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Correlations of unsteady vortex burst point and dynamic stability over a pitching double-delta wing

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Abstract

Pitching dynamic stability is significant for the aerodynamic performance of an aircraft at a large angle of attack (AoA). Commonly, the dynamic behaviour of vortex breakdown flows over an aircraft with a delta or double-delta wing (DW or DDW) configuration is closely related to the pitching dynamic stability. An 80°/65° DDW subjected to sinusoidal pitching motions around the stall AoA was numerically investigated using the delayed detached eddy simulation method [1]. This study is focused on the correlation between the unsteady behaviour of the vortex burst point (BP) and pitching dynamic stability. The reverse of the pitching dynamic stability is closely related to the inconsistent movement of the BP during the upstroke and downstroke in one pitching period. When the upstream speed of the BP is higher than the downstream speed, the variation in the pitching moment is ahead of the AoA, which leads to dynamic instability. Conversely, when the downstream speed is higher than the upstream speed, the DDW is dynamically stable. This correlation can be interpreted through the energy transfer relationship between the vortex breakdown flows and DDW model.

Introduction

Pitching dynamic stability is significant for the aerodynamic performance of an aircraft at a large angle of attack (AoA). Delta wing (DW) and double-delta wing (DDW) configurations have been used by several fighters owing to their high aerodynamic performances at large AoAs. However, the DW and DDW suffer vortex breakdown at sufficiently high angles of incidence. In particular, when a DW with vortex breakdown underwent a pitching motion, a time lag of the burst point (BP) with respect to its variation in the quasi-steady case was observed [2]. A few studies were carried out to reveal the mechanisms [3], [4] and analyze the parameter effects [5] on the dynamic behaviour of the BP in several operations such as oscillating leading-edge flaps [6], leading-edge extensions [7] and pitching wings [8] by measurements in wind and water tunnels. The time lag constant associated with the upstream motion of the BP is commonly larger than that in the downstream motion.

The time lag is considered to be important for the flight stability and control of the aircraft [2]. To some extent, the variation in the pitching moment is closely related to the dynamic behaviour of the BP. However, the correlations between the dynamic behaviour of the BP and pitching dynamic stability have rarely been reported in the available publications.

In our previous study [1], flows with vortex breakdown over a pitching 80°/65° DDW were numerically simulated using the delayed detached eddy simulation (DDES) method. The dynamic responses of the BP and pitching moment were analysed in detail. The movement of the BP and pitching dynamic stability were largely affected by the reduced frequency (RF). In this article, the correlations between the dynamic behaviour of the BP and pitching dynamic stability are analysed in detail on basis of our previous studies.

Section snippets

Numerical methods

The simulations were conducted using our in-house computational fluid dynamic solver, Unsteady NavIer–sTokes Solver (UNITs) [1], [9], [10], [11], [12]. It is a second-order finite-volume solver based on multi-block structured mesh. It contains several turbulent modelling methods, such as the one-equation Spalart–Allmaras (S–A) method [13], two-equation kω shear stress transport (SST) [14] eddy viscosity turbulence models, and several Reynolds-averaged Navier–Stokes/large eddy simulation

Computation case

An 80°/65° DDW subjected to sinusoidal pitching motions around the stall AoA of 36° was numerically simulated by the DDES method [1]. The present DDW model is the same as that in Ref. [1], which consists of an 80° strake wing, a 65° main wing, and a cylinder sting with a round nose, as shown in Fig. 1. The mean aerodynamic chord C is 0.49 m, while the dimensionless root chord Cr/C is approximately 2.171. The moment reference centre and rotation centre coincide at xG/C=1.586.

The DDW model

Convergence study on the time step

This study is focused on the responses of the BP and pitching moment to variations in AoA. As a convergence analysis of the grid density has been carried out in our previous study [1], the effects of the time step are analysed in this study. The correlation coefficient between the AoA and displacement of the BP (αxb), or pitching moment Cm(αCm), Cij(τ), can be calculated as follows:Cij(τ)=fi(tτ)fj(t)fi,rmsfj,rms The time evolutions of Cij(τ) at kp=0.4 are presented in Fig. 3 to analyse

Conclusions

The unsteady vortex breakdown flows over an 80°/65° DDW oscillating around the AoA of 36° were investigated using the kω SST based DDES model. Mainly, the pitching effects on the unsteady behaviour of the vortex BP, pitching dynamic stability, and their correlations were investigated.

The natural oscillation frequency of the BP location at 36°, Stn, was crucial for the dynamic behaviour of the BP and dynamic stability during the harmonic pitching motion. When the pitching frequency was lower

Declaration of Competing Interest

The authors declare that they have no conflicts of interest to this work.

Acknowledgement

This work is supported by the National Natural Science Foundation of China (Grant No. 11902334, 11772174, 91952302 and 91852113) and the National Numerical Windtunnel project. The authors also would like to thank the supports from the National Key Research and Development Program of China (Grant No. 2019YFA0405300) and National Key Project (Grant No. GJXM92579).

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