**1. Introduction**

Flow around a bluff body is one of the basic subjects in fluid mechanics, because it contains not only fundamentally important problems (such as forces acting on the body, transition to turbulence, acoustics, etc.), but also a variety of practical problems (such as structural design of buildings, trains, etc.). In many engineering applications, objects often appear in the wake of an obstacle. When an obstacle is in the wake of another, the flow structure tends to be complex and differs from that of single obstacle.

Flow past two circular or rectangular cylinders in a tandem arrangement is the simplified case of the flow past an array of cylinders and has received increasing attention [1–8]. Liu and Chen [4] and Inoue and Mori [5] showed that two different flow patterns appear depending on the space between the cylinders. When the

spacing is small, the shear layer separated from the upstream cylinder does not roll up to form vortices but reattaches to the downstream of the cylinder, and the vortices are shed from the downstream only, and this flow pattern is called *Mode I*. When the spacing is large, the shear layer separated from the upstream cylinder rolls up and forms vortices in front of the downstream of the cylinder, and the rollup vortices impinge on the downstream cylinder (body-vortex interaction, BVI, wake-body interaction), and this flow pattern is called *Mode II*. Furthermore, Inoue and Mori [5] showed that in *Mode I,* the sound is generated only by the vortex shedding of the downstream cylinder, and in *Mode II,* the sound and strong pressure fluctuation around the downstream cylinder are generated mainly by BVI. The magnitude of the generated sound is much larger in *Mode II* than both *Mode I* and the single cylinder.

The airfoil-airfoil model (airfoils in tandem) is also a typical model for the wakebody interaction or body-vortex interaction (BVI). Liu et al. [22–23] performed the measurements to understand the effect of using serration on the aerodynamic and acoustic performance of airfoils in tandem. They studied the wake development, static pressure distributions, and surface pressure fluctuations in detail for a cambered NACA 65-710 airfoil with and without the serration. They showed that the

In this chapter, we simulate the flow around the rod-airfoil model and the noise generated by the wake-body interaction or body-vortex interaction for the cases of *L/d* = 2 and 10 at a Reynolds number based on the rod diameter (*d =* 6 mm) 28,800 (288,000 based on the airfoil chord, *c*) by the coupling method using commercial CFD and acoustic BEM codes in which the acoustic sources are solved in the CFD code and the acoustic field is solved by means of BEM, and compare the results with those obtained by Jacob et al. [9] and Jiang et al. [21]. Then, we simulate the flow around the airfoil-airfoil model (airfoils in tandem) and the noise generation and propagation for the cases of *L/c* = 0.2, 0.6, and 1 at a Reynolds number based on the airfoil chord (*c =* 60 mm) 288,000, and compare the results with those for the

A schematic diagram of the flow model is presented in **Figure 1**. The origin is at the leading edge of the airfoil. The coordinates parallel and normal to the free stream are denoted by *x* and *y,* respectively. The coordinate in the spanwise direction is denoted by *z*. The symbol *L* denotes the spacing between the rod and the airfoil. The lengths are made dimensionless by the rod diameter *d* and the velocity is scaled by the speed of sound *c*∞*.* The normalized spacing *L/d* is prescribed to be 2 and 10. The Mach number, *M*, of a uniform flow is defined by *M* = *U*∞*/c*∞, where *U*<sup>∞</sup> denotes the velocity of the uniform flow. In this chapter, the Reynolds number is fixed to be *Red* = 28,800 or *Rec* = 288,000, and those are based on the rod diameter and the airfoil chord *c*, respectively. The spanwise length of the rod and the airfoil is 3*d*.

A schematic diagram of the flow model is presented in **Figure 2**. The origin is at

the leading edge of the downstream airfoil. The normalized spacing *L/c* is

*Schematic diagram of rod-airfoil model. (a) Rod-airfoil model; (b) parameters.*

noise is reduced in the case that the upstream airfoil is with the serration.

*Wake-Body Interaction Noise Simulated by the Coupling Method Using CFD and BEM*

*DOI: http://dx.doi.org/10.5772/intechopen.92783*

rod-airfoil model.

**2. Analysis model**

**2.1 Rod-airfoil flow model**

**2.2 Airfoil-airfoil flow model**

**Figure 1.**

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Since a *von Karman* vortex street can be regarded as a gust impinging on the obstacle or blade, a rod-airfoil model is another typical one for the study of the body (blade) vortex interaction or wake-body interaction. In this model, a rod is immersed upstream of the blade or airfoil, the wake formed behind the rod interacts with the leading edge of the blade or airfoil. Many studies concerned with the rodairfoil model have been done both experimentally and numerically [9–21]. Jacob et al. [9] measured the flow field of the rod-NACA0012 airfoil model at the fixed spacing between the rod and the airfoil with varying the inflow velocity, and also measured the far field radiated noise spectra that are generated mainly by the bodywake interaction. They also performed numerical calculations using the Reynoldsaveraged Navier-Stokes (RANS) and the large eddy simulation (LES) approaches and compared numerical results with the measured data. Munekata et al. [10–11] measured the flow field of the rod-airfoil model to research the effects of the spacing between the rod (cylinder) and the airfoil and the characteristics of the flow-induced sound generated by the flow around rod-airfoil. They showed that the roll up of the shear layer separated from the upstream rod is suppressed when the spacing between the rod and the airfoil is small, and the interaction between the wake from the rod upstream and the airfoil downstream becomes weak and it results in decreasing the level of the noise radiation. They also showed that the attack angle of the airfoil located downstream affects the characteristics of the flowinduced sound and wake structure at a given spacing between the rod and the airfoil, and the generated sound pressure decreases with the increase of the attack angle of the airfoil. Li et al. [12] performed the experiments of the body-wake interaction noise radiated from the flow around the rod-airfoil model by focusing on the noise control using "air blowing" on the upstream rod and a soft-vane leading edge on the airfoil. Numerical investigations by using the RANS approach have been done by Casalino et al. [13], Jacob et al. [9] and Jiang et al. [14], and those by using the LES approach have been done by Casalino et al. [13], Magagnato et al. [15], Boudet et al. [16], Jacob et al. [9], Greschner et al. [17], Agrawal and Sharma [18], Giret et al. [19], Daude et al. [20], and Jiang et al. [21]. Jiang et al. [21] performed LES simulations of the flow around the rod-airfoil for the inflow velocity *U*<sup>∞</sup> *=* 72 m/s and a Reynolds number based on the rod diameter (*d*) 48,000 (480,000 based on the airfoil chord, *c*) to clarify the flow patterns, velocity and pressure fluctuations, and noise radiation with varying the spacing between the rod and airfoil. They varied the spacing between the rod and the airfoil, such as *L/d* = 2, 4, 6, 8, and 10. They showed that when the spacing is small (*L/d =* 2), the vortex shedding of the rod upstream, the pressure fluctuation, and the noise radiation are suppressed as shown by Munekata et al. [10–11] and when the spacing is large (*L/d* = 6, 10), the pressure fluctuation, the noise radiation, and the fluid resonant oscillation due to the feedback loop between the rod and the airfoil become stronger.

*Wake-Body Interaction Noise Simulated by the Coupling Method Using CFD and BEM DOI: http://dx.doi.org/10.5772/intechopen.92783*

The airfoil-airfoil model (airfoils in tandem) is also a typical model for the wakebody interaction or body-vortex interaction (BVI). Liu et al. [22–23] performed the measurements to understand the effect of using serration on the aerodynamic and acoustic performance of airfoils in tandem. They studied the wake development, static pressure distributions, and surface pressure fluctuations in detail for a cambered NACA 65-710 airfoil with and without the serration. They showed that the noise is reduced in the case that the upstream airfoil is with the serration.

In this chapter, we simulate the flow around the rod-airfoil model and the noise generated by the wake-body interaction or body-vortex interaction for the cases of *L/d* = 2 and 10 at a Reynolds number based on the rod diameter (*d =* 6 mm) 28,800 (288,000 based on the airfoil chord, *c*) by the coupling method using commercial CFD and acoustic BEM codes in which the acoustic sources are solved in the CFD code and the acoustic field is solved by means of BEM, and compare the results with those obtained by Jacob et al. [9] and Jiang et al. [21]. Then, we simulate the flow around the airfoil-airfoil model (airfoils in tandem) and the noise generation and propagation for the cases of *L/c* = 0.2, 0.6, and 1 at a Reynolds number based on the airfoil chord (*c =* 60 mm) 288,000, and compare the results with those for the rod-airfoil model.
