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The superiority of the DNS method in jet noise calculation was fully proved. The DNS method propounds high-performance computer equipment when used to simulate the high Reynolds number turbulence. It not only greatly reduces the cost of the aerodynamic noise simulation but also makes the far-field acoustic calculation possible. As the calculation cost of the large eddy simulation LES method is much smaller than that of the DNS method, it is often adopted in the hybrid method to calculate the unsteady turbulence jet flow and the results are then used to forecast the radiated noise.

The studies by Wang and Moin 9 and Zhao et al. The process of generation of the jet noise is an unsteady process, while the LES method performs well in the calculation of the unsteady data varying with time. The method was found to be effective to avoid the growth of the instability wave, and the calculated results were in good agreement with the classical solutions. The results verified that the method was reliable.

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A primary objective of this work was to develop a hybrid method to provide a potential prediction tool for numerical simulation of aerodynamic noise. The LES simulation was used to study the unsteady turbulence field and then the calculation of the sound field was carried out accordingly. The radiated sound in the near field was obtained using the LEE with acoustic source terms.

A calculation model was established based on the two-dimensional cavity and the simulation of the unsteady flow, and jet noise was conducted based on the established method. Then, the unsteady turbulence jet noises of the elliptical and rectangular nozzles were analyzed using the developed hybrid method. It is suitable only when the turbulent flow pulsation frequency is lower than the time scale. For the calculation of unsteady turbulent flow with transition process, the RANS turbulence model cannot catch the special flow structure accurately.

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Usually, the quasi steady-state flow field is calculated using the RANS model, and then the transient flow characteristics are studied by the LES model. Finally, the simulation of aerodynamic sound is carried out according to the simulation results of the LES model. Both the computational cost and the counting period are reduced. The filter function is adopted to classify the flow structures, and the turbulence is calculated directly by the unsteady Navier—Stokes equation.

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The sub-grid stress SGS model is set up to link large-scale vortexes and small-scale vortexes. In the LES model, the unsteady Navier—Stokes equations are filtered by the spatial grids, as expressed by the following equations. Equations 1 and 2 are not closed as the SGS stress is unknown.

Acoustic Control of Turbulent Jets

Therefore, the lattice model is established using the related physical quantities to solve the equations. In this article, the Smagorinsky—Lilly lattice model is adopted which supposing the SGS stress to be. The variables in the flow field can be decomposed into time-averaged terms and fluctuation terms.

Then, the variables are inserted in the unsteady Navier—Stokes equation, and the viscosity fluctuation sources are omitted. The following equations can be obtained after rearranging. Then, equations 4 and 5 can be simplified as. The volume integrals are dropped and replaced by a so-called permeable FW-H formulation in Fluent.

The sound pressure at an observer location, x , can be written as In the aerodynamic noise simulation, the accuracy requirements both in space and time should be satisfied. As a fact, the sound wave propagates in free space, while calculation area is limited, and the boundary conditions of fluid field cannot be considered to be far-field free boundary. Therefore, special treatment must be taken on the flow calculation boundary of the flow field. In order to reduce the influence of the outlet boundary on the acoustic calculation, a damp truncation region is set in the front of the outlet boundary of the calculation region.

In the damp truncation region, the grids are stretched gradually, as shown in Figure 1. An additional source term is introduced into the control equation of this region to force the transient calculation results to be infinitely close to the corresponding reference value of the quasi steady flow field. The additional source term introduced into the control equation of the damp truncation region is as follows. On the premise of guarantee the convergence speed, the magnitude of the damp intensity coefficient of the damp truncation region can be 10 4. In order to solve the flow field and aerodynamic noise field, the finite volume method is used to discrete the calculation region, then the unsteady Navier—Stokes equations are solved.

The calculated flow results are substituted into the LEE with source item to compute the acoustic pressure field of near field after proper modification. Thereafter, a control surface is set in the flow field and the sound pressure of arbitrary points of far field employing the FW-H equation. The solution strategy is as follows:. The turbulence field is described by RANS model.

The simulations on the unsteady flow field are carried out using the LES simulation on the basis of the steady flow calculation results. Then, the LEE with source terms is employed to modify the transient simulation results. A program is written using the user-defined function UDF to solve the liner Euler equation, and the noise sources of the unsteady flow are determined and the sound pressure propagation of near field can be calculated.

Corresponding control surface is set in the flow field and the calculation time step and the grid number of the control plane are adjusted to guarantee the veracity of the sound field calculation. Then, the FW-H equation is applied to solve the field variables of the control surface and to acquire the sound pressure of arbitrary points of far field.

A damp truncation region is arranged in the simulation region, and appropriate source terms are introduced into the control equation of the damp truncation region to reduce the influence of the limited flow field boundary on the noise signal. A two-dimensional cavity was taken as the calculation model to conduct the unsteady flow dynamic numerical calculation.

The cavity front edge was 5 D away from the import boundary of the calculation area and the trailing edge of the cavity was 10 D away from the export boundary of the calculation area. The schematic of the cavity calculation area is shown in Figure 2. The import boundary of the calculation area was set to be pressure inlet and the export boundary was set to be pressure outlet, and the pressures were set as the same as the ambient pressure. The damp truncation region was also given in the schematic. The whole calculation domain was meshed using quadrilateral grids. The grids had to be fine enough to resolve all the important physics, and the boundary conditions must not affect the solution significantly.

The sound pressure in the cavity calculation area at different times is shown in Figure 3 a. It can be seen that calculated sound pressure using the three grids was almost the same except only slight changes in pressure amplitude at some times. The Reynolds number R e was 12, and the Mach number M was 0.

A vortex was shed from the cavity front edge and moved to the downstream until it impinged onto the trailing edge of the cavity, generating an acoustic pressure wave, which traveled upstream and led to instabilities in the shear layer and to the shedding of a new vortex.

Rossiter 14 developed an empirical formula to predict the resulting oscillation frequencies, which was based on previous studies on edge tones. A Fourier analysis of the pressure near the corner of the trailing edge is given in Figure 4. It can be seen that the dominant frequency was obvious. Table 1 shows the comparison of the calculated spectral frequencies and the Rossiter formula.

Only the first two modes are shown. The calculation errors were within the acceptable range compared to the results estimated by Rossiter formula. Fourier analysis of the pressure near the corner of the trailing edge. Comparison of the calculated spectral frequencies and the estimated results by Rossiter formula. Figure 5 shows the generation and propagation of the vortexes in the cavity at different times. The formed vortexes moved to the downstream and merged with the surrounding small-scale vortexes. It can be seen that many vortex filaments split from the edge of the vortex core continuously.

One part moved downstream along the trailing edge of the cavity and the boundary layer thickness increased. The other part was involved into the cavity under the effect of cavity flow, and as a result, the flow form changed by the interaction with the rest vortex.

Vorticity at different times: According to the calculated noise source, the sound pressure of the unsteady flow in the cavity was simulated. Figure 6 shows the instantaneous pressure perturbation contours in near field of the cavity. It can be seen that the acoustic wave was corrugated. The shed vortexes moved downstream along with the flow, and radiated acoustic would generate when the vortexes impact the trailing edge of the cavity.

The acoustic wave propagated to the upstream and caused the boundary layer to be unsteady. There were strong convection and surface scattering in the front edge of the cavity. The radiated acoustic produced by the boundary layer separation and vortex impact cavity wall intervened, and an obvious interference phenomenon appeared. This was in good agreement with the experimental results carried out by Karamcheti, 15 as shown in Figure 7.

Obvious directivity can be seen in the near acoustic field. The sound pressure level curves of each observation point were obtained by analyzing the detected sound pressure signals, as shown in Figure 8. It meant that the sound wave attenuated gradually with the increase in the propagation distance. The radiated acoustic in the far field of the cavities also showed obvious directivity as in the near field.

Sound pressure level of different observation angles in far field. The hybrid algorithm was applied to study the effects of nozzle structure on the radiation noise. Two nozzles were designed: The two nozzles were of the same export area and the ratio of long to short half axises of the elliptical nozzle was 1. Figure 10 shows the grid structure of the model. The model was meshed by the hexahedral grid, and the grids in the nozzle exit and the jet boundary layer whose velocity gradient was great were refined to guarantee high computational accuracy.

A damp truncation region was set in the export region near the outlet boundary to reduce the influence of the outlet boundary on the calculation of the sound field. The total grid number was 1,, The calculation region and the boundary conditions of the model are shown in Figure The environment boundary was set to be the pressure outlet. The impact of air from the environment in the simulation was ignored and the nozzle wall was set to be standard wall condition. When the airflow jet into the environment by the gradual change nozzle, the jet flow intensity attenuated as the strong airflow mixing was generated nearby the border of the jet.

Figure 12 shows the velocity distribution of the two different nozzles along the axis of the nozzle center. It can be seen that the flow velocity was maximum near the nozzle exit and the jet was complete turbulence. Velocity distribution along the axis of the nozzle center. When the airflow jet into the environment through the nozzle, large-scale vortexes were formed.

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Reducing jet noise by controlling turbulence

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