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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 7 September 2024
Source: Computers & Fluids
Author(s): Feng Zheng, Jianxian Qiu
Publication date: 30 October 2024
Source: Computers & Fluids, Volume 283
Author(s): Shuyang Zhang, Weidong Li, Ming Fang, Zhaoli Guo
Publication date: 30 October 2024
Source: Computers & Fluids, Volume 283
Author(s): Filippos Sofos, Dimitris Drikakis, Ioannis William Kokkinakis
Publication date: Available online 6 September 2024
Source: Computers & Fluids
Author(s): Feng Wang
Publication date: Available online 6 September 2024
Source: Computers & Fluids
Author(s): Mark A. George, Nicholas Williamson, Steven W. Armfield
Publication date: Available online 17 August 2024
Source: Computers & Fluids
Author(s): Seyedmohammadjavad Zeidi, L. Srujana Sarvepalli, Andrés E. Tejada-Martínez
Publication date: Available online 3 September 2024
Source: Computers & Fluids
Author(s): Kun Zhao, Dongyan Shi, Zhikai Wang, Zhibo Liu, Jingzhou Zheng
Publication date: Available online 4 September 2024
Source: Computers & Fluids
Author(s): Runze Sun, Hyogu Jeong, Jiachen Zhao, Yixing Gou, Emilie Sauret, Zirui Li, Yuantong Gu
Publication date: 30 October 2024
Source: Computers & Fluids, Volume 283
Author(s): Laura Prieto Saavedra, Catherine E. Niamh Radburn, Audrey Collard-Daigneault, Bruno Blais
Publication date: 30 October 2024
Source: Computers & Fluids, Volume 283
Author(s): Bibin John, Deepu Dinesan, Michal Jan Geca, Srijith M.S.
Response surface method-based hydraulic performance optimization of a single-stage centrifugal pump.
In this article, the response surface approach was employed to enhance the hydraulic performance of the pump at the rated point. Specifically, an approximate link between the design head and efficiency of the single-stage centrifugal pump and the parameters of the impeller's design was established. The first step in creating a one-factor experimental design involved selecting significant geometric variables as factors. Decision variables such as the number of blades, flow rate, and rotation were chosen due to their significant impact on hydraulic performance, while head and efficiency were considered as responses. Subsequently, the best-optimized values for each level of the parameters were identified using response surface analysis and a central composite design. The impeller schemes of the Design-Expert software were evaluated for head and efficiency using Computational fluid dynamics, and a total of 20 experiments were conducted. The simulated results were then validated with experimental data. Through the analysis of the individual parameters and the approximation model, the ideal parameter combination that increased head and efficiency by 7.90% and 2.06%, respectively, at the rated value was discovered. It is worth noting that in cases of a high rate of flow, the inner flow was also enhanced.
The paper presents an improved approach for modelling multi-component gas mixtures based on quasi-gasdynamic equations. The proposed numerical algorithm is implemented as a reactingQGDFoam solver based on the open-source OpenFOAM platform. This solver has been extensively validated and verified through a variety of well-described test problems. The stability and convergence parameters of the proposed numerical algorithm are determined. The simulation results are found to be in agreement with analytical solutions and experimental data.
The paper presents an improved approach for modeling multicomponent gas mixtures based on quasi-gasdynamic equations. The proposed numerical algorithm is implemented as a reactingQGDFoam solver based on the open-source OpenFOAM platform. The following problems have been considered for validation: the Riemann problems, the backward facing step problem, the interaction of a shock wave with a heavy and a light gas bubble, the unsteady underexpanded hydrogen jet flow in an air. The stability and convergence parameters of the proposed numerical algorithm are determined. The simulation results are found to be in agreement with analytical solutions and experimental data.
We construct a decoupled and unconditionally stable iteration method to solve the stationary Navier–Stokes equations by adopting the pressure projection method to the temporal disturbed Navier–Stokes system whose solution approximates the steady state over time. Our iterative method is more efficient and stable than the extensively used T-S and Oseen iterations, and could solve the fluid flow with high Reynolds number.
It is well known the Oseen iteration for the stationary Navier–Stokes equations is unconditionally stable. However, it is a coupled type scheme where the velocity u$$ \boldsymbol{u} $$ and pressure p$$ p $$ are coupled together at each iteration. By treating pressure p$$ p $$ explicitly would lead to a decoupled iteration, but this treatment is unstable. In this article, we construct a decoupled and unconditionally stable iteration method to solve the stationary Navier–Stokes equations by adopting the pressure projection method to the temporal disturbed Navier–Stokes system whose solution approximates the steady state solution over time (t→+∞$$ t\to +\infty $$). We also rigorously prove its unconditional stability. Numerical simulations demonstrate that our iterative method is more efficient and stable than the extensively used T-S and Oseen iterations, and could solve the fluid flow with high Reynolds number.
A modified fifth-order WENO-Z scheme is developed by modifying the non-normalized nonlinear weights of a reformulated fifth-order adaptive order WENO scheme. The modified scheme has significantly higher resolution compared with the existing WENO-Z+ and WENO-Z+M schemes with a little more computational overhead per time step.
A modified fifth-order WENO-Z scheme is proposed by analogy with the non-normalized weights of the reformulated fifth-order adaptive order (AO) WENO scheme. We show that if the original fifth-order WENO-AO scheme is rewritten as the form of the conventional WENO combination, the resulting non-normalized weights can be divided into three parts: a constant one term, a local stencil smoothness measure term and a global stencil smoothness measure term. In order to make use of the latter two terms for constructing a modified WENO-Z scheme with enhanced performance, we change the form of the third term and introduce an adaptive scaling factor to adjust the contributions from the second and third terms. Numerical examples show that the modified fifth-order WENO-Z scheme has the advantage of high resolution in smooth regions and sharp capturing of discontinuities, and it can obtain evidently better results for shocked flows with small-scale structures compared with the recently developed WENO-Z+ and WENO-Z+M schemes.
A fully-explicit, iteration-free, weakly-compressible method to simulate immiscible incompressible two-phase flows is presented. This computationally efficient algorithm combines the general pressure equation (GPE), modified switching technique for advection and capturing of surfaces (MSTACS) which is an algebraic volume-of-fluid approach for interface capturing and the operator-split (OS) method. It can accurately handle problems involving a range of density and viscosity ratios and surface tension effects. Since it is fully-explicit, the algorithm is highly scalable for parallel computing.
We present a fully-explicit, iteration-free, weakly-compressible method to simulate immiscible incompressible two-phase flows. To update pressure, we circumvent the computationally expensive Poisson equation and use the general pressure equation which is solved explicitly. In addition, a less diffusive algebraic volume-of-fluid approach is used as the interface capturing technique and in order to facilitate improved parallel computing scalability, the technique is discretised temporally using the operator-split methodology. Our method is fully-explicit and stable with simple local spatial discretization, and hence, it is easy to implement. Several two- and three-dimensional canonical two-phase flows are simulated. The qualitative and quantitative results prove that our method is capable of accurately handling problems involving a range of density and viscosity ratios and surface tension effects.
The IBBMOPSO algorithm can effectively balance diversity and convergence. The KPCA method can reduce the interference of subjective factors. The optimization method can provide support for green design and manufacturing
Multi-objective optimization of ship form can effectively reduce ship energy consumption, and is one of the important research topics of green ships. However, the computational cost of numerical simulation based on computational fluid dynamics (CFD) theory is relatively high, which affects the efficiency of optimization. Traditional subjective weighting methods mostly rely on expert's experience, which affects the scientificity of optimization. This paper effectively integrates the CFD method, the improved multi-objective optimization algorithm and the objective weighting method to build a ship form multi-objective optimization framework. Conduct multi-objective optimization research on resistance and seakeeping performance of a very large crude oil carrier (KVLCC) ship. The improved bare-bones multi-objective particle swarm optimization (IBBMOPSO) algorithm is used to obtain the pareto front, and the kernel principal component analysis (KPCA) method is used to objectively assign the weight of each target. Finally, the optimal ship form scheme with high satisfaction was obtained. The multi-objective optimization framework constructed in this paper can provide a certain theoretical basis and technical support for the development of ship greening and digital transformation.
We have developed an arbitrary Lagrangian–Eulerian (ALE) technique-based monolithic solver for analyzing fully coupled fluid-structure-electrostatic interactions in micro-electro-mechanical systems (MEMS). Numerical investigations show that fluid compressibility plays a significant role in the dynamics of MEMS actuators, in the cases of constrained flow geometries and high frequency electrostatic actuation. Comparative studies show that the nonlinear compressible Reynolds equation is not always a good approximation to the compressible Navier–Stokes equation, especially at low pressure and high viscosity values.
This work presents a monolithic finite element strategy for the accurate solution of strongly-coupled fluid-structure-electrostatics interaction problems involving a compressible fluid. The complete set of equations for a compressible fluid is employed within the framework of the arbitrary Lagrangian–Eulerian (ALE) fluid formulation on the reference configuration. The proposed numerical approach incorporates geometric nonlinearities of both the structural and fluid domains, and can thus be used for investigating dynamic pull-in phenomena and squeeze film damping in high aspect-ratio micro-electro-mechanical systems (MEMS) structures immersed in a compressible fluid. Through various illustrative examples, we demonstrate the significant influence of fluid compressibility on the dynamics of MEMS devices subjected to constrained geometry and/or high-frequency electrostatic actuation. Moreover, we compare the proposed formulation with the nonlinear compressible Reynolds equation and highlight that, particularly at low pressures and high fluid viscosity, the Reynolds equation fails to provide a reliable approximation to the complete set of equations utilized in our proposed formulation.
1. We proposed a new nonlinear finite element methods for advection-diffusion problems. 2. The new method preserving the discrete strong extremum principle unconditionally. 3. Our method is free from non-physical numerical oscillations with advection dominate regions.
A nonlinear correction technique for finite element methods of advection-diffusion problems on general triangular meshes is introduced. The classic linear finite element method is modified, and the resulting scheme satisfies discrete strong extremum principle unconditionally, which means that it is unnecessary to impose the well-known restrictions on diffusion coefficients and geometry of mesh-cell (e.g., “acute angle” condition), and we need not to perform upwind treatment on the advection term separately. Moreover, numerical example shows that when a discrete scheme does not satisfy the strong extremum principle, even if it maintains the global physical bound, non-physical numerical oscillations may still occur within local regions where no numerical result is beyond the physical bound. Thus, it is worth to point out that our new nonlinear finite element scheme can avoid non-physical oscillations around sharp layers in advection-dominate regions, due to maintaining discrete strong extremum principle. Convergence rates are verified by numerical tests for both diffusion-dominate and advection-dominate problems.
We establish a compact finite difference algorithm in general curvilinear coordinates with fourth-order spatial accuracy and second-order temporal accuracy for the pure streamfunction formulation of the unsteady incompressible Navier-Stokes equations. This method extends the high-order pure streamfunction method to general unsteady flow problems with complex geometry and non-conformal grids. The stability analysis is validated by von-Neumann linear stability analysis. The accuracy and robustness of the newly proposed method are verified by five numerical experiments.
In this paper, a high-order compact finite difference method in general curvilinear coordinates is proposed for solving unsteady incompressible Navier-Stokes equations. By constructing the fourth-order spatial discretization schemes for all partial derivative terms of the pure streamfunction formulation in general curvilinear coordinates, especially for the fourth-order mixed derivative terms, and applying a Crank-Nicolson scheme for the second-order temporal discretization, we extend the unsteady high-order pure streamfunction algorithm to flow problems with more general non-conformal grids. Furthermore, the stability of the newly proposed method for the linear model is validated by von-Neumann linear stability analysis. Five numerical experiments are conducted to verify the accuracy and robustness of the proposed method. The results show that our method not only effectively solves problems with non-conformal grids, but also allows grid generation and local refinement using commercial software. The solutions are in good agreement with the established numerical and experimental results.
Publication date: 1 December 2024
Source: Journal of Computational Physics, Volume 518
Author(s): Alina Chertock, Alexander Kurganov, Michael Redle, Vladimir Zeitlin
Publication date: 1 December 2024
Source: Journal of Computational Physics, Volume 518
Author(s): Petr Knobloch, Dmitri Kuzmin, Abhinav Jha
Publication date: 1 December 2024
Source: Journal of Computational Physics, Volume 518
Author(s): I.M. Wiragunarsa, L.R. Zuhal, T. Dirgantara, I.S. Putra, E. Febrianto
Publication date: 1 December 2024
Source: Journal of Computational Physics, Volume 518
Author(s): Christian Diddens, Duarte Rocha
Publication date: 1 December 2024
Source: Journal of Computational Physics, Volume 518
Author(s): Nguyen Ly, Matthias Ihme
Publication date: 1 December 2024
Source: Journal of Computational Physics, Volume 518
Author(s): Shaoshuai Chu, Alexander Kurganov, Ruixiao Xin
Publication date: 1 December 2024
Source: Journal of Computational Physics, Volume 518
Author(s): Xavier Blanc, Francois Hermeline, Emmanuel Labourasse, Julie Patela
Publication date: 1 December 2024
Source: Journal of Computational Physics, Volume 518
Author(s): Yang Kuang, Yedan Shen, Guanghui Hu
Publication date: 1 December 2024
Source: Journal of Computational Physics, Volume 518
Author(s): Hamad El Kahza, William Taitano, Jing-Mei Qiu, Luis Chacón
Publication date: 1 December 2024
Source: Journal of Computational Physics, Volume 518
Author(s): Yaqian Zhan, Zhongbo Hu, Jisheng Kou, Nan Hong, Qinghua Su
Resolvent analysis is a powerful tool that can reveal the linear amplification mechanisms between the forcing inputs and the response outputs about a base flow. These mechanisms can be revealed in terms of a pair of forcing and response modes and the associated energy gains (amplification magnitude) at a given frequency. The linear relationship that ties the forcing and the response is represented through the resolvent operator (transfer function), which is constructed through spatially discretizing the linearized Navier–Stokes operator. One of the unique strengths of resolvent analysis is its ability to analyze statistically stationary turbulent flows. In light of the increasing interest in using resolvent analysis to study a variety of flows, we offer this guide in hopes of removing the hurdle for students and researchers to initiate the development of a resolvent analysis code and its applications to their problems of interest. To achieve this goal, we discuss various aspects of resolvent analysis and its role in identifying dominant flow structures about the base flow. The discussion in this paper revolves around the compressible Navier–Stokes equations in the most general manner. We cover essential considerations ranging from selecting the base flow and appropriate energy norms to the intricacies of constructing the linear operator and performing eigenvalue and singular value decompositions. Throughout the paper, we offer details and know-how that may not be available to readers in a collective manner elsewhere. Towards the end of this paper, examples are offered to demonstrate the practical applicability of resolvent analysis, aiming to guide readers through its implementation and inspire further extensions. We invite readers to consider resolvent analysis as a companion for their research endeavors.
We present LinStab2D, an easy-to-use linear stability analysis MATLAB tool capable of handling complex domains, performing temporal and spatial linear stability, and resolvent analysis. We present the theoretical foundations of the code, including the linear stability and resolvent analysis frameworks, finite differences discretization schemes, and the Floquet ansatz. These concepts are explored in five different examples, highlighting and illustrating the different code capabilities, including mesh masking, mapping, imposition of boundary constraints, and the analysis of periodic flows using Cartesian or axisymmetric coordinates. These examples were constructed to be a departure point for studying other flows.
Cluster and void formations are key processes in the dynamics of particle-laden turbulence. In this work, we assess the performance of various neural network models for synthesizing preferential concentration fields of particles in turbulence. A database of direct numerical simulations of homogeneous isotropic two-dimensional turbulence with one-way coupled inertial point particles, is used to train the models using vorticity as the input to predict the particle number density fields. We compare encoder–decoder, U-Net, generative adversarial network (GAN), and diffusion model approaches, and assess the statistical properties of the generated particle number density fields. We find that the GANs are superior in predicting clusters and voids, and therefore result in the best performance. Additionally, we explore a concept of “supersampling”, where neural networks can be used to predict full particle data using only the information of few particles, which yields promising perspectives for reducing the computational cost of expensive DNS computations by avoiding the tracking of millions of particles. We also explore the inverse problem of synthesizing the absolute values of the vorticity fields using the particle number density distribution as the input at different Stokes numbers. Hence, our study also indicates the potential use of neural networks to predict turbulent flow statistics using experimental measurements of inertial particles.
The use of heaving and pitching fins for underwater propulsion of engineering devices poses an attractive outlook given the efficiency and adaptability of natural fish. However, significant knowledge gaps need to be bridged before biologically inspired propulsion is able to operate at competitive performances in a practical setting. One of these relates to the design of structures that can leverage passive deformation and active morphing in order to achieve optimal hydrodynamic performance. To provide insights into the performance improvements associated with passive and active fin deformations, we provide here a systematic numerical investigation in the thrust, power, and efficiency of 2D heaving and pitching fins with imposed curvature variations. The results show that for a given chordline kinematics, the use of curvature can improve thrust by 70% or efficiency by 35% over a rigid fin. Maximum thrust is achieved when the camber variations are synchronized with the maximum heave velocity, increasing the overall magnitude of the force vector while increasing efficiency as well. Maximum efficiency is achieved when camber is applied during the first half of the stroke, tilting the force vector to create thrust earlier in the cycle than a comparable rigid fin. Overall, our results demonstrate that curving fins are consistently able to significantly outperform rigid fins with the same chord line kinematics on both thrust and hydrodynamic efficiency.
A previously developed numerical-multilayer modeling approach for systems of governing equations is extended so that unwanted terms, resulting from vertical variations in certain background parameters, can be removed from the dispersion-relation polynomial associated with the system. The new approach is applied to linearized anelastic and compressible systems of governing equations for gravity waves including molecular viscosity and thermal diffusion. The ability to remove unwanted terms from the dispersion-relation polynomial is crucial for solving the governing equations when realistic background parameters, such as horizontal velocity and temperature, with strong vertical gradients, are included. With the unwanted terms removed, previously studied dispersion-relation polynomials, for which methods for defining upgoing and downgoing vertical wavenumber roots already exist, are obtained. The new methods are applied to a comprehensive set of medium-scale time-wavepacket examples, with realistic background parameters, lower boundary conditions at 30 km altitude, and modeled wavefields extending up to 500 km altitude. Results from the compressible and anelastic model versions are compared, with compressible governing-equation solutions understood as the more physically accurate of the two. The new methods provide significantly less computationally expensive alternatives to nonlinear time-step methods, which makes them useful for comprehensive studies of the behavior of viscous/diffusive gravity waves and also for large studies of cases based on observational data. Additionally, they generalize previously existing Fourier methods that have been applied to inviscid problems while providing a theoretical framework for the study of viscous/diffusive gravity waves.
In open flow simulations, the dispersion characteristics of disturbances near synthetic boundaries can lead to unphysical boundary scattering interactions that contaminate the resolved flow upstream by propagating numerical artifacts back into the domain interior. This issue is exacerbated in flows influenced by real or apparent body forces, which can significantly disrupt the normal stress balance along outflow boundaries and generate spurious pressure disturbances. To address this problem, this paper develops a zero-parameter, physics-based outflow boundary condition (BC) designed to minimize pressure scattering from body forces and pseudo-forces and enhance transparency of the artificial boundary. This “balanced outflow BC” is then compared against other common BCs from the literature using example axisymmetric and three-dimensional open swirling flow computations. Due to centrifugal and Coriolis forces, swirling flows are known to be particularly challenging to simulate in open geometries, as these apparent forces induce non-trivial hydrostatic stress distributions along artificial boundaries that cause scattering issues. In this context, the balanced outflow BC is shown to correspond to a geostrophic hydrostatic stress correction that balances the induced pressure gradients. Unlike the alternatives, the balanced outflow BC yields accurate results in truncated domains for both linear and nonlinear computations without requiring assumptions about wave characteristics along the boundary.
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.
The effects of inlet Mach number on the unsteadiness of shock-boundary layer interactions (SBLIs) over curved surfaces are investigated for a supersonic turbine cascade using wall-resolved large eddy simulations. Three inlet Mach numbers, 1.85, 2.00, and 2.15 are considered at a chord-based Reynolds number 395,000. The curved walls of the airfoils impact the SBLIs due to the state of the incoming boundary layers and local pressure gradients. On the suction side, due to the convex wall, the boundary layer entering the SBLI evolves under a favorable pressure gradient and bulk dilatation. On the other hand, the concave wall on the pressure side imposes an adverse pressure gradient and bulk compression. Variations in the inlet Mach number induce different shock impingement locations, enhancing these effects. A detailed characterization of the suction side boundary layers indicates that a higher Mach number leads to larger shape factors, favoring separation and larger bubbles, while the reverse holds for the pressure side. A time-frequency analysis reveals the presence of intermittent events in the separated flow occurring predominantly at low-frequencies on the suction side and at mid-frequencies on the pressure side. Increasing the inlet Mach number leads to an increase in the time scales of the intermittent events on the suction side, which are associated with instants when high-speed streaks penetrate the bubble, causing local flow reattachment and bubble contractions. Instantaneous flow visualizations show the presence of streamwise vortices developing on the turbulent boundary layers on both airfoil sides and along the bubbles. These vortices influence the formation of the large-scale longitudinal structures in the boundary layers, affecting the mass imbalance inside the separation bubbles.
Two-dimensional free-surface flow past a submerged rectangular disturbance in an open channel is considered. The forced Korteweg–de Vries model of Binder et al. (Theor Comput Fluid Dyn 20:125–144, 2006) is modified to examine the effect of varying obstacle length and height on the response of the free-surface. For a given obstacle height and flow rate in the subcritical flow regime an analysis of the steady solutions in the phase plane of the problem determines a countably infinite set of discrete obstacle lengths for which there are no waves downstream of the obstacle. A rich structure of nonlinear behaviour is also found as the height of the obstacle approaches critical values in the steady problem. The stability of the steady solutions is investigated numerically in the time-dependent problem with a pseudospectral method.
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.
