Understanding of the Flow Behaviour on a Helmholtz Resonator Excited by Grazing Flow

Transcription

1 Understanding of the Flow Behaviour on a Helmholtz Resonator Excited by Grazing Flow Abstract Grazing flow passing over the quiescent fluid inside the cavity of a Helmholtz resonator can excite the resonator. When the frequency of the instabilities within the shear layer is near the natural frequency of the resonator then flow-excited resonance will occur. This process causes self-sustained periodic oscillations of the flow over the orifice of the resonator. Quantitative numerical prediction of the characteristics of these fluctuations requires accurate modelling of the grazing flow over the Helmholtz resonator. In the present study a Large Eddy Simulation (LES) of the three dimensional shear flow over the orifice of a threedimensional Helmholtz resonator was implemented at low Mach numbers. The simulations were performed over a wide range of Reynolds numbers to analyse the effect of the inlet flow properties on the excitation condition. It was assumed that the excitation phenomena are associated with external pressure fluctuations within the turbulent boundary layer of the grazing flow and the acoustic response of the cavity. For validation proposes, the results obtained from the numerical simulations have been compared with published experimental data and show that the numerical modelling provides an accurate representation of the pressure fluctuations inside the cavity. The main objective of this paper is an understanding of the flow features over a flow-excited Helmholtz resonator. To this end using the numerical model the interaction of a turbulent boundary layer with a Helmholtz resonator has been considered and the characteristics of the flow inside the resonator and over the orifice for various flow conditions are also analysed. 1. Introduction A Helmholtz resonator exposed to a grazing flow with a specific speed can produce strong flow fluctuations. These oscillations can generate desired or undesired pressure fluctuations within the flow over the resonator opening. Examples of this process have been described in the literature, such as gas fluctuations inside pipelines with closed side branches, the grazing flow over aircraft landing gear, and cabin pressure fluctuations inside a vehicle with an open window or sunroof (Inagaki et al. 2002). Pressure oscillations inside the resonator generated by external excitation have been extensively studied in the literature (Charwat & Walker 1983). Understanding the mechanism of a self-excited resonator requires extremely accurate 1

2 prediction of the shear flow properties and the inflow and outflow cycles over the orifice. The motivation for the current study originates from the desire to model the excitation of a resonator caused by the turbulent boundary layer grazing flow in order to predict the flow characteristics over the resonator. The simulations can also provide an accurate quantitative description of the capability of a Helmholtz resonator to reduce innate disturbances within the turbulent boundary layer. A Helmholtz resonator is an alternative type of side branch resonator for suppressing pure tones of constant frequency, which consists of a short neck which is connected to a large cavity with a fixed volume of compressible fluid (Kinsler et al. 1999; Von Helmholtz 1896). As can be seen in Figure 1, the behaviour of the flow within a Helmholtz resonator can be described as a second-order mass-spring system using a mechanical analogy. U(y) M R K Figure 1: Schematic of a mechanical analogy of a Helmholtz resonator In the mass-spring system, the mass is comprised of the mass of fluid in the neck, whereas compressibility of the fluid within the cavity acts as a spring, where is the cross-sectional area of the orifice, is the density of air, is the speed of the sound, is the cavity volume and is the effective length of the orifice. Owing to the viscous effects of the flow and acoustic radiation at the orifice, the system acts as a massspring-damper with a damping constant of,. Self excitation occurs when the frequency of the instabilities inside the grazing flow over the orifice is near or equal to the resonance frequency of the resonator,. By means of a lumped element analysis, the natural frequency of the resonator can be derived as (1) 2

3 where the resonance frequency is related to the natural frequency by the expression, where is the damping ratio (Rockwell & Naudascher 1978). The excitation of the resonator can occur at both high and low Mach numbers; however, in the present study only the subsonic flow regime was considered. When the wall boundary layer of the grazing flow reaches the upstream edge of the orifice, it suddenly separates resulting in the formation of vortices, which, in turn, form a shear layer in this area. As illustrated in Figure 2, the quasi-periodic vortices shed from the leading edge of the orifice travel to the trailing edge with a convection velocity of,. When these vortices reach the trailing edge of the resonator, they produce acoustic pulses which in turn can excite the acoustic resonances in the cavity. This excitation produces an intense energy exchange between the grazing flow and the air within the cavity. When the frequency of the flow oscillations (, where is orifice length) is far from the natural frequency of the resonator, the two processes are weakly coupled. If the frequency of the flow fluctuations over the orifice is near the natural frequency of the resonator, it is excited and a small pressure fluctuation at the orifice can produce a relatively large magnitude velocity fluctuation around the neck, which is accompanied by the large pressure fluctuations inside the cavity. Figure 2: Schematic of convection of vortices over the orifice In this paper a number of cases have been simulated to provide an explanation for the interaction between the grazing flow and the resonator which generates velocity and pressure perturbations in the area very close to the orifice. The simulations show the excitation condition and predict the flow behaviour within the turbulent boundary layer downstream of the orifice for various flow conditions and resonator geometries. This understanding assists with skin friction changes within the wall-bounded flow in downstream of the orifice. One of the earliest experimental investigations of flow excited cavities was carried out by Rossiter (1964) who examined shallow cavities at subsonic and transonic flow regimes. A 3

4 semi-empirical correlation was suggested to predict the frequency of natural hydrodynamic instability of low Mach number ( grazing flow over the opening as (2) in which is the mode number of the resonator ( =1, 2, 3,.), is the Mach number, is the phase lag between the external force and the pressure inside the cavity and is the normalized convection velocity of the vortices based on free stream velocity,, over the orifice. Using shadow graph images it was also shown that the interaction of vortices with the trailing edge of the cavity opening results in the generation of the acoustic pressure waves which trigger the next vortices at the leading edge of the cavity. Using hotwire anemometry in the neck and microphones inside the cavity, Panton & Miller (1975) proved that a Helmholtz resonator can be excited by a turbulent boundary layer provided that the orifice diameter is smaller than the thickness of the boundary layer. It was concluded that a resonator can be excited by turbulent boundary layer when the diameter of eddies in the turbulent boundary layer are twice the diameter of opening. In their work the boundary layer was only affected in the regions very close to the orifice as the pressure spectra upstream and downstream of the orifice stayed unchanged. Panton (1990) also carried out another experimental study for six different resonator geometries to determine the effects of the resonator shape on the excitation condition. It was concluded that the planform shape of the orifice and the ratio of cavity length to the boundary layer thickness affect the pressure response of the Helmholtz resonator. Using a Laser Doppler Velocimetry system in the neck of the resonator, Nelson et al. (1981) proved that the excitation is associated with the periodic shedding of the compact vortices from the upstream edge of the orifice to the downstream edge. A recent experimental attempt to explore flow characteristics within and outside the resonator was also carried out by Ma et al. (2009) who tested a self-excited Helmholtz resonator with various free stream velocities. It was concluded that the external force which comes from shedding vortices has a constant magnitude over a wide flow speed range. There are also some studies that have taken a theoretical approach to the subject of flow-excited Helmholtz resonators. For example in analytical model proposed by the Nelson et al (1981), it was assumed that the total velocity field is a superposition of one purely rotational flow and the potential. The fluctuating part of potential flow is related to acoustic field whilst combination of the rotational and mean potential flows generates the hydrodynamic flow. It was concluded that the fluctuating vortical flow generates a force which is responsible for 4

5 excitation of the resonator flow. A feedback loop analysis to calculate the hydrodynamic force of vortex shedding was also implemented by describing two forward and backward functions, resulting from the superposition of aerodynamic and acoustic flows (Kook, Mongeau & Franchek 2002; Mast & Pierce 1995). This method can accurately predict the external forces of the vortices and pressure fluctuations inside the cavity. As an example of the application of this method, Inagaki et al. (2002) developed equations for the numerical prediction of the flow oscillations over a Helmholtz resonator at low Mach number. Their method was based on the prediction of the frequency of pressure fluctuations within the flow over a resonator orifice with a high aspect ratio at a low Mach number using the compressible Navier-Stokes equations. They showed that the frequency of the pressure fluctuations is very close to the natural frequency of a resonator over a wide range of velocities. Mallick et al. (2003) later applied a modified Lattice Boltzmann equation for calculation of the pressure fluctuation spectrum within the grazing flow, excited by a Helmholtz resonator. Using Re- Normalization Group methods (RNG) based turbulence model, they showed that for the case of the velocity of grazing flow was multiplied by a factor of 0.7, the predicted pressure fluctuations were very close to the experimental data of Nelson et al. s (1981). The reason for applying the factor of 0.7 was described as being due to the effects of boundary layer thickness on the convection velocity of the vortex within the shear layer over the orifice. The remainder of this paper is organized as follows: applicability of the LES model and its governing equations are described in 2. In 3 the results of the simulations are compared with experimental published data for validation purposes. Then in the 4 the effects of flow conditions on the characteristics of the shear flow over the orifice are discussed. In the last section the conclusions and a summary of this study are presented. 2. Numerical set up and procedure In order to calculate the fluctuation parameters of the shear flow over the orifice and the flow field inside the resonator, an appropriate modelling tool is required to adequately simulate the complex three dimensional flow. Therefore the model must have very low dissipation to predict the fluctuations in shear flow over the orifice and the acoustic field accurately. It has been shown that Reynolds-averaged Navier-Stokes (RANS) methods are typically too dissipative and thus these models under-predict the velocity and pressure fluctuations in the flow field (Georges et al. 2009; Sinha, Arunajatesan & Ukeiley 2000). 5

6 These methods are appropriate for steady flows, or unsteady flows with very weak nonresonant coupling, but are not suitable for highly unsteady flows with strong vortex acoustic coupling (Arunajatesan & Menon 2000). Therefore the RANS models are not considered suitable for modelling the flow excited by a Helmholtz resonator. Among the turbulence models, the Large Eddy Simulation (LES) has been reported to be the most suitable one for obtaining the velocity and pressure fluctuations within the turbulent boundary layer (Moin 1978). This model represents a three dimensional and time dependant solution of the Navier-Stokes equations and it is capable of handling the flows involving strong vortex-acoustic coupling, including pressure disturbances associated with resonance (Blazek 2005). The LES model separates the small and large scale structures by using filtering and resolves the large scale flow features. This model, using sub-grid model for the small-scale structures, can also accurately predict flow fluctuations in the wall bounded regions (Schlatter 2005, Ghanadi et al. 2013). In this paper a simulation based on LES was used as a tool for modelling the fluctuations associated with coherent structures in the turbulent boundary layer and perturbations within the separated flow at the resonator opening. Using this method, the pressure fluctuations in the acoustic feedback field can be modelled with adequate accuracy. Moreover, the velocity perturbations generated by the grazing flow passing over the resonator can be calculated. The details of the numerical method and its governing equations are presented in the following section. 2.1 Governing equations Owing to the compressibility of the air inside the cavity, the filtered compressible Navier Stokes equations for a Newtonian fluid must be used. According to Wagner et al. s (2007) work to simplify the equations a mass-weighted change of a variable based on is defined as (3) where can be velocity in all three directions and is the air density. It is worthwhile nothing that the ~ and operators correspond to change of variables and filtered variables, respectively. Therefore, the conservation and Navier-Stockes equations are then given by (the following derivations are based on Wagner et al. s (2007) work) 6

7 (4) (5) where is the air velocity, is the static pressure of the flow, is time, is the filtered stress tensor and is the computable stress tensor. The filtered Navier-Stokes equations govern the evolution of the large scale features of the flow. The effect of the small structures is represented through a subgrid scale stress term, which is given by, (6) where is the Kronecker delta, is eddy viscosity and is the deformation tensor of the subgrid field,. (7) The most popular subgrid model is the Smagorinsky model (Addad et al. 2003; Chai & Mahesh 2010; Kato 2011), but this model is of the order of one and it is simply related to the strain rate of the turbulent structures. In this project the Wale subgrid model has been used which can accurately predict the flow behaviour of the subgrid viscosity on the wall in a zero pressure gradient incompressible boundary layer, and is of the order of 3 (Nicoud & Ducros 1999), where the eddy viscosity is given by (8) where is a constant and the best results were obtained with (Nicoud and Ducros 1993; Moin 1978) and (9) In the next section the characteristics of the simulations are described, including a study of the effects of the mesh grid and the nature of the inflow condition. 7

8 2.2 Simulation Characteristics As shown in Figure 3, the resonator has a cavity of with a square cross section of 50 by 50 cm and a height of 59 cm. The 12.5 by 12.5 cm orifice with sharp edges has a thickness of 0.16 cm. 25 cm Orifice 59 cm Cavity 50 cm Figure 3: Cross-section through resonator centreline illustrating the Helmholtz resonator geometry studied in this research The free stream velocity was varied in the range of 10 to 30 m/s with a boundary layer thickness of 0.5 cm to 2 cm at the orifice upstream lip. Since the LES only models the small turbulence structures and the large eddies are directly computed, the model requires high grid resolution in the near wall region in the streamwise and the crosswise directions (Wagner et al. 2007). Therefore, the first task is the development of an accurate physical geometry with a suitable mesh for the computational domain. Figure 4 illustrates a 2D view of the three dimensional mesh around the orifice of the resonator. In order to capture the behaviour of the near-wall flow, a sufficiently fine mesh has been used. An accumulated mesh structure has been utilized in the region near the resonator orifice to ensure that there are at least a few cells in the buffer layer of the turbulent boundary layer. Using this kind of grid allows a fine mesh within the turbulent boundary layer and fits the geometry very well. In order to calculate the characteristics of the flow in the outer region of the boundary layer the number of grid points (cells) in total is proportional to and in the viscous region this is increased to. Although these cell sizes result in relatively fine meshes, in comparison with DNS this method allows reduced computational costs. However the highest grid 8

9 resolution needs to be applied over the surface to capture the characteristics of the boundary layer. Leading edge Trailing edge Figure 4: Volumetric fine mesh in the orifice of the resonator. The mesh-sensitivity study has also been studied and then a computational mesh containing 2.5 million cells (1 million vertices) was used. In order to evaluate near-wall fluctuations, a non-dimensional wall distance to the first grid point,, should be less than unity. In the present study for all the cases investigated this parameter was around 0.2. Based on the location of turbulence onset, the resonator orifice is placed at 200 cm from the inlet surface. As illustrated in Figure 5, at the inlet the velocity of the free stream was defined, while for the outlet condition a pressure of one atmosphere was used since it is plausible for flow in a channel. Moreover, the rigid wall boundaries are assigned for the channel and the resonator surfaces. The boundary layers over the channel walls should not have any effects on the grazing flow over the orifice, thus it was assumed that there is no friction over the upper and side walls of the channel. Wall (with slip condition) Outlet Inlet Wall (with no slip condition) Resonator Figure 5: Cross-section showing boundary conditions for the CFD model. 9

10 3. Results and discussion The LES model described in Section 2 was used to generate the numerical results described in the following sections. Based on Equation (1) the resonator natural frequency,, is 45 Hz. The primary non-dimensional parameter of interest,, was defined based on free-stream velocity. Using the turbulence model and boundary conditions described previously, velocity and pressure distributions within and over the resonator were calculated. 3.1 Validation procedure The pressure fluctuations inside the cavity were measured using microphones in Ma et al. s (2009) experimental work. Therefore to validate the results of simulations the pressure fluctuation within the flow-excited Helmholtz resonator,, is analysed in this section. In order to show the results in terms of frequency, another non-dimensional parameter based on natural frequency of the resonator was defined;. where is the natural hydrodynamic instability frequency. Figure 6 shows the calculated sound pressure level (SPL) as a function of at three different inlet velocities of and 6. When the free stream velocity was around 6.7 m/s, which corresponds to, a dual mode pattern was observed in the simulation results, with the first peak at around (first subharmonic) and the second at (the fundamental). Figure (6a) shows that a strong peak appears at a frequency very close to the natural frequency of the resonator with peak amplitude of around 103 db. Using Equation (3), the frequency of instabilities within the shear layer was calculated. In this case, which is the phase lag between the shear layer forcing and acoustic feedback, is typically 0.25 for high speed flows and around zero for low speed flows. The nondimensional convection velocity of the instabilities within the shear flow,, is between 0.35 to 0.6. In the present paper and and thus using Equation (2) the first and second mode instability frequencies are around 20 and 46.7 Hz, corresponding to and. As can be seen in the Figure (6a), these peaks at these two frequencies appear in both the experimental and numerical results. As illustrated in Figure (6b), increasing the flow velocity to 15 m/s produces results with just one dominant mode which is very close to the resonance frequency of the resonator and with an amplitude of 116 db. By further increasing the free stream velocity the strong peak is significantly reduced in amplitude (Figure 6c). 10

11 20 log 10 (p res / p ref ) (db) 20 log 10 (p res / p ref ) (db) 20 log 10 (p res/ p ref ) (db) a) Ma et al. (2009) LES model f* b) Ma et al. (2009) LES model f* c) Ma et al. (2009) LES model f* Figure 6: Sound Pressure Level (SPL) of the resonator at different inlet flow velocities a) ; b) ; c) Therefore it appears that there is a specific range of free stream velocities for which a strong peak in SPL is observed and there is little or no sign of resonance for other free-stream velocities. The model was also used to calculate the pressure fluctuation inside the resonator and this information was examined to assess the ability of the LES to match the frequency and amplitude of the fluctuations observed experimentally in the literature. The magnitudes 11

12 log (P* res ) of the pressure fluctuations within the resonator in the region of the resonance frequency were determined by integrating the power spectrum of the pressure inside the resonator, normalized by the free stream dynamic pressure (as per Ma et al. 2009), (10) where is the power spectral density of the pressure within the turbulent boundary layer. Figure 7 shows the calculated unsteady pressure fluctuations within the resonator over a range of free stream velocities. The results are presented as open circles along with the measured pressure amplitudes by Ma et al. (2009). The simulation shows that the pressure fluctuation is maximum at, which is the same as the experimental result Ma et al LES model U* Figure 7: The non-dimensional resonator pressure amplitude as a function of the non-dimensional free stream velocity Although in Figure 7 the amplitude of the simulations results are slightly lower than experimental data, the model exhibits the same trend as experiments and accurately predicts the correct frequency associated with maximum pressure fluctuations within the resonator. It should be noted that the width of the integral in Equation (10) does have a significant impact on the amplitude of the pressure estimate. The choice of integral bandwidth was based on Ma et al. s (2009) work. A slightly larger bandwidth makes the simulated results and 12

13 u+ experimental results collapse. Another reason for mismatch between experiment and simulation is due to energy dissipation of the model for subgrid scales. 3.2 Flow characteristics It is essential to ensure that there is a fully developed turbulent boundary layer over the wall surface just before the orifice leading edge. Figure 8 shows the mean velocity profile obtained from the simulation within the near wall and the logarithmic region of the turbulent boundary layer over a flat plate with zero pressure gradient. The comparison between the simulation results and the experimental data of Marusic et al. s (2012) study shows the expected trend in the mean velocity and proves that there is a fully turbulent boundary layer at Re= Marusic et al. (2012) LES model y+ Figure 8: Mean velocity profiles within the turbulent boundary layer over the flat plate at Re=10 6 In order to determine the behaviour of the shear flow over the orifice length, velocity distributions were calculated within the shear layer at locations spanning the leading edge to the trailing edge of the orifice. Therefore the mean and fluctuating components of the flow velocity over the resonator opening were determined using the LES model. The velocity of vortices inside the shear layer plays an important role in generating high pressure fluctuations within the resonator and the exchange of energy between the boundary layer and the cavity flow. It has been found that vortices in a thick turbulent boundary layer convect more slowly compared to a thin boundary layer (Panton 1990). Flow visualizations from the literature 13

14 report that the convection speed is a function of the boundary layer thickness and free stream velocity (Elder, Farabee & DeMetz 1982; Kook, Mongeau & Franchek 2002), where the convection velocity is given by (12) where is the boundary layer thickness. In the present study the convection velocity of the vortices has been calculated using simulation for various free stream velocities. As an example for, Figure 9 shows at the mid-point of the orifice the velocity of the flow is between 6 to 7 m/s. When the free stream velocity is around 15 m/s, the velocity profile at the leading edge of the orifice shows that the turbulent boundary layer thickness is approximately 1 cm. Therefore, the value of boundary layer thickness and convection velocity of vortices for this free stream velocity is perfectly predicted by Equation (12). It should be stated that for other velocities this agreement was also observed. y x Figure 9: Stream-wise velocity (m/s) over the resonator In the present paper component of the instantaneous velocity,, at the exit of the orifice, over one period,, for three different free stream velocities was calculated. This calculation illustrates the interaction of the turbulent boundary layer grazing flow with the flow inside the resonator. As shown in Figure (10), for there is no flow fluctuations in the first half of the orifice length. The maximum injection with rather low vertical velocity occurs in the middle of the orifice exit and the maximum suction with more 14

15 magnitude takes place near the leading edge of the orifice. It can also be seen that the displacement velocity of the peaks over the orifice is very slow. t = 0 t = 0.2 T t = 0.4 T t = 0.6 T t = 0.8 T t = T Figure 10: component of the instantaneous velocity over the orifice exit at (scale unit is in m/s) In the first half of the period when, the injection peak is increased and moved toward the leading edge (Figure 11). After t= 0.6 T, the suction cycle is dominant and growth from trailing edge to leading edge of the orifice. As figure shows in this free stream velocity blowing and suction have more force than before so that the maximum value of the vertical velocity reaches to 0.3U. t = 0 t = 0.2 T 15

16 t = 0.4 T t = 0.6 T t = 0.8 T t = T Figure 11: component of the instantaneous velocity over the orifice exit at (scale unit is in m/s) By further increasing the free stream velocity to, as demonstrated in Figure (12) the peak of the vertical velocity fluctuations occurs close to the leading edge of the orifice with a very low magnitude. The figure also shows that there are no significant fluctuations in the second half of the orifice length. t = 0 t = 0.2 T t = 0.4 T t = 0.6 T t = 0.8 T t = T Figure 12: component of the instantaneous velocity over the orifice exit at (scale unit is in m/s) 16

17 Power Spectral Density of W (db ref 1mm 2 /Hz) The spectral analysis on the, over the orifice was also performed. To this end the power spectral density (PSD) of velocity fluctuations has been calculated along six locations over the orifice. In order to achieve the PSD results a Hanning window was used along with FFT points with 50% overlap when averaging. The results for the distance from the leading edge of the orifice are plotted in Figure 13. It can be seen that when the maximum peak occurs at 30 Hz whilst for 15 m/s the maximum peak is very close to the natural frequency of the resonator (45 Hz). Hence in a specific free stream velocity, maximum velocity fluctuations take place at the natural frequency which means that selfsustained oscillations occur. The figure shows that the difference in magnitude between the fundamental frequency (50 Hz) and the first harmonic (100 Hz) for is approximately 28 db. This difference in magnitude proves that the shear layer over the orifice is dominated by the fundamental resonance frequency m/s 15 m/s 30 m/s Frequecny (Hz) Figure 13: Power Spectral Density (PSD) of the component of the instantaneous velocity in from the leading edge for three free stream velocities. By further increasing the free stream velocity to 30 m/s, the frequency associated with the amplitude of the fundamental mode is decreased and the first harmonic is more strongly excited. Therefore, the trend that was observed with pressure amplitude versus free stream velocity, shown in Section 3.1, is repeated for velocity. 17

18 Power Spectral Density of W (db ref 1mm 2 /Hz) Figure 14 presents the PSD of the component of the instantaneous velocity at a location from the leading edge of the orifice. It can be seen that the amplitude of the velocity fluctuations at this location for all range of velocities is higher than before. It can be stated that at this location eddies within shear layer have more energy than those at, and it comes from the higher flow fluctuations within the resonator. It is also observed that increasing the free stream velocity to 30 m/s causes lower fluctuations at this position which demonstrates that at this speed the self excitation is negligible m/s 15 m/s 30 m/s Frequecny (Hz) Figure 14: PSD of the component of the instantaneous velocity in from the leading edge 4. Conclusions Owing to the difficulties and time constraints associated with experimental tests, CFD investigations have been conducted to find the various parameters affecting Helmholtz resonator performance. To this end the three-dimensional turbulent boundary layer over a Helmholtz resonator inside a channel was simulated and time dependent pressures and velocity fluctuations were calculated. Since RANS models cannot accurately model the fluctuation parameters of turbulent flows an LES model was utilized, which was shown to have minimal dissipation effects at subgrid scales. Initially, the calculated sound pressure level of the acoustic response of the resonator was compared with experimental results and it was observed that at specific free stream velocities strong excitation of the resonator occurs. Characteristics of the inlet flow were changed to 18

19 evaluate their effects on the excitation condition. It was observed that when instability mode frequency is very close to the natural frequency of the resonator and high pressure amplitude can be achieved. The magnitude of the pressure fluctuations within the resonator was also calculated using the LES model and it was observed that the maximum pressure fluctuations occur in a specific free stream velocity and geometry of the resonator. This flow behaviour shows that over a particular velocity range of the grazing flow, the resonator can be excited. A comparison between experimental data and the model results proved that there is a quite good agreement over the speed range although the values in simulation were slightly lower than actual ones. The reason for this error is likely due to the fact that the model cannot predict exact values of the pressure fluctuations since it uses an approximation at subgrid scales and only directly calculates the large eddies. The velocity fluctuations within the shear layer over the orifice were predicted. First it was proved that there is a fully developed turbulent boundary layer just before the resonator opening. Then the convection velocity of the vortices inside the shear layer was computed and it was demonstrated that the results are very close to the experimental observations and therefore the model can predict the instantaneous velocity within the turbulent boundary layer over the orifice. The vertical component of the velocity fluctuations over the orifice exit was computed and it was concluded that the maximum value of the suction and injection occurs when the free stream velocity is around 15 m/s, the. Moreover it was observed that the maximum interaction of the grazing flow with the resonator flow moves to the leading edge of the orifice by increasing the free stream velocity. The power spectral density of the component of the velocity fluctuations over the orifice was calculated at six locations. It was demonstrated that when the non-dimensional free stream velocity is close to, the amplitude of velocity fluctuations at frequencies close to the natural frequency of the resonator is a maximum. Therefore it shows that for a particular geometry of the resonator in the specific range of velocity self-excitation occurs. The results also illustrate that for References the shear layer oscillated largely with the natural frequency. Addad, Y, Laurence, D, Talotte, C & Jacob, M 2003, 'Large eddy simulation of a forward backward facing step for acoustic source identification', International Journal of Heat and Fluid Flow, vol. 24, no. 4, pp Arunajatesan, S & Menon, S 2000, 'Towards hybrid LES-RANS computations of cavity flowfields', 8th AIAA, Aerospace Sciences Meeting and Exhibit, vol. 401, pp

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21 Rockwell, D & Naudascher, E 1978, 'Review-self-sustaining oscillations of flow past cavities', ASME Transactions Journal of Fluids Engineering, vol. 100, pp Rossiter, J & Britain, G 1964, 'Wind tunnel experiments on the flow over rectangular cavities at subsonic and transonic speeds', Ministry of Aviation, Aeronautical Research Council Reports and Memoranda, Technical report 64307, RAE. Schlatter, P 2005, 'Large-eddy simulation of transition and turbulence in wall-bounded shear flow', PhD thesis, Swiss Federal Institute of Technology, Zurich. Sinha, N, Arunajatesan, S & Ukeiley, L 2000, 'High Fidelity Simulation Of Weapons Bay Aeroacoustics Attenuation Using Active Flow Control', 6th AIAA/CEAS Aeroacoustics Conference, Paper No. AIAA , Lahaina, Hawaii. Von Helmholtz, H 1896, 'Theorie der Luftschwingungen in Röhren mit offenen Enden', W. Engelmann. Wagner, CA, Huttl, T & Sagaut, P 2007, 'Large-eddy simulation for acoustics', Cambridge Univ Press. 21