Effects of Reduced Frequency on Network Configuration and Synchronization Transition

Synchronization of networked phase oscillators depends essentially on the correlation between the topological structure of the graph and the dynamical property of the elements. We propose the concept of ＇reduced frequency＇, a measure which can quantify natural frequencies of each pair of oscillators. Then we introduce an evolving network whose linking rules are controlled by its own dynamical property. The simulation results indicate that when the linking probability positively correlates with the reduced frequency, the network undergoes a first-order phase transition. Meanwhile, we discuss the circumstance under which an explosive synchronization can be ignited. The numerical results show that the peculiar butterfly shape correlation between frequencies and degrees of the nodes contributes to an explosive synchronization transition.

CFD Based Determination of Dynamic Stability Derivatives in Yaw for a Bird

Dynamic yaw stability derivatives of a gull bird are determined using Computational Fluid Dynamics（CFD） method. Two kinds of motions are applied for calculating the dynamic yaw stability derivatives CNr and CNβ. The first one relates to a lateral translation and, separately, to a yaw rotation. The second one consists of a combined translational and rotational motion. To determine dynamic yaw stability derivatives, the simulation of an unsteady flow with a bird model showing a harmonic motion is performed. The flow solution for each time step is obtained by solving unsteady Euler equations based on a finite volume approach for a small reduced frequency. Then, an evaluation of unsteady forces and moments for one cycle is conducted using harmonic Fourier analysis. The results of the dynamic yaw stability derivatives for both simulations of the model show a good agreement.

Dynamic stall control over an airfoil by NS-DBD actuation

The wind tunnel test was conducted with an NACA 0012 airfoil to explore the flow control effects on airfoil dynamic stall by NS-DBD plasma actuation. Firstly, light and deep dynamic stall states were set, based on the static stall characteristics of airfoil at a Reynolds number of 5.8 × 105. Then, the flow control effect of NS-DBD on dynamic stall was studied and the influence law of three typical reduced frequencies (k = 0.05, k = 0.05, and k = 0.15) was examined at various dimensionless actuation frequencies (F+ = 1, F+ = 2, and F+ = 3). For both light and deep dynamic stall states, NS-DBD had almost no effect on upstroke. However, the lift coefficients on downstroke were increased significantly and the flow control effect at F+ = 1 is the best. The flow control effect of the light stall state is more obvious than that of deep stall state under the same actuation conditions. For the same stall state, with the reduced frequency increasing, the control effect became worse. Based on the in being principles of flow separation control by NS-DBD, the mechanism of dynamic stall control was discussed and the influence of reduced frequency on the dynamic flow control was analyzed. Different from the static airfoil flow separation control, the separated angle of leading-edge shear layer for the airfoil in dynamic stall state is larger and flow control with dynamic oscillation is more difficult. The separated angle is closely related to the effective angle of attack, so the effect of dynamic stall control is greatly dependent on the history of angles of attack.

折合频率对三维跨声速压气机颤振稳定性的影响

It is well known that fan/compressor blade flutter stability increases with the increase of reduced frequency.Less well-known is that the least stable inter blade phase angle(IBPA)increases with the drop of reduced frequency.However,it is quite striking that little can be found in the open literature about the mechanism to the observations.In this paper,a numerical investigation is carried out to uncover the mechanism of the effect of reduced frequency on flutter stability and the least stable IBPA.The NASA rotor 67 has been used as the test vehicle with its first bending and torsion modes being considered.The time domain harmonic balance method together with the influence coefficient method is used to obtain the worksum-IBPA curves for all cases.It is found that:1)the deterioration of flutter stability with the decrease of reduced frequency is dictated by the dominant decrease of aerodamping due to a blade own vibration;2)the increase of the least stable IBPA with the decrease of reduced frequency arises largely from the increase of the least stable IBPA of the aerodamping from the nearest blade on a blade pressure side.

Abnormal changes of dynamic derivatives at low reduced frequencies

A number of studies have found that abnormal changes of dynamic derivatives occurred at very low reduced frequencies, but its inducement mechanism is not very clear. This paper has researched the abnormal changes and analyzed the influence on some parameters by solving the unsteady flow around forced oscillation airfoils based on Navier-Stokes equations. Results indicate that when the reduced frequency approaches to zero, the dynamic derivatives obtained by the numerical method will diverge. We have also proven it in theory that this phenomenon is not physical but completely caused by numerical singularity. Furthermore, the abnormal phenomenon can be effectively mitigated by using the time spectral method to solve the aerodynamic forces and the integral method to obtain the dynamic derivatives. When the reduced frequency is in the range of 0.001–0.01, the dynamic derivative maintains nearly unchanged for the whole speed region. This study can provide a reference for the reasonable choice of the reduced frequency in calculations and experiments of dynamic derivatives.

Numerical investigation of an advanced aircraft model during pitching motion at high incidence

An unsteady Reynolds averaged Navier–Stokes(URANS) method combined with a rigid dynamic mesh technique was developed to simulate unsteady flows around complex configurations during pitching motion. First, a test case with the NACA0012 airfoil was selected to validate the numerical methods and our in-house codes. Then, we evaluated the unsteady flows around an advanced aircraft model during harmonic pitching motion at high incidence. The effects of pitching motion on the hysteresis of aerodynamic force, the evolution of the leading-edge vortex, and the distribution of pressure on the model's surface were analyzed in detail. The roles of several significant parameters such as the reduced frequency and pitching amplitude were revealed. Several conclusions were found: pitching motion would delay the initiation of the leading-edge vortex, strengthen the vorticity, postpone the occurrence of vortex breakdown, and weaken the massively separated flows, thus causing additional aerodynamic force. Two categories of critical reduced frequency have been found, which divide the influence of reduced frequency on aerodynamic force into three stages, called the linear increasing range, slowly increasing range, and constant range. The first-order phase lag between the aerodynamic force and the incidence is a constant that is independent of the amplitude when the reduced frequency is sufficiently high. A scaled maximum value of C_L is proposed; it depends only on the reduced frequency(instead of the amplitude), and increases linearly when the reduced frequency is sufficiently low.

Wake structure and similar behavior of wake profiles downstream of a plunging airfoil

Very limited attention has already been paid to the velocity behavior in the wake region in unsteady aerodynamic problems. A series of tests has been performed on a flapping airfoil in a subsonic wind tunnel to study the wake structure for different sets of mean angle of attack, plunging amplitude and reduced frequency. In this study, the velocity profiles in the wake for various oscillation parameters have been measured using a wide shoulder rake, especially designed for the present experiments. The airfoil under consideration was a critical section of a 660 k W wind turbine.The results show that for a flapping airfoil the wake structure can be of drag producing type, thrust producing or neutral, depending on the mean angle of attack, oscillation amplitude and reduced frequency. In a thrust producing wake, a high-momentum high-velocity jet flow is formed in the core region of the wake instead of the conventional low-momentum flow. As a result, the drag force normally experienced by the body due to the momentum deficit would be replaced by a thrust force.According to the results, the momentum loss in the wake decreases as the reduced frequency increases. The thrust producing wake pattern for the flapping airfoil has been observed for sufficiently low angles of attack in the absence of the viscous effects. This phenomenon has also been observed for either high oscillation amplitudes or high reduced frequencies. According to the results, for different reduced frequencies and plunging amplitudes, such that the product of them be a constant, the velocity profiles exhibit similar behavior and coalesce on each other. This similarity parameter works excellently at small angles of attack. However, at near stall boundaries, the similarity is not as evident as before.

Numerical Simulation of Uniform Flow past an In-Line Oscillating Circular Cylinder

The time-dependent viscous incompressible flow around an in-line oscillating circular cylinder at Reynolds numbers of 200 and 855 was analyzed using a finite volume method. The Navier-Stokes equations were solved on a moving grid system using a time-dependent coordinate transformation. Several numerical schemes were tested to investigate the vortex-shedding characteristics and the effects of Reynolds number and other dimensionless parameters such as the reduced amplitude and the reduced frequency. The numerical results indicate that several types of vortex shedding modes depend on the reduced frequency and the reduced amplitude due to synchronization or lock-on.

Numerical Method for Evaluating Aircraft's Stability Parameters through an Aerodynamic Model

A numerical method is developed to evaluate the dynamic stability parameters of aircraft. This method is based on the aerodynamic model proposed by Etkin. His model is analyzed and generalized. After giving the specific forms of the aerodynamic model, the dynamic stability parameters are determined by the unsteady flow field computation and a parameter identification technique. Numerical experiments show that this method is accurate in predicting the dynamic stability characteristics of blunt cones in hypersonic flight.