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Publication date: 15 April 2024
Source: Computers & Fluids, Volume 273
Author(s): Nan Zhang
Publication date: 15 April 2024
Source: Computers & Fluids, Volume 273
Author(s): Pedro Paredes, Meelan Choudhari, Mark H. Carpenter, Fei Li
Publication date: Available online 20 February 2024
Source: Computers & Fluids
Author(s): Xuepeng Fu, Shixiao Fu, Chang Liu, Mengmeng Zhang, Qihan Hu
Publication date: Available online 16 February 2024
Source: Computers & Fluids
Author(s): X. Chang, P.R. Wellens
Publication date: Available online 6 February 2024
Source: Computers & Fluids
Author(s): Yu Jiao, Steffen J. Schmidt, Nikolaus A. Adams
Publication date: Available online 8 February 2024
Source: Computers & Fluids
Author(s): James G. Coder, Benjamin L.S. Couchman, Marshall C. Galbraith, Steven R. Allmaras, Nick Wyman
Publication date: 15 April 2024
Source: Computers & Fluids, Volume 273
Author(s): Pratik Suchde, Heinrich Kraus, Benjamin BockMarbach, Jörg Kuhnert
Publication date: 15 April 2024
Source: Computers & Fluids, Volume 273
Author(s): Alex J. Lang, David P. Connolly, Gregory de Boer, Shahrokh Shahpar, Benjamin Hinchliffe, Carl A. Gilkeson
Publication date: 15 April 2024
Source: Computers & Fluids, Volume 273
Author(s): Jiangxu Huang, Lei Wang, Xuguang Yang
Publication date: 30 April 2024
Source: Computers & Fluids, Volume 274
Author(s): Koji Nishiguchi, Tokimasa Shimada, Christian Peco, Keito Kondo, Shigenobu Okazawa, Makoto Tsubokura
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 onestep fullydiscrete scheme, and constructs a thirdorder scheme which is written into a compact form via a new limiter. The highlights of this study and advantages of new thirdorder scheme are as follows: ① We proposed a very simple new methodology of constructing onestep, consistent highorder and nonoscillation schemes that do not rely on Runge–Kutta method; ② We systematically studied new scheme's theoretical problems about entropy conditions, error analysis, and nonoscillation 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 shockcapturing 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 multidimensional 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.
A parallel graddiv 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 graddiv 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.
The present study shows that the number of particle timesteps required to reach the statistically steadystate condition is at least onesixth 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 particletrackingmanaging algorithm in the framework of a hybrid pressurebased finitevolume/probabilitydensityfunction (FV/PDF) MonteCarlo (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 velocityturbulent frequency joint PDF equation in turbulent flow simulations. Contrary to the densitybased algorithms, the pressurebased algorithms have stable convergence rates even in zeroMach 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 timestep. Also, they had to calculate the linear basis functions at every timestep to estimate the particle mean fields and interpolate the data. These calculations would be computationally very expensive, timeconsuming, and inefficient in computational domains with arbitraryshaped 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 bluffbody 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 timesteps required to reach the statistically steadystate condition is at least onesixth less than the previously developed algorithms. This also approves a faster convergence rate for the present hybrid pressurebased algorithm.
This study presents a stabilized PFEM formulation to simulate an incompressible fluid with freesurface flow. Comparisons results demonstrate the strong ability of the proposed stabilized PFEM to solve incompressible freesurface flow with high accuracy and promising application prospects.
In simulations using the particle finite element method (PFEM) with nodebased strain smoothing technique (NSPFEM) to simulate the incompressible flow, spatial and temporal instabilities have been identified as crucial problems. Accordingly, this study presents a stabilized NSPFEMFIC formulation to simulate an incompressible fluid with freesurface flow. In the proposed approach, (1) stabilization is achieved by implementing the gradient strain field in place of the constant strain field over the smoothing domains, handling spatial and temporal instabilities in direct nodal integration; (2) the finite increment calculus (FIC) stabilization terms are added using nodal integration, and a threestep fractional step method is adopted to update pressures and velocities; and (3) a novel slip boundary with the predictor–corrector algorithm is developed to deal with the interaction between the freesurface flow with rigid walls, avoiding the pressure concentration induced by standard noslip condition. The proposed stabilized NSPFEMFIC is validated via several classical numerical cases (hydrostatic test, water jet impinging, water dam break, and water dam break on a rigid obstacle). Comparisons of all simulations to the experimental results and other numerical solutions reveal good agreement, demonstrating the strong ability of the proposed stabilized NSPFEMFIC to solve incompressible freesurface flow with high accuracy and promising application prospects.
In the present study, describes the rheological transition from dry to wet sedimentary materials as a transition from shear thinning behavior to shear thickness behavior. This transition can clearly have a significant effect on saturated materials. In this study, a transition period is defined which the sliding materials are saturated. Although this period is constant, for each particle based on the time it reaches the initial water level, it is separately initialized.
Landslides, which are the sources of most catastrophic natural disasters, can be subaerial (dry), submerged (underwater), or semisubmerged (transitional). Semisubmerged or transitional landslides occur when a subaerial landslide enters water and turns to submerged condition. Predicting the behavior of such a highly dynamic multiphase granular flow system is challenging, mainly due to the water entry effects, such as wave impact and partial saturation (and resulted cohesion). The meshfree particle methods, such as the moving particle semiimplicit (MPS) method, have proven their capabilities for the simulation of the highly dynamic multiphase systems. This study develops and evaluates a numerical model, based on the MPS particle method in combination with the μ(I) rheological model, to simulate the morphodynamic of the granular mass in semisubmerged landslides in two and three dimensions. An algorithm is developed to consider partial saturation (and resulting cohesion) during the water entry. Comparing the numerical results with the experimental measurements shows the ability of the proposed model to accurately reproduce the morphological evolution of the granular mass, especially at the moment of water entry.
Many physical and industrial problems comprise one or more moving parts, which change the flow domain during a process, such as lubrication and mixing. For such problems, we have suggested a new method, which uses a fixed background mesh to avoid the timeconsuming task of boundaryfitted grid generation. The new technique, which is based on the finite element method, uses the moving leastsquares interpolation functions, where the solid and fluid meet each other in the flow domain.
With the assistance of the moving leastsquares (MLS) interpolation functions, a twodimensional finite element code is developed to consider the effects of a stationary or moving solid body in a flow domain. At the same time, the mesh or grid is independent of the shape of the solid body. We achieve this goal in two steps. In the first step, we use MLS interpolants to enhance the pressure (P) and velocity (V) shape functions. By this means, we capture different discontinuities in a flow domain. In our previous publications, we have named this technique the PVMLS method (pressure and velocity shape functions enhanced by the MLS interpolants) and described it thoroughly. In the second step, we modify the PVMLS method (the MPVMLS method) to consider the effect of a solid part(s) in a flow domain. To evaluate the new method's performance, we compare the results of the MPVMLS method with a finite element code that uses boundaryfitted meshes.
A weighted essentially nonoscillatorybased gas kinetic flux solver for viscous compressible flow is proposed. The proposed CGKFS could improve the accuracy because the highorder WENO scheme is adopted. The current method can use fewer grids to achieve more details of viscous compressible flows.
Although the gas kinetic schemes (GKS) have emerged as one of the powerful tools for simulating compressible flows, they exhibit several shortcomings. Since the local solution of continuous Boltzmann equation with the Maxwellian distribution function is used to calculate the numerical fluxes at the cell interface, the flux expression in GKS is usually more complicated. In this paper, a highorder simplified gas kinetic flux solver (GKFS) is presented for simulating twodimensional compressible flows. Circular functionbased GKFS (CGKFS), which simplifies the Maxwellian distribution function into the circular function, combined with an improved weighted essentially nonoscillatory (WENOZ) scheme is applied to capture more details of the flow fields with fewer grids. As a result, a simple highorder accurate CGKFS is obtained, which improves the computing efficiency and reduce its complexity to facilitate the practical application of engineering. A series of benchmarktest problems are simulated and good agreement can be obtained compared with the references, which demonstrate that the highorder CGKFS can achieve the desired accuracy.
An adaptive sharp immersed method is proposed to simulate electrohydrodynamic flows accompanied by ion evaporation. A splitting errorfree iterative projection algorithm is used to solve the Navier–Stokes equations, and a robust iterative algorithm is used to address the surface charge transport. Our simulations captured the protrusion structure caused by charge evaporation and showed that charge evaporation can suppress the sharp development of Taylor cones at the ends of the drops.
This article presents a sharp immersed method for simulating electrohydrodynamic (EHD) flows that involve charge evaporation. This wellknown multiscale, multiphysics problem is widely used in various fields, including industry and medicine. The method adopts a fully sharp model, where surface tension and Maxwell stress are treated as surface forces and free charges are concentrated on the zero thickness liquidvacuum interface. Incorporating charge evaporation imposes strict restrictions on the timestep, as the rate of evaporation sharply increases with surface evolution. To overcome this challenge, an iterative algorithm that couples the electric field and surface charge density is proposed to obtain accurate results, even with significantly large timesteps. To mitigate the numerical residuals near the interface, which may introduce parasitic flows and cause numerical instability, an immersed interface methodbased iterative projection method for the Navier–Stokes equations is proposed, in which a traction boundary condition involving multiple surface forces is imposed on the sharp interface. Numerical experiments were carried out, and the results show that the method is splittingerrorfree and stable. The sharp immersed method is applied to simulate the electricinduced deformation of an ionic liquid drop with charge evaporation. The results indicate that charge evaporation can suppress the sharp development of Taylor cones at the ends of the drops. These findings have significant implications for the design and optimization of EHD systems in various applications.
A hybrid explicit/implicit method is developed to accommodate the nonlinear vibroacoustic interaction. Theoretical formulations for stability analysis of the implicit methods is proposed and verified numerically. The methods are applied to investigate the nonlinear dynamic behaviors of a coupled hyperelastic elliptical ring and infinite acoustic fluid system. An interesting nonlinear phenomenon of 4:2:1 internal resonance is simulated and discussed.
This paper addresses the challenges in studying the interaction between highintensity sound waves and largedeformable hyperelastic solids, which are characterized by nonlinearities of the hyperelastic material, the finiteamplitude acoustic wave, and the largedeformable fluid–solid interface. An implicit coupling method is proposed for predicting nonlinear structuralacoustic responses of the largedeformable hyperelastic solid submerged in a compressible viscous fluid of infinite extent. An arbitrary Lagrangian–Eulerian (ALE) formulation based on an unsplit complexfrequencyshifted perfectly matched layer method is developed for longtime simulation of the nonlinear acoustic wave propagation without exhibiting longtime instabilities. The solid and acoustic fluid domains are discretized using the finite element method, and two different options of staggered implicit coupling procedures for nonlinear structuralacoustic interactions are developed. Theoretical formulations for stability analysis of the implicit methods are provided. The accuracy, robustness, and convergence properties of the proposed methods are evaluated by a benchmark problem, that is, a hyperelastic rod interacting with finiteamplitude acoustic waves. The numerical results substantiate that the present methods are able to provide longtime steadystate solutions for a nonlinear coupled hyperelastic solid and viscous acoustic fluid system without numerical constraints of small time step sizes and longtime instabilities. The methods are applied to investigate nonlinear dynamic behaviors of coupled hyperelastic elliptical ring and acoustic fluid systems. Physical insights into 2:1 and 4:2:1 internal resonances of the hyperelastic elliptical ring and perioddoubling bifurcations of the structural and acoustic responses of the system are provided.
Publication date: 1 April 2024
Source: Journal of Computational Physics, Volume 502
Author(s): Shixiao Willing Jiang, Rongji Li, Qile Yan, John Harlim
Publication date: 1 April 2024
Source: Journal of Computational Physics, Volume 502
Author(s): Tao Yin, Lu Zhang, Xiaopeng Zhu
Publication date: 1 April 2024
Source: Journal of Computational Physics, Volume 502
Author(s): Joris Cazé, Fabien Petitpas, Eric Daniel, Matthieu Queguineur, Sébastien Le Martelot
Publication date: 1 April 2024
Source: Journal of Computational Physics, Volume 502
Author(s): Merel A. Schalkers, Matthias Möller
Publication date: 1 April 2024
Source: Journal of Computational Physics, Volume 502
Author(s): Liwei Lu, Zhijun Zeng, Yan Jiang, Yi Zhu, Pipi Hu
Publication date: 1 April 2024
Source: Journal of Computational Physics, Volume 502
Author(s): Elena Zappon, Andrea Manzoni, Alfio Quarteroni
Publication date: 1 April 2024
Source: Journal of Computational Physics, Volume 502
Author(s): J. Husson, M. Terracol, S. Deck, T. Le Garrec
Publication date: 1 April 2024
Source: Journal of Computational Physics, Volume 502
Author(s): Tianyi Chu, Oliver T. Schmidt
Publication date: 1 April 2024
Source: Journal of Computational Physics, Volume 502
Author(s): Xinjie Wang, Maoquan Sun, Yundong Guo, Chunxin Yuan, Xiang Sun, Zhiqiang Wei, Xiaogang Jin
Publication date: 1 April 2024
Source: Journal of Computational Physics, Volume 502
Author(s): YuHong Yeung, David A. BarajasSolano, Alexandre M. Tartakovsky
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 nearground 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 nearsingular 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 largescale sidetoside oscillations. In the case of \(\text {Fr}=1\) , the plate motion is a combination of sidetoside 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.
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, highspeed 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 focus here is on a thin solid body passing through a channel flow and interacting with the flow. Unsteady twodimensional 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. Finitetime 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 fullsystem and reducedsystem responses is found for increased body mass.
Recently, Rim (Ocean Engng 239:711, 2021; J Ocean Engng Mar Energy 9:4151, 2023 ) suggested an exact DtN artificial boundary condition to study the threedimensional wave diffraction by stationary bodies. This paper is concerned with threedimensional linear interaction between a submerged oscillating body with arbitrary shape and the regular water wave with finite depth. An exact DirichlettoNeumann (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 6DoF oscillatory motion of the body under the free surface wave.
The effect of nonBoltzmann energy distributions on the free propagation of shock waves through a monoatomic gas is investigated via theory and simulation. First, the nonBoltzmann 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 wellknown \(\gamma = 5/3\) for Boltzmann energydistributed gas to \(\gamma \rightarrow 1\) for delta energydistributed gas. The molecular dynamics simulations of Boltzmann and nonBoltzmann driven gases suggest that the shock wave propagates about 9% slower through the nonBoltzmann driven gas, while the contact wave appears to be about 4% faster if it trails nonBoltzmann driven gas. The observed slowdown of the shock wave through applying a nonBoltzmann energy distribution was found to be consistent with the classical shock wave equations when applying the nonBoltzmann heat capacity ratio. These fundamental findings provide insights into the behavior of nonBoltzmann gases and might help to improve the understanding of gas dynamical phenomena.
Under the lownoise Mach 3 flight conditions for a supersonic passenger aircraft having unswept wings with a thin parabolic airfoil, laminarturbulent transition is due to amplification of the first mode. Stability of a local selfsimilar 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.
An adjointbased 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 secondorder 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.
A loworder physicsbased model to simulate the unsteady flow response to airfoils undergoing largeamplitude variations of the camber is presented in this paper. Potentialflow theory adapted for unsteady airfoils and numerical methods using discretevortex elements are combined to obtain rapid predictions of flow behavior and force evolution. To elude the inherent restriction of thinairfoil theory to small flow disturbances, a timevarying 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 loworder model for a wide range of dynamic trailingedge flap deflections. By allowing the chord line to rotate with trailingedge deflections, aerodynamic loads predictions are greatly enhanced as compared to the classical approach where the chord line is fixed. This is especially evident for largeamplitude deformations.
Flickering buoyant diffusion methane flames in weakly rotatory flows were computationally and theoretically investigated. The prominent computational finding is that the flicker frequency nonlinearly increases with the nondimensional rotational intensity R (up to 0.24), which is proportional to the nondimensional circumferential circulation. This finding is consistent with the previous experimental observations that rotatory flows enhance flame flicker to a certain extent. Based on the vortexdynamical understanding of flickering flames that the flame flicker is caused by the periodic shedding of buoyancyinduced toroidal vortices, a scaling theory is formulated for flickering buoyant diffusion flames in weakly rotatory flows. The theory predicts that the increase of flicker frequency f obeys the scaling relation \(\left( ff_{0} \right) \propto R^{2}\) , which agrees very well with the present computational results. In physics, the external rotatory flow enhances the radial pressure gradient around the flame, and the significant baroclinic effect \(\mathrm {\nabla }p\times \mathrm {\nabla }\rho \) contributes an additional source for the growth of toroidal vortices so that their periodic shedding is faster.