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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): V.K. Suman, P. Sundaram, Soumyo Sengupta, Tapan K. Sengupta
Publication date: 30 May 2024
Source: Computers & Fluids, Volume 276
Author(s):
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): 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: Available online 11 May 2024
Source: Computers & Fluids
Author(s): Daniele Vivaldi
Publication date: Available online 8 May 2024
Source: Computers & Fluids
Author(s): Anis Younes, Lingai Guo, François Lehmann, Marwan Fahs, Hussein Hoteit
Publication date: Available online 3 May 2024
Source: Computers & Fluids
Author(s): Jacob E. Lotz, Marco F.P. ten Eikelder, Ido Akkerman
Publication date: Available online 4 May 2024
Source: Computers & Fluids
Author(s): R. Nemer, A. Larcher, E. Hachem
Publication date: Available online 6 May 2024
Source: Computers & Fluids
Author(s): Marthe de Crouy-Chanel, Chloé Mimeau, Iraj Mortazavi, Alessandro Mariotti, Maria Vittoria Salvetti
The present study shows that the number of particle time-steps required to reach the statistically steady-state condition is at least one-sixth less than the previously developed algorithms. This indicates that the current hybrid algorithm requires much less computational work and time to converge to solution. Moreover, the implementation of the present extended method can highly improve its capabilities in numerical prediction of turbulent flows in very complex geometries.
One main concern of this work is to develop an efficient particle-tracking-managing algorithm in the framework of a hybrid pressure-based finite-volume/probability-density-function (FV/PDF) Monte-Carlo (MC) solution algorithm to extend the application of FV/PDF MC methods to absolutely incompressible flows and speedup the convergence rate of solving the fluctuating velocity-turbulent frequency joint PDF equation in turbulent flow simulations. Contrary to the density-based algorithms, the pressure-based algorithms have stable convergence rates even in zero-Mach number flows. As another contribution, literature shows that the past developed methods mostly used mesh searching techniques to attribute particles to cells at the beginning of each tracking time-step. Also, they had to calculate the linear basis functions at every time-step to estimate the particle mean fields and interpolate the data. These calculations would be computationally very expensive, time-consuming, and inefficient in computational domains with arbitrary-shaped 3D meshes. As known, the barycentric tracking is a continuous particle tracking method, which provides more efficiency in case of handling 3D domains with general mesh shapes. The barycentric tracking eliminates any mesh searching technique and readily provides the convenient linear basis functions. So, this work benefits from these advantages and tracks the particles based on their barycentric coordinates. It leads to less computational work and a better efficiency for the present method. A bluff-body turbulent flow case is examined to validate the present FV/PDF MC method. From the accuracy perspective, it is shown that the results of the present algorithm are in great agreement with experimental data and available numerical solutions. The present study shows that the number of particle time-steps required to reach the statistically steady-state condition is at least one-sixth less than the previously developed algorithms. This also approves a faster convergence rate for the present hybrid pressure-based algorithm.
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 propose in this article a discretization of the momentum convection operator for the approximation of the Navier–Stokes equations by the low-order nonconforming Rannacher–Turek finite element. This operator is of finite volume type, and its almost second order expression is derived by an algebraic MUSCL-like technique; it satisfies a discrete and local kinetic energy conservation identity. The stability, consistency, and accuracy of the resulting scheme is assessed by numerical experiments for incompressible, barotropic and compressible flows, including the Euler equations.
We propose in this article a discretization of the momentum convection operator for fluid flow simulations on quadrangular or generalized hexahedral meshes. The space discretization is performed by the low-order nonconforming Rannacher–Turek finite element: the scalar unknowns are associated with the cells of the mesh while the velocities unknowns are associated with the edges or faces. The momentum convection operator is of finite volume type, and its expression is derived, as in MUSCL schemes, by a two-step technique: (i)$$ (i) $$ computation of a tentative flux, here, with a centered approximation of the velocity, and (ii)$$ (ii) $$ limitation of this flux using monotonicity arguments. The limitation procedure is of algebraic type, in the sense that its does not invoke any slope reconstruction, and is independent from the geometry of the cells. The derived discrete convection operator applies both to constant or variable density flows and may thus be implemented in a scheme for incompressible or compressible flows. To achieve this goal, we derive a discrete analogue of the computation ui(∂t(ρui)+div(ρuiu)=12∂t(ρui2)+12div(ρui2u)$$ {u}_i\kern0.3em \Big({\partial}_t\left(\rho {u}_i\right)+\operatorname{div}\left(\rho {u}_i\boldsymbol{u}\right)=\frac{1}{2}{\partial}_t\left(\rho {u}_i^2\right)+\frac{1}{2}\operatorname{div}\left(\rho {u}_i^2\boldsymbol{u}\right) $$ (with u$$ \boldsymbol{u} $$ the velocity, ui$$ {u}_i $$ one of its component, ρ$$ \rho $$ the density, and assuming that the mass balance holds) and discuss two applications of this result: first, we obtain stability results for a semi-implicit in time scheme for incompressible and barotropic compressible flows; second, we build a consistent, semi-implicit in time scheme that is based on the discretization of the internal energy balance rather than the total energy. The performance of the proposed discrete convection operator is assessed by numerical tests on the incompressible Navier–Stokes equations, the barotropic and the full compressible Navier–Stokes equations and the compressible Euler equations.
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.
Following the solution formula method given in Dong et al. (High order discontinuities decomposition entropy condition schemes for Euler equations. CFD J. 2002;10(4): 448–457), this article studies a type of one-step fully-discrete scheme, and constructs a third-order scheme which is written into a compact form via a new limiter. The highlights of this study and advantages of new third-order scheme are as follows: ① We proposed a very simple new methodology of constructing one-step, consistent high-order and non-oscillation schemes that do not rely on Runge–Kutta method; ② We systematically studied new scheme's theoretical problems about entropy conditions, error analysis, and non-oscillation conditions; ③ The new scheme achieves exact solution in linear cases and performing better in nonlinear cases when CFL → 1; ④ The new scheme is third order but high resolution with excellent shock-capturing capacity which is comparable to fifth order WENO scheme; ⑤ CPU time of new scheme is only a quarter of WENO5 + RK3 under same computing condition; ⑥ For engineering applications, the new scheme is extended to multi-dimensional Euler equations under curvilinear coordinates. Numerical experiments contain 1D scalar equation, 1D,2D,3D Euler equations. Accuracy tests are carried out using 1D linear scalar equation, 1D Burgers equation and 2D Euler equations and two sonic point tests are carried out to show the effect of entropy condition linearization. All tests are compared with results of WENO5 and finally indicate EC3 is cheaper in computational expense.
Previously developed anisotropic mesh adaptation framework is coupled with a hybridized discontinuous Galerkin (HDG) solver for general time-dependent balance laws. Special emphasis is placed on the solution transfer between anisotropically adapted meshes such that the conservation of physically relevant quantities is preserved and the accuracy of high-order method is not compromised. This is achieved by so called Galerkin projection on each element of the mesh. These properties are verified by means of test cases having both smooth and discontinuous solutions.
We present a hybridized discontinuous Galerkin (HDG) solver for general time-dependent balance laws. In particular, we focus on a coupling of the solution process for unsteady problems with our anisotropic mesh refinement framework. The goal is to properly resolve all relevant unsteady features with the smallest possible number of mesh elements, and hence to reduce the computational cost of numerical simulations while maintaining its accuracy. A crucial step is then to transfer the numerical solution between two meshes, as the anisotropic mesh adaptation is producing highly skewed, non-nested sequences of triangular grids. For this purpose, we adopt the Galerkin projection for the HDG solution transfer as it preserves the conservation of physically relevant quantities and does not compromise the accuracy of high-order method. We present numerical experiments verifying these properties of the anisotropically adaptive HDG method.
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.
We are interested in the efficient solution of the saddle-point linear systems arising from isogeometric analysis approach of Navier–Stokes equations. We use a preconditioned Krylov subspace method (GMRES) with efficient approximate solvers for solving subsystems within preconditioning. We investigate the impact on the convergence of the outer solver and aim to identify an effective combination preconditioners and inner solvers with respect problem parameters.
We deal with efficient numerical solution of the steady incompressible Navier–Stokes equations (NSE) using our in-house solver based on the isogeometric analysis (IgA) approach. We are interested in the solution of the arising saddle-point linear systems using preconditioned Krylov subspace methods. Based on our comparison of ideal versions of several state-of-the-art block preconditioners for linear systems arising from the IgA discretization of the incompressible NSE, suitable candidates have been selected. In the present paper, we focus on selecting efficient approximate solvers for solving subsystems within these preconditioning methods. We investigate the impact on the convergence of the outer solver and aim to identify an effective combination. For this purpose, we compare convergence properties of the selected solution approaches for problems with different viscosity values, mesh refinement levels and discretization bases.
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.
Publication date: Available online 10 May 2024
Source: Journal of Computational Physics
Author(s): Jie Ding, Shenggao Zhou
Publication date: Available online 10 May 2024
Source: Journal of Computational Physics
Author(s): Danjie Xu, Oriol Colomés, Alex Main, Kangan Li, Nabil M. Atallah, Nabil Abboud, Guglielmo Scovazzi
Publication date: Available online 10 May 2024
Source: Journal of Computational Physics
Author(s): Ling Guo, Hao Wu, Yan Wang, Wenwen Zhou, Tao Zhou
Publication date: Available online 10 May 2024
Source: Journal of Computational Physics
Author(s): Yiqi Feng, Josef Winter, Nikolaus A. Adams, Felix S. Schranner
Publication date: Available online 9 May 2024
Source: Journal of Computational Physics
Author(s): J.M. Goff, C. Sievers, M.A. Wood, A.P. Thompson
Publication date: Available online 10 May 2024
Source: Journal of Computational Physics
Author(s): Juncai Pu, Yong Chen
Publication date: Available online 10 May 2024
Source: Journal of Computational Physics
Author(s): Xian Xie, Haiyun Dong, Maojun Li
Publication date: 15 July 2024
Source: Journal of Computational Physics, Volume 509
Author(s): Yasuya Nakayama, Yuki Matsuoka, Toshihisa Kajiwara
Publication date: 15 July 2024
Source: Journal of Computational Physics, Volume 509
Author(s): Yanjiao Zhou, Dong Liang
Publication date: 15 July 2024
Source: Journal of Computational Physics, Volume 509
Author(s): Dhwanit Agarwal, George Biros
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.
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.
