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Although the vortex is ubiquitous in nature, its definition is somewhat ambiguous in the field of fluid dynamics. In this absence of a rigorous mathematical definition, considerable confusion appears to exist in visualizing and understanding the coherent vortical structures in turbulence. Cited in the previous studies, a vortex cannot be fully described by vorticity, and vorticity should be further decomposed into a rotational and a non-rotational part to represent the rotation and the shear, respectively. In this paper, we introduce several new concepts, including local fluid rotation at a point and the direction of the local fluid rotation axis. The direction and the strength of local fluid rotation are examined by investigating the kinematics of the fluid element in two- and three-dimensional flows. A new vector quantity, which is called the vortex vector in this paper, is defined to describe the local fluid rotation and it is the rotational part of the vorticity. This can be understood as that the direction of the vortex vector is equivalent to the direction of the local fluid rotation axis, and the magnitude of vortex vector is the strength of the location fluid rotation. With these new revelations, a vortex is defined as a connected region where the vortex vector is not zero. In addition, through direct numerical simulation (DNS) and large eddy simulation (LES) examples, it is demonstrated that the newly defined vortex vector can fully describe the complex vertical structures of turbulence.

Traditional elastic correction methods fail to address the significant aeroelastic interactions arising from unsteady flow fields and structural deformations during aggressive maneuvers. To resolve this, a numerical method is developed by solving unsteady aerodynamic equations coupled with a rigid–flexible dynamics equations derived from Lagrangian mechanics in quasi-coordinates. Validation via a flexible pendulum test and AGARD445.6 wing flutter simulations demonstrates excellent agreement with experimental data, confirming the method’s accuracy. Application to a slender air-to-air missile reveals that reducing structural stiffness can destabilize the aircraft, transitioning it from stable to unstable states during forced pitching motions. Studies on longitudinal flight under preset rudder deflection control indicate that the aeroelastic effect increases both the amplitude and period of pitch angles, ultimately resulting in larger equilibrium angles compared to a rigid-body model. The free-flight simulations highlight trajectory deviations due to deformation-induced aerodynamic forces, which emphasizes the necessity of multidisciplinary coupling analysis. The numerical results show that the proposed CFD/CSD-based coupling methodology offers a robust aeroelastic effect analysis tool for flexible flight vehicles during aggressive maneuvers.

The stage separation of hypersonic vehicles is critically challenged by severe aerodynamic interference, which induces significant attitude deviations and jeopardizes subsequent flight missions. This study investigates open-loop and closed-loop attitude control methods utilizing lateral jets to stabilize the forebody during separation. Dynamic CFD-based numerical simulations were conducted for a tandem hypersonic vehicle, analyzing trajectories and aerodynamic characteristics under free separation, open-loop, and closed-loop control. Results show that open-loop control achieves a maximum forebody pitch angle of only 0.27° at α=0°, but performance degrades drastically to 24.88° at α=2.5°, highlighting its sensitivity to freestream variations. In contrast, a cascade PID-based closed-loop control system dynamically adjusts lateral jet total pressure, reducing the maximum pitch angle to 0.006° at α=0° and maintaining it below 0.2° even at α=5.0°. The closed-loop system exhibits periodic fluctuations in jet pressure, with amplitude increasing alongside angle of attack, yet demonstrates superior robustness against aerodynamic disturbances. Flow field analysis reveals enhanced shockwave interactions and vortex dynamics under closed-loop control, effectively mitigating pitch instability. While open-loop methods are constrained to specific conditions, closed-loop control significantly broadens applicability across variable flight environments.

Under the condition of supersonic incoming flow, a missile lateral jet flow field has complex flow structures, such as a strong shock wave, an unsteady vortex and flow separation. In order to improve ability to capture complex flow structures in numerical simulation of lateral jets, this paper proposes a combined-grid adaptive method. When combined with finite volume approximation of second-order and h-type adaptive technology, our method was verified by numerical experiments, which shows that wave structure and vortex structure in the jet flow field can be effectively captured at the same time. In comparison of uniformly refined mesh results, it was found that accuracy of computed results and resolution of characteristic flow structures were significantly improved after mesh adaptation. In comparison of the pressure coefficient, it was found that the error between the adaptive mesh and the uniformly refined mesh was smaller, and the maximum errors of the base grid, adaptive grid and uniformly refined grid were 92.1% and 12.3%.

There is a strong aerodynamic interference when launching the missile in the embedded mode. During the separation process, the carrier aircraft safety may be threatened due to large slenderness ratio, low structural stiffness, and aeroelasticity effects of the missile. The present study simulates missile separation in the presence of the aeroelasticity effects based on the computational fluid dynamics (CFD), rigid body dynamics (RBD), and computational structure dynamics (CSD) coupling method. A hybrid dynamic grid method consisting of the mixed overset unstructured grid and deformation grid is utilized. In order to verify the accuracy of the coupled numerical method, store separation from a wing and AGARD 445.6 wing flutter are first simulated as two standard test cases. The verification results imply that the present coupled numerical method is reliable and capable in simulation of the aeroelastic effect in missile separation. The influence of aeroelasticity on the separation trajectory of a missile from the internal bay is systematically studied at different states. Numerical results show that aeroelasticity substantially affects the missile angular displacement, while it has a slight impact on the linear displacement of the center of mass. Mach number and flight altitude are two important flight parameters that characterize the aeroelasticity effect on missile separation from the internal bay.

Flight tests and wind tunnel experiments face difficulties in investigating the impact of aircraft carrier air-wake on the landing process. Meanwhile, numerical methods generally exhibit low overall computational efficiency in solving such problems. To address the computational challenges posed by the disparate spatiotemporal scales of the ship air-wake and aircraft motion, a domain precursor inflow method is developed to efficiently generate unsteady inflow boundary conditions from precomputed full-domain air-wake simulations. This study investigates the aerodynamic variability of carrier-based aircraft during landing through the turbulent air-wake generated by an aircraft carrier, employing a hybrid RANS-LES methodology on dynamic unstructured overset grids. The numerical framework integrates a delayed detached-eddy simulation (DDES) model with a parallel dynamic overset grid approach, enabling high-fidelity simulations of coupled aircraft carrier interactions. Validation confirms the accuracy of the precursor inflow method in reproducing air-wake characteristics and aerodynamic loads compared to full-domain simulations. Parametric analyses of 15 distinct landing trajectories reveal significant aerodynamic variability, particularly within 250 m of the carrier, where interactions with island-generated vortices induce fluctuations in lift (up to 25%), drag (18%), and pitching moments (30%). Ground effects near the deck further amplify load variations, while lateral deviations in landing paths generate asymmetric forces and moments. The proposed methodology demonstrates computational efficiency for multi-scenario analysis, providing critical insights into aerodynamic uncertainties during carrier operations.

At cryogenic temperatures, gases exhibit significant deviations from ideal behaviour, and the commonly employed gas model may inadequately represent the thermodynamic properties of cryogenic gases, subsequently impacting numerical simulations using various thermodynamic and transport models at cryogenic temperatures. The findings of this study reveal that the relative errors in aerodynamic characteristics obtained through different isentropic relations are noteworthy, with the maximum relative error in the drag coefficient reaching 16%. The impact of the equation of state, viscosity model, and thermal conductivity model is relatively minor, with relative errors in the pressure drag coefficient and viscous drag coefficient remaining well below 1%. Nevertheless, the relative error in the skin friction coefficient cannot be ignored due to transonic shock wave/boundary layer interactions. Consequently, when conducting numerical simulations of cryogenic flow, it is imperative to select appropriate gas models to attain precise results.

This research investigated the impact of complex low-speed wake flow structures on the aerodynamic characteristics of objects downstream. It employed the proper orthogonal decomposition (POD) method and the domain precursor simulation method to compare traditional methods and validate this approach. The study generated several flow structures of parallel dual-cylinder wakes with different scales and spacing. The variations in the aerodynamic coefficient of three downstream objects at various times passing through wakes of varying scales were appropriately compared and analyzed. The study established that the wake with a cylinder spacing of G = 1.5 has a more compact and concentrated modal structure than that with a cylinder spacing of G = 0.35. Smaller objects were more responsive to the wake flow structure with a spacing of G = 1.5, whereas larger objects responded more to the flow structure with a spacing of G = 0.35. The achieved results also revealed that the aerodynamic force coefficients of objects passing through the wakefield at different times were closely related to the temporal characteristics of the wake flow structure with different scales.

Accurate simulation of vortex-dominated flows has been an important issue for numerical methods in computational fluid dynamics. The recently proposed dual-solver framework provides an attracting direction for complex vortex structure resolving. In current research, we develop a dual-solver fluid solving system, in which the near-body region uses traditional finite volume method for complex geometries treatment, and apply high-order flux reconstruction (FR) method in off-body region to capture the evolution of vortex structures effectively. The parallel overset grid method is adopted in mesh assembly and data exchange process between solvers. The FR solver is developed under the framework of open-source adaptive mesh refinement (AMR) library p4est, which manages h-refinement efficiently. Cartesian cell with AMR is used in FR scheme to improve solving performance. The time marching method of coupled solvers is investigated. All modules in current system are verified, respectively. In the simulations where flow is dominated by vortex, we choose NACA0015 and S76 rotor wake resolving to verify the proposed system. The results reveal that the flow solver accurately resolves the vortex, the mesh distribution with AMR is reasonable. The results confirm the efficacy of proposed dual-solver framework.

Vorticity and vortex are two different but related concepts. This paper focuses on the investigation of vorticity generation and development, and vorticity structure inside/ outside the vortex. Vortex is a region where the vorticity overtakes deformation. Vortex cannot be directly represented by the vorticity. Except for those vorticity lines which come from and end at side boundaries, another type of vorticity, self-closed vorticity lines named vorticity rings, is numerously generated inside the domain during flow transition. These new vorticity rings are found around the hairpin vortex heads and legs. The generation and growth of vorticity rings are produced by the buildup of the vortices according to the vorticity transport equation. On the other hand, vortex buildup is a consequence of vorticity line stretching, tilting and twisting. Both new vorticity and new vortices are generated during the flow transition. According to the Helmholtz vorticity flux conservation law, vorticity line cannot be interrupted, started, or ended inside the flow field, the newly produced vorticity has only one form which is the vorticity rings. In addition, an interesting finding is that a single hairpin vortex consists of several types of vorticity lines which could come from the side boundaries, whole vorticity rings and part of vorticity rings.