: 30 May 2024
Source: Computers & Fluids, Volume 276
Author(s): Jaideep Ray, Jeffrey S. Horner, Ian Winter, David J. Kemmenoe, Edward R. Arata, Michael Chandross, Scott A. Roberts, Anne M. Grillet
Publication date: 30 May 2024
Source: Computers & Fluids, Volume 276
Author(s): Han Tang, Guannan Zheng, Yuchen Zhang
Publication date: 30 May 2024
Source: Computers & Fluids, Volume 276
Author(s): Bing Cui, Lei Wu, Zuoli Xiao, Yu Liu
Publication date: 30 May 2024
Source: Computers & Fluids, Volume 276
Author(s): Phanindra Paravastu, Srikanth Vedantam
In this work by Jakob Vandergrift* and Florian Kummer, “an extended discontinuous Galerkin shock tracking method” for PDEs with discontinuities is proposed and successfully applied to 2D problems showing promising results. At the heart of the method a level set is employed, implicitly enrichening the approximation space, allowing for accurate representation of solution discontinuities within cut-cells and without requiring additional stabilization. The shock-fitted level set and the PDE solution are computed simultaneously using an optimization approach.
In this paper, we introduce a novel high-order shock tracking method and provide a proof of concept. Our method leverages concepts from implicit shock tracking and extended discontinuous Galerkin methods, primarily designed for solving partial differential equations featuring discontinuities. To address this challenge, we solve a constrained optimization problem aiming at accurately fitting the zero iso-contour of a level set function to the discontinuities. Additionally, we discuss various robustness measures inspired by both numerical experiments and existing literature. Finally, we showcase the capabilities of our method through a series of two-dimensional problems, progressively increasing in complexity.
This work proposes a modified forcing term in the Rothman–Keller (RK) model to minimize spurious velocities and provide more accurate results at lower capillary numbers. The current approach converges quickly and shows parallel flow accurately for all the capillary numbers as opposed to the traditional RK model (Guo approach). Leakage is also successfully captured by the current approach for most of the capillary numbers, which wasn't the case for Volume of Fluid and phase field methods.
The lattice-Boltzmann method (LBM) is becoming increasingly popular for simulating multi-phase flows on the microscale because of its advantages in terms of computational efficiency. Many applications of the method are restricted to relatively simple geometries. When a more complex geometry is considered—circular and inclined microchannels—some important physical phenomena may not be accurately captured, especially at low capillary numbers. A Y-Y micro-fluidic channel, widely used for a range of applications, is an example of a more complex geometry. This work aims to capture the various flow phenomena, with an emphasis on parallel flow and leakage, using the Rothman–Keller (RK) model of the LBM. To this purpose, we modify the forcing term to implement the surface tension for use at low capillary numbers. We compare the simulation results of the RK model with and without the force modification with experiments, Volume of Fluid and the phase field method and observe that the modified forcing term is an improvement over the current RK model at low capillary numbers, and it also captures parallel flow and leakage more accurately than the other simulation techniques.
In the present study, describes the rheological transition from dry to wet sedimentary materials as a transition from shear thinning behavior to shear thickness behavior. This transition can clearly have a significant effect on saturated materials. In this study, a transition period is defined which the sliding materials are saturated. Although this period is constant, for each particle based on the time it reaches the initial water level, it is separately initialized.
Landslides, which are the sources of most catastrophic natural disasters, can be subaerial (dry), submerged (underwater), or semi-submerged (transitional). Semi-submerged or transitional landslides occur when a subaerial landslide enters water and turns to submerged condition. Predicting the behavior of such a highly dynamic multi-phase granular flow system is challenging, mainly due to the water entry effects, such as wave impact and partial saturation (and resulted cohesion). The mesh-free particle methods, such as the moving particle semi-implicit (MPS) method, have proven their capabilities for the simulation of the highly dynamic multiphase systems. This study develops and evaluates a numerical model, based on the MPS particle method in combination with the μ(I) rheological model, to simulate the morphodynamic of the granular mass in semi-submerged landslides in two and three dimensions. An algorithm is developed to consider partial saturation (and resulting cohesion) during the water entry. Comparing the numerical results with the experimental measurements shows the ability of the proposed model to accurately reproduce the morphological evolution of the granular mass, especially at the moment of water entry.
Researchers can incorporate uncertainties in computational fluid dynamics (CFD) that go beyond the inaccuracies caused by numerical discretization thanks to stochastic simulations. This study confirms the validity of current stochastic modeling tools by providing examples of stochastic simulations in conjunction with numerical solutions for incompressible flows. A numerical technique for solving deterministic and stochastic models is developed in this work. Our approach employs the Euler-Maruyama method for stochastic modeling, representing a stochastic version of the third-order explicit-implicit scheme. For the deterministic model, the scheme is third-order accurate. The consistency and stability of the constructed scheme are provided in the mean square sense. The scheme is the predictor–corrector type that is built on two time levels. Moreover, a mathematical model of the Casson nanofluid flow with variable thermal conductivity is given with the effect of the chemical reaction. The appropriate transformations are used to condense the set of partial differential equations (PDEs) down to one that is dimensionless. The scheme is applied for the deterministic and stochastic models of dimensionless flow problems. The velocity profile's deterministic and stochastic behavior are shown using contour plots. Results show that growing values of the thermal mixed convection parameter enhance the velocity profile. This article presents the progress made in stochastic computational fluid dynamics (SCFD) and highlights the energy-related aspects of our discoveries. Our computational approach and stochastic modeling techniques provide new insights into the energy properties of Casson nanofluid flow, specifically regarding the variability of thermal conductivity and chemical processes. Our objective is to clarify the complex interaction of these factors on energy dynamics. This article presents a contemporary summary of the latest SCFD advancements. Additionally, it highlights potential directions for future research and unresolved issues that require attention from the members of the field of computational mathematics.
Researchers can incorporate uncertainties in computational fluid dynamics (CFD) that go beyond the inaccuracies caused by numerical discretization thanks to stochastic simulations. This study confirms the validity of current stochastic modeling tools by providing examples of stochastic simulations in conjunction with numerical solutions for incompressible flows. A numerical technique for solving deterministic and stochastic models is developed in this work. Our approach employs the Euler-Maruyama method for stochastic modeling, representing a stochastic version of the third-order explicit-implicit scheme. For the deterministic model, the scheme is third-order accurate. The consistency and stability of the constructed scheme are provided in the mean square sense. The scheme is the predictor–corrector type that is built on two time levels. Moreover, a mathematical model of the Casson nanofluid flow with variable thermal conductivity is given with the effect of the chemical reaction. The appropriate transformations are used to condense the set of partial differential equations (PDEs) down to one that is dimensionless. The scheme is applied for the deterministic and stochastic models of dimensionless flow problems. The velocity profile's deterministic and stochastic behavior are shown using contour plots. Results show that growing values of the thermal mixed convection parameter enhance the velocity profile. This article presents the progress made in stochastic computational fluid dynamics (SCFD) and highlights the energy-related aspects of our discoveries. Our computational approach and stochastic modeling techniques provide new insights into the energy properties of Casson nanofluid flow, specifically regarding the variability of thermal conductivity and chemical processes. Our objective is to clarify the complex interaction of these factors on energy dynamics. This article presents a contemporary summary of the latest SCFD advancements. Additionally, it highlights potential directions for future research and unresolved issues that require attention from the members of the field of computational mathematics.
The second-order Gauge–Uzawa method is combined with the finite element method to solve the active fluid model with the fourth derivative term and strong nonlinear terms. A large number of numerical experiments show that the scheme not only has superior accuracy and efficiency, but also proves that it has good simulation effect through comparison with the laboratory results.
In this paper, we propose a linear, decoupled, unconditionally stable fully-discrete finite element scheme for the active fluid model, which is derived from the gradient flow approach for an effective non-equilibrium free energy. The developed scheme is employed by an implicit-explicit treatment of the nonlinear terms and a second-order Gauge–Uzawa method for the decoupling of computations for the velocity and pressure. We rigorously prove the unique solvability and unconditional stability of the proposed scheme. Several numerical tests are presented to verify the accuracy, stability, and efficiency of the proposed scheme. We also simulate the self-organized motion under the various external body forces in 2D and 3D cases, including the motion direction of active fluid from disorder to order. Numerical results show that the scheme has a good performance in accurately capturing and handling the complex dynamics of active fluid motion.
An adaptive sharp immersed method is proposed to simulate electrohydrodynamic flows accompanied by ion evaporation. A splitting error-free iterative projection algorithm is used to solve the Navier–Stokes equations, and a robust iterative algorithm is used to address the surface charge transport. Our simulations captured the protrusion structure caused by charge evaporation and showed that charge evaporation can suppress the sharp development of Taylor cones at the ends of the drops.
This article presents a sharp immersed method for simulating electrohydrodynamic (EHD) flows that involve charge evaporation. This well-known multi-scale, multi-physics problem is widely used in various fields, including industry and medicine. The method adopts a fully sharp model, where surface tension and Maxwell stress are treated as surface forces and free charges are concentrated on the zero thickness liquid-vacuum interface. Incorporating charge evaporation imposes strict restrictions on the time-step, as the rate of evaporation sharply increases with surface evolution. To overcome this challenge, an iterative algorithm that couples the electric field and surface charge density is proposed to obtain accurate results, even with significantly large time-steps. To mitigate the numerical residuals near the interface, which may introduce parasitic flows and cause numerical instability, an immersed interface method-based iterative projection method for the Navier–Stokes equations is proposed, in which a traction boundary condition involving multiple surface forces is imposed on the sharp interface. Numerical experiments were carried out, and the results show that the method is splitting-error-free and stable. The sharp immersed method is applied to simulate the electric-induced deformation of an ionic liquid drop with charge evaporation. The results indicate that charge evaporation can suppress the sharp development of Taylor cones at the ends of the drops. These findings have significant implications for the design and optimization of EHD systems in various applications.
A Fourier-expansion based differential quadrature method (FDQ) with lattice Boltzmann flux solvers (LBFS) for simulating isothermal and thermal flows. The method possesses several merits such as simple formulation and implementation, easy boundary condition treatments and flexibility on curved geometries. Numerical experiments confirm the superior performance in terms of accuracy and efficiency compared with other high-order methods.
This paper presents a high-order Fourier-expansion based differential quadrature method with isothermal and thermal lattice Boltzmann flux solvers (LBFS-FDQ and TLBFS-FDQ) for simulating incompressible flows. The numerical solution in the present method is approximated via trigonometric basis. Therefore, both periodic and non-periodic boundary conditions can be handled straightforwardly without the special treatments as required by polynomial-based differential quadrature methods. The incorporation of LBFS/TLBFS enables the present methods to efficiently simulated various types of flow problems on considerably coarse grids with spectral accuracy. The high-order accuracy, efficiency and competitiveness of the proposed method are comprehensively demonstrated through a wide selection of isothermal and thermal flow benchmarks.
A finite element model for the study of a channel with semi-permeable walls using the Nitsche method is presented. Several numerical experiments are performed for validation of the method. We show that our method accurately predicts the pressure drop from classical analytical models. Also, Nitsche's method allows obtaining accurate results on the membrane as long as it is discretized with an adequate number of elements. Discussion and comparison between different operational conditions are presented, where we observe that transmembrane pressure causes the most increase in average permeate flux
In this article, we study a mathematical model that represents the concentration polarization and osmosis effects in a reverse osmosis cross-flow channel with dense membranes at some of its boundaries. The fluid is modeled using the Navier–Stokes equations and the solution-diffusion is used to impose the momentum balance on the membrane. The scheme consist of a conforming finite element method with the velocity–pressure formulation for the Navier–Stokes equations, together with a primal scheme for the convection–diffusion equations. The Nitsche's method is used to impose the permeability condition across the membrane. Several numerical experiments are performed to show the robustness of the method. The resulting model accurately replicates the analytical models and predicts similar results to previous works. It is found that the submerged configuration has the highest permeate production, but also has the greatest pressure loss of all three configurations studied.
The paper shows results from an implicit meshless method suitable for the analysis of external aerodynamic flows. This research is using a cloud of points instead of cells, and several stencils are compared for the discretization of the flow equations, along with a least-squares method. Different adaptive refinement schemes are compared, and the results shows that a weighted pressure gradient metric was suitable for driving the adaptation process. With the tested stencils and given enough points in the cloud, the method was able to capture the formation on shocks on transonic aerofoils and wings, and delivered results of good accuracy.
This work presents details and assesses implicit and adaptive mesh-free CFD modelling approaches, to alleviate laborious mesh generation in modern CFD processes. A weighted-least-squares-based, mesh-free, discretisation scheme was first derived for the compressible RANS equations, and the implicit dual-time stepping was adopted for improved stability and convergence. A novel weight balancing concept was introduced to improve the mesh-free modelling on highly irregular point clouds. Automatic point cloud generations based on strand and level-set points were also discussed. A novel, polar selection approach, was also introduced to establish high-quality point collocations. The spatial accuracy and convergence properties were validated using 2D and 3D benchmark cases. The impact of irregular point clouds and various point collocation search methods were evaluated in detail. The proposed weight balancing and the polar selection approaches were found capable of improving the mesh-free modelling on highly irregular point clouds. The mesh-free flexibility was then exploited for adaptive modelling. Various adaptation strategies were assessed using simulations of an isentropic vortex, combining different point refinement mechanisms and collocation search methods. The mesh-free modelling was then successfully applied to transonic aerofoil simulations with automated point generation. A weighted pressure gradient metric prioritising high gradient regions with large point sizes was introduced to drive the adaptation. The mesh-free adaptation was found to effectively improve the shock resolution. The results highlight the potential of mesh-free methods in alleviating the meshing bottleneck in modern CFD.
Many physical and industrial problems comprise one or more moving parts, which change the flow domain during a process, such as lubrication and mixing. For such problems, we have suggested a new method, which uses a fixed background mesh to avoid the time-consuming task of boundary-fitted grid generation. The new technique, which is based on the finite element method, uses the moving least-squares interpolation functions, where the solid and fluid meet each other in the flow domain.
With the assistance of the moving least-squares (MLS) interpolation functions, a two-dimensional finite element code is developed to consider the effects of a stationary or moving solid body in a flow domain. At the same time, the mesh or grid is independent of the shape of the solid body. We achieve this goal in two steps. In the first step, we use MLS interpolants to enhance the pressure (P) and velocity (V) shape functions. By this means, we capture different discontinuities in a flow domain. In our previous publications, we have named this technique the PVMLS method (pressure and velocity shape functions enhanced by the MLS interpolants) and described it thoroughly. In the second step, we modify the PVMLS method (the M-PVMLS method) to consider the effect of a solid part(s) in a flow domain. To evaluate the new method's performance, we compare the results of the M-PVMLS method with a finite element code that uses boundary-fitted meshes.
Publication date: 1 July 2024
Source: Journal of Computational Physics, Volume 508
Author(s): Niccolò Tonicello, Matthias Ihme
Publication date: 1 July 2024
Source: Journal of Computational Physics, Volume 508
Author(s): Guosheng Fu, Stanley Osher, Will Pazner, Wuchen Li
Publication date: 1 July 2024
Source: Journal of Computational Physics, Volume 508
Author(s): Mariella Kast, Jan S. Hesthaven
Publication date: 1 July 2024
Source: Journal of Computational Physics, Volume 508
Author(s): Davoud Mirzaei, Navid Soodbakhsh
Publication date: 1 July 2024
Source: Journal of Computational Physics, Volume 508
Author(s): Yuan Chen, Dongbin Xiu
Publication date: 1 July 2024
Source: Journal of Computational Physics, Volume 508
Author(s): Jinyan Guo, Chenchen Mou, Xianjin Yang, Chao Zhou
Publication date: 1 July 2024
Source: Journal of Computational Physics, Volume 508
Author(s): Evan K. Massaro, Michael A. Gallis, Nicolas G. Hadjiconstantinou
Publication date: 1 July 2024
Source: Journal of Computational Physics, Volume 508
Author(s): T. van Gastelen, W. Edeling, B. Sanderse
Publication date: 1 July 2024
Source: Journal of Computational Physics, Volume 508
Author(s): Minsoo Kim, Seungsoo Lee
Publication date: 1 July 2024
Source: Journal of Computational Physics, Volume 508
Author(s): Min Ki Jung, Hakhyeon Kim, Su-San Park, Eung Soo Kim, Yong-Su Na, Sang June Hahn
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.
Modal decomposition techniques are important tools for the analysis of unsteady flows and, in order to provide meaningful insights with respect to coherent structures and their characteristic frequencies, the modes must possess a robust spatial support. In this context, although widely used, methods based on singular value decomposition (SVD) may produce modes that are difficult to interpret when applied to problems dominated by intermittent and transient events. Fortunately, specific modal decomposition techniques have been recently developed to analyze such problems, but a proper comparison between them is still lacking from the literature. Therefore, this work compares two recent methods: the fast adaptive multivariate empirical mode decomposition (FA-MVEMD) and the multiresolution dynamic mode decomposition (mrDMD). These techniques are employed here for the study of flow databases involving transient and intermittent dynamics. Specifically, the investigated problems include an SD7003 airfoil subjected to deep dynamic stall conditions, and a steady NACA0012 airfoil operating at a transitional Reynolds number. In the former case, the methods are employed to investigate the onset and evolution of the dynamic stall vortex (DSV), while in the latter case, intermittent vortex pairing is analyzed. We show that the combination of a multidimensional EMD with the Hilbert transform provides modes with superior spatial support when compared to the mrDMD, also allowing the characterization of instantaneous frequencies of coherent structures. Moreover, the EMD also condenses a larger amount of information within a single intrinsic mode function (IMF).
The stability of the flow past a circular cylinder in the presence of a wavy ground is investigated numerically in this paper. The wavy ground consists of two complete waves with a wavelength of 4D and an amplitude of 0.5D, where D is the cylinder diameter. The vertical distance between the cylinder and the ground is varied, and four different cases are considered. The stability analysis shows that the critical Reynolds number increases for cases close to the ground when compared to the flow past a cylinder away from the ground. The maximum critical Reynolds number is obtained when the cylinder is located in front of the waves. The wavy ground adds layers of clockwise (negative) vorticity due to flow separation from the wave peak, to the oscillating Kármán vortex. This negative vorticity from the wave peak also cancels part of the positive (counterclockwise) vorticity shed from the bottom half of the cylinder. In addition, the negative vorticity from the wave peak strengthens the clockwise (negative) vorticity shed from the top half of the cylinder. These interactions combined with the ground effect skewed the flow away from the ground. The base flow is skewed upward for all the near-ground cases. However, this skew is larger when the cylinder is located over the wavy ground. The vortex shedding frequency is also altered due to the presence of the waves. The main eigenmode found for plain flow past a cylinder appears to become suppressed for cases closer to the ground. Limited particle image velocimetry experiments are reported which corroborate the finding from the stability analysis.
An inviscid vortex shedding model is numerically extended to simulate falling flat plates. The body and vortices separated from the edge of the body are described by vortex sheets. The vortex shedding model has computational limitations when the angle of incidence is small and the free vortex sheet approaches the body closely. These problems are overcome by using numerical procedures such as a method for a near-singular integral and the suppression of vortex shedding at the plate edge. The model is applied to a falling plate of flow regimes of various Froude numbers. For \(\text {Fr}=0.5\) , the plate develops large-scale side-to-side oscillations. In the case of \(\text {Fr}=1\) , the plate motion is a combination of side-to-side oscillations and tumbling and is identified as a chaotic type. For \(\text {Fr}=1.5\) , the plate develops to autorotating motion. Comparisons with previous experimental results show good agreement for the falling pattern. The dependence of change in the vortex structure on the Froude number and its relation with the plate motion is also examined.
Pressure-driven Newtonian fluid flow between grooved and flat surfaces is analysed with no-slip boundary conditions at walls. The effect of corrugation on the fluid flow is investigated using the mesh-free spectral method. The primary aim of the present work is to develop an asymptotic/semi-analytical theory for confined transverse flows to bridge the gap between the limits of thin and thick channels. The secondary aim is to calculate permeability with reference to the effect of wall corrugation (roughness) without the restriction of pattern amplitude. We performed mathematical modelling and evaluated the analytical solution for hydraulic permeability with respect to the flat channel. The Pad \(\acute{e}\) approximate is employed to improve the solution accuracy of an asymptotic model. The results elucidate that permeability always follows a decreasing trend with increasing pattern amplitude using the spectral approach at the long-wave and short-wave limits. The prediction of the spectral model is more accurate than the asymptotic-based model by Stroock et al. (Anal Chem 74(20):5306, 2002) and Pad \(\acute{e}\) approximate, regardless of the grooved depth and wavelength of the channel. The finite-element-based numerical simulation is also used to understand the usefulness of theoretical models. A very low computational time is required using the mesh-free spectral model as compared to the numerical study. The agreement between the present model and the fully resolved numerical results is gratifying. Regarding numerical values, we calculated the relative error for different theoretical models such as an asymptotic model, Pad \(\acute{e}\) approximate, and a mesh-free spectral model. The spectral model always predicts the maximum relative error as less than \(3 \%\) , regardless of the large pattern amplitude and wavelength. In addition, the results of the molecular dynamic (MD) simulations by Guo et al. (Phys Rev Fluids 1(7):074102, 2016) and the theoretical model by Wang (Phys Fluids 15(5):1121, 2003) are found to be quantitatively compatible with the predictions of effective slip length from the spectral model in the thick channel limit.
Recently, Rim (Ocean Engng 239:711, 2021; J Ocean Engng Mar Energy 9:41-51, 2023 ) suggested an exact DtN artificial boundary condition to study the three-dimensional wave diffraction by stationary bodies. This paper is concerned with three-dimensional linear interaction between a submerged oscillating body with arbitrary shape and the regular water wave with finite depth. An exact Dirichlet-to-Neumann (DtN) boundary condition on a virtual cylindrical surface is derived, where the virtual surface is chosen so as to enclose the body and extract an interior subdomain with finite volume from the horizontally unbounded water domain. The DtN boundary condition is then applied to solve the interaction between the body and the linear wave in the interior subdomain by using boundary integral equation. Based on verification of the present model for a submerged vertical cylinder, the model is extended to the case of a submerged chamfer box with fillet radius in order to study 6-DoF oscillatory motion of the body under the free surface wave.
An adjoint-based method is presented for determining manufacturing tolerances for aerodynamic surfaces with natural laminar flow subjected to wavy excrescences. The growth of convective unstable disturbances is computed by solving Euler, boundary layer, and parabolized stability equations. The gradient of the kinetic energy of disturbances in the boundary layer (E) with respect to surface grid points is calculated by solving adjoints of the governing equations. The accuracy of approximations of \(\Delta E\) , using gradients obtained from adjoint, is investigated for several waviness heights. It is also shown how second-order derivatives increase the accuracy of approximations of \(\Delta E\) when surface deformations are large. Then, for specific flight conditions, using the steepest ascent and the sequential least squares programming methodologies, the waviness profile with minimum \(L2-\) norm that causes a specific increase in the maximum value of N- factor, \(\Delta N\) , is found. Finally, numerical tests are performed using the NLF(2)-0415 airfoil to specify tolerance levels for \(\Delta {N}\) up to 2.0 for different flight conditions. Most simulations are carried out for a Mach number and angle of attack equal to 0.5 and \(1.25^{\circ }\) , respectively, and with Reynolds numbers between \(9\times 10^6\) and \(15\times 10^6\) and for waviness profiles with different ranges of wavelengths. Finally, some additional studies are presented for different angles of attack and Mach numbers to show their effects on the computed tolerances.
