Study on the flow characteristics in the supersonic morphing cavities using direct numerical simulation and proper orthogonal decomposition

Highlights

• A morphing cavity for adjusting the ramp angles of walls is proposed.

• Unsteady flows past the morphing cavities at Ma 1.8 are investigated by DNS.

• Flow structures in the morphing cavities are analyzed by POD.

• Flow characteristics of the fixed-geometry cavity are compared.

Abstract

Supersonic flows past the morphing cavities with different ramp angles of the trailing wall are studied by the direct numerical simulation (DNS) method. As the ramp angle increases, the sound pressure level of the dominant mode and overall sound pressure level gradually decrease at the last monitor point. The number of the feedback shock waves and the size of the large-scale vortices also gradually decreases. The vortex wave moving downstream slowly disappears. When the ramp angle increases to 30 and 40 degrees, the dominant mode at the front of the cavity shifts from mode 3 to mode 1. In addition, the flow structures in the morphing cavities are analyzed using proper orthogonal decomposition (POD). Results indicate that the energy occupied by the POD modes, the size of the flow structures, and the amplitude of POD coefficients all decrease with the ramp angle increase. Compared with the fixed-geometry cavity with the ramp of the trailing wall, the results show that there is a better noise reduction effect and the flow structure is changed in the morphing cavity. In a word, the morphing cavity control method effectively suppresses cavity noise, greatly weakens the sensitivity of the shear layer, and obviously changes the flow structure in the cavity.

Introduction

Cavity flows have been studied for many years in different fields, such as internal weapon bays of military aircraft [1], [2], wheel wells of civil aircraft [3], [4], [5], car cabins [6], and combustors of scramjet engines [7]. The internal structures of cavities are not complicated. However, when the high-speed airflow passes over cavities, the interaction between the shear layer and the airflow in cavities will lead to vortex flow, shock wave or expansion wave interference, unstable shear layer. The self-sustained oscillation in cavities and the high acoustic oscillations will be generated [8], [9]. Therefore, suppressing cavity noise is very significant.

There are many control methods to suppress cavity noise, such as fences [10], [11], spoilers [12], [13], serrations [14], and ramps [15], [16], [17]. Vikramaditya et al. [15] experimentally investigated supersonic flow over cavities with different ramp angles of the trailing wall when the free-stream velocity is 484 m/s. They observed that the modal sound pressure levels (SPLs) decline rapidly with a ramp angle of 45-deg, and the maximal decrease is 40 dB. Maurya et al. [16] found that when the ramp angle is reduced from 60-deg to 30-deg at Ma 1.65, the static pressure fluctuation inside the cavity is gradually mitigated. Ren et al. [17] found that the ramp of the trailing wall can suppress effectively pressure oscillations in a rectangular cavity with a length-to-depth ratio L/D of 3.88 at Ma 1.75, but the effectiveness may degrade at other free-stream speeds. These works indicate that the ramp of the trailing wall is an efficient way to suppress cavity noise.

In most studies, the fixed geometry structure is used to control cavity noise. The disadvantage of the method is that there is a good control effect only under certain initial conditions and geometric conditions. In order to realize real-time adjustment and achieve the best noise reduction effect under different initial conditions, a new control method named morphing cavity is proposed in this paper. The idea is inspired by the morphing-wing aircraft. The wing shape in the aircraft can change in real-time [18], [19], to improve aircraft performance, reduce aerodynamic drag, and expand its flight envelope [20], [21]. As can be seen in Fig. 1, a slider-crank mechanism installed within the cavity is used to construct the morphing cavity. The sliders inside the guide are driven horizontally by a motor. The sliders are connected with the trailing edge, and the trailing wall is connected with the trailing edge and the bottom wall by hinges. Therefore, the trailing wall and bottom wall are inclined simultaneously with the movement of the sliders. Fig. 2 illustrates a morphing state of the cavity with a ramp angle $\alpha$. The ramp angles of the trailing wall and the bottom wall can be adjusted simultaneously.

In the present work, in order to understand the flow characteristics of the morphing cavities at supersonic speed, simulations of the morphing cavities were carried out by direct numerical simulation (DNS) [22], [23]. Then, the proper orthogonal decomposition (POD) method [24], [25] was employed to analyze the flow structures in the morphing cavities. The present studies are helpful in understanding the flow characteristics in a cavity with irregular geometry.

The paper is organized as follows: In Section 2, the DNS method, and the details of the computation are introduced. The basic process of the POD method is described in Section 3. Section 4 analyzes the simulation and POD results in the morphing cavities, and compares with the flow characteristics in the fixed-geometry cavity. Conclusions are summarized in Section 5.