... results.¹

In a workshop on the use of computer simulation for aeroacoustics organized by the Deutsches Zentrum für Luft and Raumfahrt (DLR) in Göttingen (Germany) researchers from all over Europe and the United States, including myself, have presented their computational results. The general conclusion of this workshop was that there was a serious lack of reliable experimental data to validate the numerical results and that such data is necessary for the advancement of computational techniques for acoustics (for which there is a clear demand). This conclusion has formed one of the sources of inspiration for this proposal.

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... equations²

The Navier-Stokes equations read:

$${\frac{\partial \rho }{\partial t}}+{\frac{\partial \rho u_{i}}{\partial x_{i}}}=m$$

$${\frac{\partial \rho u_{i}}{\partial t}}+{\frac{\partial \rh... ...x_{i}}}+{\frac{\partial }{%% \partial x_{j}}}2\mu S_{ij}+F_{i}$$

In which $\rho$ is the density, $u_{i}$ the velocity vector, $m$ a mass source, $p$ the pressure, $\mu$ the dynamic viscosity, $S_{ij}$ the strain rate tensor, and $F$ is an externally applied force. The Lighthill equation can be obtained by differentiating the first equation with respect to the time $t$ and applying the divergence operator to the second equation. Together with the definition of the speed of sound

$$\left( {\frac{\partial p}{\partial \rho }}\right) _{S}=c^{2}... ...^{\prime }=p-p_{\infty },\rho ^{\prime }=\rho -\rho _{\infty }$$

gives this the Lighthill equation.

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... flow³

Some researchers prefer to write this term as

$${\frac{\partial ^{2}\rho u_{i}u_{j}}{\partial x_{i}x_{j}}}\a... ..._{i}x_{j}}}=-{\frac{1}{4}}\rho (\Omega \cdot \Omega -S\cdot S)$$

where $\Omega$ is the vorticity vector and $S$ the strain rate. This form shows that sound, vorticity and strain are strongly linked to each other, i.e. in a region with high vorticity and/or high strain sound will be produced.

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... methods.⁴

A turbulent flow is characterized by a large range of spatial and temporal scales where the extent of the range is proportional to the Reynolds number. In DNS all length and time scales present in the flow are resolved. Even with todays large computer facilities this is only possible for flows with rather low Reynolds numbers. In LES only the large energy containing scales are resolved and the small scales are modelled with help of a so-called subgrid model. Therefore, with LES the Reynolds numbers can be much higher at the cost of some uncertainty related to the subgrid model.

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... method.⁵

In this method a parallel light beam is sent through the flow field. The refraction of light depends on the density of the gas. Regions with high density will give a different light intensity than regions with a low density. Construction of such a setup is fairly straightforward and does not require substantial investments.

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... (PIV).⁶

In this technique two pictures of the flow field, separated in time by a few micro seconds are recorded. The displacement of small seeding particles which are added to the flow are calculated over this time separation, yielding velocity vectors of the small particles. The particles are so small that it can be assumed that they will follow all the fluid motions. In this way we can construct a vector field of the flow. A result of such a measurement, performed in our laboratory, is given in figure 5.

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... measurements.⁷

The LDA method uses the diffraction pattern of the light emitted by a small particle traveling through two crossed laser beams. This method is very accurate and can be used to obtain very reliable point measurements.

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