Mathematical Problems in Engineering

Volume 2017 (2017), Article ID 3704324, 12 pages

https://doi.org/10.1155/2017/3704324

## Numerical Investigation on Vortex-Structure Interaction Generating Aerodynamic Noises for Rod-Airfoil Models

^{1}State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, China^{2}Shaanxi Key Laboratory for Environment and Control of Flight Vehicle, Xi’an Jiaotong University, Xi’an 710049, China^{3}China Aerodynamics Research and Development Center, Mianyang 621000, China

Correspondence should be addressed to Gang Chen

Received 14 March 2017; Revised 20 June 2017; Accepted 25 July 2017; Published 17 October 2017

Academic Editor: Maria Patrizia Pera

Copyright © 2017 FeiFei Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In past several decades, vortex-structure interaction generated aerodynamic noise became one of the main concerns in aircraft design. In order to understand the mechanism, the acoustic analogy method combined with the RANS-based nonlinear acoustics solver (NLAS) is investigated. The numerical method is firstly evaluated by the experiment data of the classic rod-airfoil model. Compared with the traditional analogy methods, the RANS/NLAS can capture the nonlinear aerodynamic noise more accurately with lower gird requirements. Then different rod-airfoil configurations were simulated to investigate the aeroacoustic interaction effects. The numerical results are in good agreement with those of the earlier experimental research. It is found that the vortex-shedding crash to the airfoil is the main reason for the noise generation which is dependent on the configurations, distance, and flow conditions.

#### 1. Introduction

In recent years, aircraft noise has become one of the major problems due to the rapid increase of air traffic. Aerodynamic noise reduction is also one of the key issues in modern civil aircraft design in past several decades. However, the mechanism of aircraft aerodynamic noise is very complex. For example, the airfoil self-noise is one of the main noise sources which is induced by the interactions between the airfoil blade and the turbulence flow produced by its own boundary layer and near wake [1]. The strong interactions between the vortex from the upstream flow and the airfoils downstream are one of the most important effects in airframe noise generation, especially in the aircraft take-off and landing on the ground [2–4].

There are mainly four types of numerical aeroacoustic prediction methods [5], including the pure theoretical method [6], the semiempirical method [7], the direct numerical method, and the hybrid method [3, 8]. In particular, the Lattice-Boltzmann-Method (LBM) has shown being a very promising technique for far field aeroacoustic prediction (Benjamin Duda, Ehab Fares, 2017), such as LAGOON landing-gear configuration [9] and Jet-plate interaction noise [10]. Currently the hybrid method is the most popular method which predicts the sound by combination of the computation fluid dynamics solvers for acoustic source identification [11–13] and the Lighthill’s analogy theory for sound propagation [14]. The RANS/FW-H method was used to predict the aerodynamic noise of helicopter rotor successfully [6]. The LES/FW-H method was applied to calculate the boundary induced airfoil noise [15].

The RANS/LES hybrid method was then used to simulate the noise generated by the pressure fluctuations on the airfoil in which the numerical results were very similar to the experiment data [16]. However, the RANS/LES method is still very expensive for aeroacoustic prediction because of the large amount of high-resolved grids and long-time cost required by the LES simulation. A well-known benchmark study for a 2-wheel gear named LAGOON showed the comparisons between different CFD solvers for aeroacoustic prediction [3, 9]. So how to predict the aeroacoustics with more efficiency with good accuracy is a challenging task. Interestingly PJ Morris proposed a nonlinear acoustics solver (NLAS) to predict the noise generation and transmission from an initial statistically steady model of the turbulent flow data, which can be provided by a simple RANS model and no requirement from the LES simulation [17]. Lately this method was improved and generalized the original NLAS method with more robustness and efficiency [18]. Compared with the traditional analogy methods, the RANS/NLAS method is easy to be implemented and can predict the nonlinear noise more accurately and fast with less gird requirements.

The rod-airfoil model is a typical benchmark for aerodynamic noise numerical and experiment research. It represents the main characteristics of the turbulence from the upstream flow by the simple geometric structure and is widely used for the unsteady aeroacoustic validation [19]. The aeroacoustic characteristics of the cylinder type rod-airfoil model proposed by Jacob were numerically investigated and validated by many researchers even including the DES/FW-H method [20]. However, the detailed mechanism of the rod-airfoil noise generation is still seldom investigated, such as the configuration of the rod and the distance between the rod and the airfoil, which are very important to the vortex-structure interaction noise reduction. We will numerically investigate the mechanism of the vortex-structure interaction generating noise for different rod-airfoil configuration models by comparing with the experimental results carried in the 0.55 m 0.4 m aeroacoustic wind tunnel in China Aerodynamics Research and Development Center (CARDC). The paper is organized as follows. Section 2 briefly describes the RANS/NLAS numerical methods. Section 3 presents the results of the benchmark and validation of the numerical method. Section 4 shows the numerical results of different rod-airfoil models which are compared with the aeroacoustic wind tunnel experiment data. Finally, the vortex-structure interaction mechanism to aerodynamic noise generation is discussed.

#### 2. Numerical Method

##### 2.1. Nonlinear Acoustics Solver

The nonlinear acoustics solver has many interesting advantages compared with the traditional LES solvers, hybrid RANS/LES solvers, and more conventional linearized acoustics solvers [17, 18]. NLAS provides a more sophisticated subgrid treatment that allows the extraction of acoustic sources from the temporal variation within the modeled subgrid structures. The quasi-steady near-wall RANS solution is obtained a priori so that the grid requirements can be relaxed and reduced in the near-wall region during the NLAS transient calculation, compared to the LES solvers. At the same time the dissipative effects of a subgrid eddy viscosity model are avoided; thus the NLAS solver proves less diffusive than the classic LES or hybrid RANS/LES simulation on coarser meshes. One of the most important advantages of the NLAS is able to account for both the turbulence-related broadband noise and the discrete tones produced from coherent structures or resonance [18]. A very brief introduction of the NLAS method is as follows.

The NLAS solver considers a perturbation to the Navier-Stokes equations, in which the quantities are split into the mean and the fluctuation parts, . Substituting the above equation into the Navier-Stokes equations and rearranging the fluctuation and mean quantities, the nonlinear disturbance equation (NLDE) is obtained:Neglecting the density fluctuations and keeping the time averages lead toin whichThe above terms correspond to the standard Reynolds-stress tensors and turbulent heat fluxes. The key step in NLAS is to obtain these unknown terms from the classical RANS calculations in advance. Subsequently, a synthetic reconstruction of the unresolvable (short wavelength) contribution to these terms can then be generated and used to form the subgrid source terms for the NLAS simulation [21]. After both the mean levels and subgrid sources are established, the time-dependent calculations can then be carried out to determine the transmitted perturbations around the mean flows by using the above nonlinear disturbance equations.

##### 2.2. Sound Pressure Level Correction

The required large meshes for aeroacoustic numerical simulation of real configuration usually lead to too expensive calculation time cost. In order to reduce the meshes and accelerate the aeroacoustic prediction, the numerical models are usually modified or simplified from the experiment models. For example, the span of the experiment airfoil is much bigger than the chord . In order to use the lower mesh number, the span of numerical airfoil model can be reduced from to , which is smaller than the chord . For the modification the aeroacoustic calculation can be speeded up extensively; however the aeroacoustic sound pressure level (SPL) obtained from the numerical results and the experimental results cannot be compared directly. In such cases, some corrections have to be introduced to the numerical sound pressure level (SPL). In the paper, we use the correction method firstly proposed by Kato [15, 22]. When , When , When ,SPL and represent the sound pressure spectrum of the experiment model and the numerical model, respectively. The span of the experiment model is and is the span of the numerical model. is defined as the equivalent coherent length such that the surface pressure fluctuation can be regarded exactly in the same phase angle within , while it is completely in independent phase angle outside . Once the equivalent coherent length is determined, it is possible to calculate the sound pressure spectrum SPL radiated from the whole airfoil model with the real span length .

#### 3. Numerical Method Verification

##### 3.1. Numerical Verification

Jacob’s experimental rod-airfoil model was used to validate the proposed numerical method [19]. The experimental set-up and the coordinates are shown in Figure 1. The reference configuration is a symmetric NACA-0012 airfoil (chord: m; thickness: = 0.12 m) located at one-chord distance after the cylinder ( m), both extending by = 0.3 m in the spanwise direction. The acoustic far field receiver is at 1.85 m from airfoil center. The incoming velocity is 72 m/s and the Reynolds number of the cylinder is 48000. The Reynolds number of airfoil is 480000 with a 0° attack angle. The experiment was conducted in the large anechoic room of the ECL (10 m × 8 m × 8 m). The air was supplied by a high-speed subsonic anechoic wind tunnel at Mach numbers ranging up to 0.34.