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Relevant analyses are presented on the base of the compressible vortex method for simulating the development of two or three co-rotating vortices with different characteristic Mach numbers. The paper aims to discuss this issue.

In addition to having vorticity and dilatation properties, the vortex particles also carry density, enthalpy, and entropy. Taking co-rotating vortices in two-dimensional unsteady compressible flow for an example, truncation of unbounded domains via a nonreflecting boundary condition was considered in order to make the method computationally efficient.

For two identical vortices, the effect of the vortex Mach number on merging process is not evident; if two vortices have the same circulation rather than different radiuses, the vorticity and dilatation fields of the vortex under a vortex Mach number will be absorbed by the vortex under a higher vortex Mach number. For three vortices, if the original arrangement of the vortices is changed, the evolvement of the vorticity and dilatation fields is different.

The paper reveals new mechanism of the three co-rotating vortices by a feasible compressible vortex method.

Advancements in aerospace technologies, which rely on unsteady fluid dynamics, are being hindered by a lack of easy to use, computationally efficient unsteady computational fluid dynamics (CFD) software. Existing CFD platforms are capable of handling unsteady flapping, but the time, money and expertise required to run even a basic flapping simulation make design iteration and optimization prohibitively expensive for the average researcher.

In the present paper, a remedy to model the effects of viscosity is introduced to the original vortex method, in which the pitching moment amplitude grew over time for simulations involving multiple flapping cycles. The new approach described herein lumps far-field wake vortices to mimic the vortex decay, which is shown to improve the accuracy of the solution while keeping the pitching moment amplitude under control, especially for simulations involving many flapping cycles.

In addition to improving the accuracy of the solution, the new method greatly reduces the computation time for simulations involving many flapping cycles. The solution of the original vortex method and the new method are compared to published Navier–Stokes solver data and show very good agreement.

By utilizing a novel unsteady vortex method, which has been designed specifically to handle the highly unsteady flapping wing problems, it has been shown that the time to compute a solution is reduced by several orders of magnitude (Denda et al., 2016). Despite the success of the vortex method, especially for a small number of flapping cycles, the solution deteriorates as the number of flapping cycles increases due to the inherent lack of viscosity in the vortex method.

The purpose of this study is to design numerical simulations of bubbly flow around a cylinder to better understand the characteristics of flow around a rigid obstacle.

The bubbly flow around a circular cylinder was numerically simulated using a semi-Lagrangian–Lagrangian method composed of a vortex-in-cell method for the liquid phase and a Lagrangian description of the gas phase. Additionally, a penalization method was applied to account for the cylinder inside the flow. The slip condition of the bubbles on the cylinder’s surface was enforced, and the outflow conditions were applied to the liquid flow at the far field.

The simulation clarified the characteristics of a bubbly flow around a circular cylinder. The bubbles were shown to move around and separate from both sides of the cylinder, because of entrainment by the liquid shear layers. Once the bubbly flow fully developed, the bubbles distributed into groups and were dispersed downstream of the cylinder. A three-dimensional vortex structure of various scales was also shown to form downstream, whereas a quasi-stable two-dimensional vortex structure was observed upstream. Overall, the proposed method captured the characteristics of a bubbly flow around a cylinder well.

A semi-Lagrangian–Lagrangian approach was applied to simulate a bubbly flow around a circular cylinder. The simulations provided the detail features of these flow phenomena.

The purpose of this paper is to develop a Vortex-In-Cell (VIC) method with the semi-Lagrangian scheme and apply it to the high-Re lid-driven cavity flow.

The VIC method is developed for simulating high Reynolds number incompressible flow. A semi-Lagrangian scheme is incorporated in the convection term to produce unconditional stability, which gets rid of the constraint of the convection Courant-Friedrichs-Lewy (CFL) condition; the adaptive time step is used to maintain the numerical stability of the diffusion term; and the velocity boundary condition is readily converted to the vorticity formulation to suit discontinuous boundary treatment. The VIC simulation results are compared with those produced by other gird methods reported in open literature studies.

The lid-driven cavity flow is simulated from Re = 100 to 100,000. Similar vortex birth mechanisms are exhibited though, but distinct flow characteristics are revealed. At Re = 100 to 7,500, the cavity flow is confirmed steady. At Re = 10,000, 15,000 and 20,000, the cavity flow is periodical with a primary vortex held spatially at the center. In particular, at Re = 100,000 highly turbulent characteristics is first revealed and an analogous primary vortex is formed but in motion rather than stationary, which is caused by the considerable flow separation at all the boundaries.

In the lid-driven cavity, the flow becomes extremely complex and highly turbulent at Re = 100,000, and the analogous primary vortex structure is observed. Boundary layer separation is observed at all walls, producing small vortices and causing the displacement of the analogous primary vortex. Such a finding original and has not yet been reported by other investigators. It may provide a basis for conducting in-depth studies of the lid-driven cavity flow.

This study aims to provide discussions of the numerical method and the bubbly flow characteristics of an annular bubble plume.

The bubbles, released from the annulus located at the bottom of the domain, rise owing to buoyant force. These released bubbles have diameters of 0.15–0.25 mm and satisfy the bubble flow rate of 4.1 mm³/s. The evolution of the three-dimensional annular bubble plume is numerically simulated using the semi-Lagrangian–Lagrangian (semi-L–L) approach. The approach is composed of a vortex-in-cell method for the liquid phase and a Lagrangian description of the gas phase.

First, a new phenomenon of fluid dynamics was discovered. The bubbly flow enters a transition state with the meandering motion of the bubble plume after the early stable stage. A vortex structure in the form of vortex rings is formed because of the inhomogeneous bubble distribution and the fluid-surface effects. The vortex structure of the flow deforms as three-dimensionality appears in the flow before the flow fully develops. Second, the superior abilities of the semi-L–L approach to analyze the vortex structure of the flow and supply physical details of bubble dynamics were demonstrated in this investigation.

The semi-L–L approach is applied to the simulation of the gas–liquid two-phase flows.

The exponential growth in computational capabilities and the increasing reliability of current simulation tools have fostered the use of computational fluid dynamics (CFD) in the design of pioneering aircraft engine architectures, such as the counter rotating open rotor (CROR) engine. Today, this design process is led by tight performance and noise constraints from a very early stage, thus requiring deep investigations of the aerodynamic and acoustic behaviour of the fluid flow. The purpose of this study is to track the trajectory of tip vortices, which is of critical importance to understand and prevent potential vortex–blade interactions with subsequent rows, as this condition strongly influences the aerodynamic and structural performance and acoustic footprints of the engine.

In this paper, a flow feature detection methodology is applied to a particular CROR test case with the goal of visualizing and tracking the development of these coherent structures from the tip of front rotating blades. The suitability and performance of four typical region-based methodologies and one line-based (LB) criteria are firstly evaluated. Then, two novel seeding methodologies are presented as an attempt to improve the performance of the LB algorithm previously investigated.

It was demonstrated that the new seeding algorithms increase the probability of the selected seeds to grow into a tip vortex line and reduce the user’s dependence upon the selection of candidate seeds, providing faster and more accurate answers during the design-to-noise iterative process.

Apart from the new vortex detection initialization methodologies, the paper also attempts to assist the user in the endeavour of extracting rotating structures from their own CFD simulations.

This paper aims to provide discussions of a numerical method for bubbly flows and the interaction between a vortex ring and a bubble plume.

Small bubbles are released into quiescent water from a cylinder tip. They rise under the buoyant force, forming a plume. A vortex ring is launched vertically upward into the bubble plume. The interactions between the vortex ring and the bubble plume are numerically simulated using a semi-Lagrangian–Lagrangian approach composed of a vortex-in-cell method for the fluid phase and a Lagrangian description of the gas phase.

A vortex ring can transport the bubbles surrounding it over a distance significantly depending on the correlative initial position between the bubbles and the core center. The motion of some bubbles is nearly periodic and gradually extinguishes with time. These bubble trajectories are similar to two-dimensional-helix shapes. The vortex is fragmented into multiple regions with high values of Q, the second invariant of velocity gradient tensor, settling at these regional centers. The entrained bubbles excite a growth rate of the vortex ring's azimuthal instability with a formation of the second- and third-harmonic oscillations of modes of 16 and 24, respectively.

A semi-Lagrangian–Lagrangian approach is applied to simulate the interactions between a vortex ring and a bubble plume. The simulations provide the detail features of the interactions.

The purpose of this paper is to present and validate an efficient time‐marching free‐vortex method for rotor wake analysis and study the rotor wake dynamics in transient and maneuvering flight conditions.

The rotor wake is represented by vortex filament elements. The equations governing the convection, strain and viscous diffusion of the vortex elements are derived from incompressible Navier‐Stokes equations based on the viscous splitting algorithm. The initial core size of the blade tip vortices is directly computed by a vortex sheet roll‐up model. Then, a second‐order time‐marching algorithm is developed for solving the governing equations. The algorithm is formulated in explicit form to improve computing efficiency. To avoid the numerical instability, a high order variable artificial dissipative term is directly introduced into the algorithm. Finally, the developed method is applied to examine rotor wake geometries in steady‐state and maneuvering flight conditions. Comparisons between predictions and experimental results are made for rotor wake geometries, induced inflow distributions and rotor transient responses, to help validate the new method.

The algorithm is found to be numerically stable and efficient. The predicted rotor responses have good agreement with experimental data. The transient behavior of the wake dominates the rotor responses following rapid control inputs in hover. The wake curvature effect induced by rotor pitching or rolling rate significantly changes the rotor off‐axis response.

This method should be further validated using experimental measurements of full‐scale helicopter rotors.

The paper presents a new time‐marching free‐vortex wake method, which is suitable for application in helicopter flight simulation.

A computational procedure based on a hybrid Lagrangian‐Eulerian discrete‐vortical element formulation and conformal transformation schemes are employed in this study to simulate the interaction of an air jet with swirling air flow inside a two‐dimensional cylinder. Such an investigation is of importance to many flow‐related industrial and environmental problems, such as mixing, cooling, combustion and dispersion of air‐borne or water‐borne contaminants because of the role of vortices in the global transport of matter and heat. The basis for the simulation is discussed and numerical results compared with theoretical results for the velocity field and streamfunction obtained by the method of images. The swirling air motion and the features of a real jet are well simulated and numerical results are validated by predictions of theory to within 20 per cent. To illustrate the merging and interaction processes of vortices and the formation of large eddies, velocity vectors, particle trajectories and streamline contours are presented.

A simple discrete vortex program written in the Occam language for implementation on transputers is presented. The programming methodology and logic are described, with an emphasis on the use of parallel features. Listings of procedures discussed in the text are given.