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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 April 2024
Source: Computers & Fluids, Volume 274
Author(s): Yu Jiao, Steffen J. Schmidt, Nikolaus A. Adams
Publication date: 30 April 2024
Source: Computers & Fluids, Volume 274
Author(s): Bo Pang, Yi Ren, Yi Shen, Hao-Ran Liu, Hang Ding
Publication date: 30 April 2024
Source: Computers & Fluids, Volume 274
Author(s): X. Chang, P.R. Wellens
Publication date: 30 April 2024
Source: Computers & Fluids, Volume 274
Author(s): Xuepeng Fu, Shixiao Fu, Chang Liu, Mengmeng Zhang, Qihan Hu
Publication date: 30 April 2024
Source: Computers & Fluids, Volume 274
Author(s): Tianbao Ma, Kun Li, Chentao Wang
Publication date: 30 April 2024
Source: Computers & Fluids, Volume 274
Author(s): Koji Nishiguchi, Tokimasa Shimada, Christian Peco, Keito Kondo, Shigenobu Okazawa, Makoto Tsubokura
Publication date: Available online 27 March 2024
Source: Computers & Fluids
Author(s): Timo Seitz, Peter Gerlinger
Publication date: Available online 8 March 2024
Source: Computers & Fluids
Author(s): Jack R. Edwards, Chinmaya Rajath, Andrew V. Navratil
Publication date: Available online 4 March 2024
Source: Computers & Fluids
Author(s): Junlin Wu, Aoping Peng, Zhihui Li, Xinyu Jiang
Publication date: Available online 15 March 2024
Source: Computers & Fluids
Author(s): Leonidas Gkimisis, Thomas Richter, Peter Benner
A data-driven turbulence model that solves the Reynolds stress transport equation along with the momentum balance is developed, the model is fueled by a source-term that combines the unclosed terms in the Reynolds stress tensor equation. Using neural networks, trained with direct numerical simulations data, we were able to predict this source-term and correct the Reynolds averaged Navier–Stokes flow in the square-duct. This is the first time that machine learning corrections of turbulent flows are driven by a coupled transport equation combined with the momentum equations.
The long lasting demand for better turbulence models and the still prohibitively computational cost of high-fidelity fluid dynamics simulations, like direct numerical simulations and large eddy simulations, have led to a rising interest in coupling available high-fidelity datasets and popular, yet limited, Reynolds averaged Navier–Stokes simulations through machine learning (ML) techniques. Many of the recent advances used the Reynolds stress tensor or, less frequently, the Reynolds force vector as the target for these corrections. In the present work, we considered an unexplored strategy, namely to use the modeled terms of the Reynolds stress transport equation as the target for the ML predictions, employing a neural network approach. After that, we solve the coupled set of governing equations to obtain the mean velocity field. We apply this strategy to solve the flow through a square duct. The obtained results consistently recover the secondary flow, which is not present in the baseline simulations that used the κ−ϵ$$ \kappa -\epsilon $$ model. The results were compared with other approaches of the literature, showing a path that can be useful in the seek of more universal models in turbulence.
This paper develops a three dimensional phase field model, based on a recently improved Allen–Cahn phase field model. The model was discretized using a finite difference method on a half-staggered grid. More important, interfacial tension was expressed in a potential form. The model was tested against a number of cases and was applied to impacts in various conditions. Besides, the model was parallelized using the shared memory parallelism, OpenMP, to facilitate computation.
The traditional Allen–Cahn phase field model doesn't conserve mass and is mostly used in solidification microstructure formation. However, a recently modified Allen–Cahn phase field model has riveted the attention of the academic community. It was obtained by subtracting the curvature-driven flow term from the advective Allen–Cahn phase field model, and thus improves the boundedness of the phase field. More recently, the model has been further refined with the recovered signed distance function to compute interface normal vectors. This paper develops a three dimensional phase field model, based on the abovementioned Allen–Cahn phase field model. The model was discretized using a finite difference method on a half-staggered grid. More important, interfacial tension was expressed in a potential form. The model was tested against a number of cases and was applied to impacts in various conditions. Besides, the model was parallelized using the shared memory parallelism, OpenMP, to facilitate computation.
Cascaded collision operator is adapted to multilayer shallow water flows. Two sets of particle distribution function (PDF) are solved separately, with external forces modeling the mutual actions between the two layers. The model is able to reproduce ideal dam break flows and gravity currents.
Many environmental phenomena, such as flows in rivers or in coastal region can be characterised by means of the ‘shallow approach’. A multi-layer scheme allows to extend it to density layered shallow water flows (e.g., gravity currents). Although a variety of models allowing numerical investigation of single and multi-layer shallow water flows, based on continuum and particle approaches, have been widely discussed, there are still some computational aspects that need further investigation. Focusing on the Lattice Boltzmann models (LBM), available multi-layer models generally use the standard linear collision operator (CO). In this work we adopt a multi relaxation time (MRT) cascaded collision operator to develop a two-layered liquid Lattice-Boltzmann model (CaLB-2). Specifically, the model solves the shallow water equations, taking into account two separate sets of particle distribution function (PDF), one for each layer, solved separately. Layers are connected through coupling terms, defined as external forces that model the mutual actions between the two layers. The model is validated through comparisons with experimental and numerical results from test cases available in literature. First results are very promising, highlighting a good correspondence between simulation results and literature benchmarks.
The auxiliary boundary condition must be specified for the discontinuous finite element methods (e.g., DG, SD, FR/CPR) to evaluate the solution gradients. Since the velocity gradient near the wall is not fully resolved in the WMLES grid, we recommend a looser auxiliary condition than the usual no-slip condition. Superior performance of the proposed WMLES framework was confirmed for a benchmarking non-equilibrium periodic hill flow with curvilinear walls compared to the results of an algebraic WMLES and a DDES.
To robustly and accurately simulate wall-bounded turbulent flows at high Reynolds numbers, we propose suitable boundary treatments for wall-modeled large-eddy simulation (WMLES) coupled with a high-order flux reconstruction (FR) method. First, we show the need to impose an auxiliary boundary condition on auxiliary variables (solution gradients) that are commonly introduced in high-order discontinuous finite element methods (DFEMs). Auxiliary boundary conditions are introduced in WMLES, where the grid resolution is too coarse to resolve the inner layer of a turbulent boundary layer. Another boundary treatment to further enhance stability with under-resolved grids, is the use of a modal filter only in the wall-normal direction of wall-adjacent cells to remove the oscillations. A grid convergence study of turbulent channel flow with a high Reynolds number (Reτ≈5200$$ R{e}_{\tau}\approx 5200 $$) shows that the present WMLES framework accurately predicts velocity profiles, Reynolds shear stress, and skin friction coefficients at the grid resolutions recommended in the literature. It was confirmed that a small amount of filtering is sufficient to stabilize computation, with negligible influence on prediction accuracy. In addition, non-equilibrium periodic hill flow with a curved wall, including flow separation, reattachment, and acceleration at a high Reynolds number (Reh≈37,000$$ R{e}_h\approx 37,000 $$), is reported. Considering stability and the prediction accuracy, we recommend a loose auxiliary wall boundary conditions with a less steep velocity gradient for WMLES using high-order DFEMs.
The boundary data immersion method smears the fluid-structure interface in the smoothing region and incurs deviations. The proposed algorithm switches to lower order difference schemes near the interfaces and applies adaptive mesh refining there to compensate the accuracy loss.
The fluid-structure interaction is simulated using the boundary data immersion method. As the fluid-structure interface is smeared in the smoothing region, deviations are incurred in fluid simulations. For compressible flow, high order difference schemes with more mesh cells for the stencils are usually employed to achieve high overall accuracy, but near interfaces it requires wider smoothing region of several mesh cells for computational stability and hence lowers its accuracy significantly. To address this issue, the proposed algorithm switches to lower order difference schemes near the interfaces and applies adaptive mesh refining there to compensate the accuracy loss. Implemented with Structured Adaptive Mesh Refinement Application Infrastructure (SAMRAI), the algorithm shows notable improvement in the overall accuracy and efficiency in cases such as channel flow and flow past a cylinder. The algorithm is used to simulate the shock wave past a fixed or free cylinder with Ma =2.67$$ =2.67 $$ and Re =1482$$ =1482 $$, which reveals the relaxation process and the temporal evolution of the drag coefficient, it goes through a valley and maintains at relatively high value for the fixed cylinder, while that of the free cylinder tends to decrease in fluctuation which is found to be caused by the interaction between the forward moving cylinder and vortexes in the unsteady wake.
In this article, the implicit-explicit RK time discretization coupled with LDG spatial discretization numerical algorithm for the micropolar fluid equations are presented. Moreover, the stability of the first-order and second-order fully discrete method are proved. Finally, the numerical experiments are given to verify the theoretical order and effectiveness of the presented method.
In this article, the spatial local discontinuous Galerkin (LDG) approximation coupled with the temporal implicit-explicit Runge–Kutta (RK) evolution for the micropolar fluid equations are adopted to construct the discretization method. To avoid the incompressibility constraint, the artificial compressibility strategy method is used to convert the micropolar fluid equations into the Cauchy–Kovalevskaja type equations. Then the LDG method based on the modal expansion and the implicit-explicit RK method are properly combined to construct the expected third-order method. Theoretically, the unconditionally stable of the fully discrete method are derived in multidimensions for triangular meshs. And the numerical experiments are given to verify the theoretical and effectiveness of the presented methods.
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 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.
For challenging volume-of-fluid based simulations of turbulent bubbly flows characterized by high Reynolds numbers, significant bubble deformations and large-eddy-simulation-like grid resolutions, severe volume errors for the gas phase can accumulate. To avoid this, two methods to accurately conserve the gas volume are proposed, which allow to perform numerical simulations that have previously been out of reach for this numerical framework. Their reliability is demonstrated based on an investigation of global flow characteristics and individual bubble dynamics.
This study proposes two different strategies to enforce accurate volume conservation in volume-of-fluid (VOF)-based simulations of turbulent bubble-laden flows on coarse grids. It is demonstrated that, without a correction, minimal volume errors on a time-step level, caused by the under-resolution of the interface, can accumulate to significant deviations from the intended flow conditions despite the comparably good volume conservation properties of the geometric VOF method. In particular, large volume errors are observed for challenging setups combining coarse grid resolutions and comparably high Reynolds and Eötvös numbers. The problem is reinforced for long-term simulations in periodic domains, which are often performed to collect flow statistics of bubbly flows. The first proposed volume conservation method simply corrects the volume error of a bubble by uniformly adding or removing the respective amount of gas volume in the interface cells. The second proposed method performs an additional reconstruction and advection step of the VOF field using a non-divergence-free velocity field, which can be interpreted as a slight dilatation or contraction of the bubble. A comparison between the global flow statistics as well as the individual bubble dynamics for both volume conservation methods reveals that the results are quasi-identical for a number of challenging test cases, while the gas volume is accurately conserved. The proposed methods allow to perform numerical simulations of freely deformable bubbles in turbulent flows for setups that have previously been out of reach for this numerical framework.
A piecewise circular interface construction (PCIC) method is described, where height functions-based curvature estimates are directly utilised for interface reconstruction under the volume of fluid method. Compared against PLIC methods, the present method supplies superior and consistent reconstructed interface in combination with an accurate radius of curvature. The method is integrated within a robust balanced force two phase flow solver and extensively validated against flow problems with complex interface dynamics.
A piecewise circular interface construction (PCIC) method is described, where height functions based curvature estimates are directly utilised for accurate interface reconstruction under the framework of volume of fluid method. The present work is an attempt to develop a robust and accurate higher order interface reconstruction algorithm that is capable of accurate simulation of surface tension dominated flows. The proposed hybrid method (H-PCIC) is thus able to take advantage of merits of both PCIC and HF methods, achieving at least second order convergence with respect to both interface reconstruction and curvature computation. This is in addition to the significantly superior quality of the reconstructed interface with respect to PLIC methods. This seamless blending of the HF and PCIC quantities is enabled by c0-correction procedures applied to base PLIC and initial PCIC steps. More recent variants of the height function method with variable stencil size are used for calculation of radius of curvature. The capability of this proposed method towards simulation of flow problems within a well-balanced two-phase solver is established with help of multiple complex two-phase flow problems. This validation exercise also demonstrates the capability of PCIC class of methods towards solutions of two-phase flows with intricate physics.
Publication date: 15 May 2024
Source: Journal of Computational Physics, Volume 505
Author(s): Thomas Chuna, Irina Sagert, Michael S. Murillo, Jeffrey R. Haack
Publication date: 15 May 2024
Source: Journal of Computational Physics, Volume 505
Author(s): Zhigang Pu, Chang Liu, Kun Xu
Publication date: 15 May 2024
Source: Journal of Computational Physics, Volume 505
Author(s): Eric J. Ching, Ryan F. Johnson, Andrew D. Kercher
Publication date: 15 May 2024
Source: Journal of Computational Physics, Volume 505
Author(s): Eric J. Ching, Ryan F. Johnson, Andrew D. Kercher
Publication date: 15 May 2024
Source: Journal of Computational Physics, Volume 505
Author(s): Ryosuke Ida, Yoshiharu Tamaki, Soshi Kawai
Publication date: 15 May 2024
Source: Journal of Computational Physics, Volume 505
Author(s): Jie Du, Yang Yang, Fangyao Zhu
Publication date: 15 May 2024
Source: Journal of Computational Physics, Volume 505
Author(s): Yingzhe Li, Florian Holderied, Stefan Possanner, Eric Sonnendrücker
Publication date: 15 May 2024
Source: Journal of Computational Physics, Volume 505
Author(s): Haodong Zhang, Fei Wang, Britta Nestler
Publication date: 15 May 2024
Source: Journal of Computational Physics, Volume 505
Author(s): R.C. Moura, L.D. Fernandes, A.F.C. da Silva, S.J. Sherwin
Publication date: 15 May 2024
Source: Journal of Computational Physics, Volume 505
Author(s): S. Guisset, G. Damour, J. Breil
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.
The focus here is on a thin solid body passing through a channel flow and interacting with the flow. Unsteady two-dimensional interactive properties from modelling, analysis and computation are presented along with comparisons. These include the effects of a finite dilation or constriction, as the body travels through, and the effects of a continuing expansion of the vessel. Finite-time clashing of the body with the channel walls is investigated as well as the means to avoid clashing. Sustained oscillations are found to be possible. Wake properties behind the body are obtained, and broad agreement in trends between full-system and reduced-system responses is found for increased body mass.
Under the low-noise Mach 3 flight conditions for a supersonic passenger aircraft having unswept wings with a thin parabolic airfoil, laminar-turbulent transition is due to amplification of the first mode. Stability of a local self-similar boundary layer over such a wing is investigated both using the \(e^{N}\) method in the framework of linear stability theory and direct numerical simulation (DNS). It is found that the instability amplitude should reach a maximum over the entire spectral range above the profiles of 2.5% and thicker. The locus of maximum appears at the trailing edge and moves to the leading edge as the profile becomes thicker, while the maximum amplitude decreases. The theoretical findings are supported by DNS of the linear wave packets propagating in the boundary layer. Significance of these results to the design of laminar supersonic wings is discussed.
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.
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.
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.
A theoretical and experimental study was conducted to investigate the effect of injection angle on surface waves. Linear stability theory was utilized to obtain the analytical relation. In the experimental study, high-speed photography and shadowgraph techniques were used. Image processing codes were developed to extract information from photos. The results obtained from the theoretical relation were validated with the experimental results at different injection angles. In addition, at the injection angle of 90 \({^\circ }\) , the theoretical results were evaluated with the experimental results of other researchers. This evaluation showed that the theory results were in good agreement with the experimental data. The proper orthogonal decomposition (POD) and the power spectra density (PSD) analysis were also used to investigate the effect of the injection angle on the flow structures. The results obtained from the linear stability were used to determine the maximum waves’ growth rate, and a relation was presented for the breakup length of the liquid jet at different injection angles. The breakup length results were compared with theory and published experimental data. The presented relation is more consistent with experimental data than other theories due to considering the nature of waves. The results showed that the instability of the liquid jet is influenced by three forces: inertial, surface tension, and aerodynamic. Therefore, Rayleigh–Taylor, Kelvin–Helmholtz, Rayleigh–Plateau, and azimuthal instabilities occur in the process. Decreasing the injection angle changes the nature of waves and shifts from Rayleigh–Taylor to Kelvin–Helmholtz. That reduces the wavelength and increases the growth rate of the waves. Axial waves have a significant impact on the physics of the waves and influence parameters. If axial waves are not formed, the growth rate of the waves is independent of the injection angle. An increase in the gas Weber number causes a change in the type of dominant waves and a greater instability of the liquid jet. In contrast, an increase in the liquid Weber number causes an enhancement in the resistance of the liquid jet against the transverse flow without changing the type of the dominant waves. Decreasing the density ratio reduces the effect of Rayleigh–Taylor waves and strengthens the Kelvin–Helmholtz waves. It causes two trends to be observed for the growth rate of waves at low spray angles, while one trend occurs at high spray angles.
The effect of non-Boltzmann energy distributions on the free propagation of shock waves through a monoatomic gas is investigated via theory and simulation. First, the non-Boltzmann heat capacity ratio \(\gamma \) , as a key property for describing shock waves, is derived from first principles via microcanonical integration. Second, atomistic molecular dynamics simulations resembling a shock tube setup are used to test the theory. The presented theory provides heat capacity ratios ranging from the well-known \(\gamma = 5/3\) for Boltzmann energy-distributed gas to \(\gamma \rightarrow 1\) for delta energy-distributed gas. The molecular dynamics simulations of Boltzmann and non-Boltzmann driven gases suggest that the shock wave propagates about 9% slower through the non-Boltzmann driven gas, while the contact wave appears to be about 4% faster if it trails non-Boltzmann driven gas. The observed slowdown of the shock wave through applying a non-Boltzmann energy distribution was found to be consistent with the classical shock wave equations when applying the non-Boltzmann heat capacity ratio. These fundamental findings provide insights into the behavior of non-Boltzmann gases and might help to improve the understanding of gas dynamical phenomena.
A low-order physics-based model to simulate the unsteady flow response to airfoils undergoing large-amplitude variations of the camber is presented in this paper. Potential-flow theory adapted for unsteady airfoils and numerical methods using discrete-vortex elements are combined to obtain rapid predictions of flow behavior and force evolution. To elude the inherent restriction of thin-airfoil theory to small flow disturbances, a time-varying chord line is proposed in this work over which to satisfy the appropriate boundary condition, enabling large deformations of the camber line to be modeled. Computational fluid dynamics simulations are performed to assess the accuracy of the low-order model for a wide range of dynamic trailing-edge flap deflections. By allowing the chord line to rotate with trailing-edge deflections, aerodynamic loads predictions are greatly enhanced as compared to the classical approach where the chord line is fixed. This is especially evident for large-amplitude deformations.