The acoustic pressure fluctuations (perceived as noise) tend to be orders of magnitude smaller than the dynamic fluctuations and propagate over large distances far from their source. Various approaches have been proposed to simulate these phenomena. The direct method solves the compressible Navier-Stokes equations and simultaneously resolves the flow and acoustic contributions. However, for practical applications this method is prohibitively expensive. Hybrid methods decouple the flow and acoustic parts, solving the aerodynamic part first to determine acoustic sources, and solving an acoustic system to obtain the associated far field radiation. Examples of such methods are: acoustic analogies (e.g. Lighthill, Ffowcs-Williams Hawkings), linearised Euler methods, Kirchhoff methods, etc. In the Alessia Project we have implemented the Ffowcs-Williams Hawkings analogy.
Large Eddy Simulation
The tools are based on the technique of Large Eddy Simulation (LES), which solves for the large-scale fluctuating flow and large eddies, and uses ‘sub-grid’ models to account for the effects of the turbulence on scales smaller than the grid size. The high computational cost of LES has meant that it was previously restricted to simple flows in simple geometries. Within Alessia, however, we have been able to relax these limitations and make LES tractable for industry-relevant applications, essentially making use of the very efficient parallel implementation and improvements in solver speed of CFX-5.
We implemented Smagorinsky’s formulation for the sub-grid scale turbulence model, which is based on an analogy to Prandtl's mixing length model. For the wall treatment, we implemented both van Driest and Piomelli’s empirical damping functions for the viscosity, where the wall distance is obtained from the solution of a differential equation, making the approach applicable to unstructured meshes. In LES, inflow/outflow boundary conditions must also represent the fluctuating nature of the flows. Hence, we included options for fully developed inlet flows, generating fluctuating profiles from prescribed mean velocities or mass fluxes and turbulence length scales. We also included the option to superimpose a random fluctuating flow on top of an initial guess to accelerate the onset of turbulence and obtain statistically converged results more quickly.
Testing showed that, as expected, first-order backward time differencing is far too diffusive for these chaotic flows and that second-order backward differencing is required. We also found that pure central spatial differencing should be used, as the other second-order methods can be too diffusive, resulting in the decay of turbulence or even laminarization of the flow.
Data analysis tools
LES provides an enormous quantity of information, the processing of which can often dominate the costs, both in computational resources (bandwidth and disk storage) and man-time. We therefore developed tools to analyze the results, providing the information in a form that can be readily interpreted by the user. We developed both quantitative and qualitative tools to provide an overall understanding of the flow, including, for example, calculation of the mean field, turbulence kinetic energy and Reynolds stresses. Macros are available to facilitate the LES and acoustics postprocessing in CFX-Post.
Prediction of noise
The approach retained for the calculation of noise propagation is the Ffowcs-Williams Hawkings (FWH) analogy (hybrid method). In this approach, a wave equation is obtained for the density fluctuations, with three types of sound sources. Firstly, sound will be generated if mass is added at an unsteady rate (examples are sirens, engine exhausts, explosions). This is called a monopole source, since it radiates equally well in all directions. Secondly, sound will be produced when time-varying forces act on the fluid (examples are bells, rotating/vibrating machinery). Such sources are called dipoles, and tend to radiate in a figure-of-eight pattern in the direction of the force. Finally, time-dependent stresses acting on the fluid can also generate sound (free turbulent jet flows, shear layers and boundary layers are examples). Such sources are called quadrupoles, because they tend to radiate in a cloverleaf pattern.
In this approach, CFX-5, which provides the fluctuating sources from both conventional Reynolds-averaged turbulence models and LES, has been interfaced with SYSNOISE, which solves the wave equation using Green-function methods. New functionality has been implemented in SYSNOISE, which allows the inclusion in an acoustic analysis of volume sources such as monopoles, dipoles and quadrupoles.
One of the highlights of the project is the extensive validation of the methodology that has been carried out by the partners. The application cases have been deliberately chosen to push the technology, so as to identify its limitations and indicate the areas where it is most useful. Cases studied include: flow past a cylinder, jet in a box, confined cylinder with end plates, fan noise, flasher, industrial cyclone, rotating cylinder and jet flow past an aerofoil.
CFX-5 LES has helped to correct k-epsilon calculations for two applications at Shell, namely an axial cyclone and a mixing chamber that involves two-phase mixing. For the mixing chamber, the results showed that conventional two-equation turbulence models tend to be over-optimistic in predicting the mixing. Alfa Laval's applications included sound propagation from the vortex shedding behind a circular cylinder and fluid flow in a rotating duct. FIAT looked at the near-field noise of an axial fan. In this case, a time-dependent RANS simulation proved to be able to predict the intensity of the near-field tonal noise. LES can also be applied to these cases, and it should improve the predictions for the broad-band noise.
As a result of the Alessia project, the CFD/computational acoustics coupling methodology has been proven and demonstrated on a number of cases. Thanks to the confidence they have gained through the work and because of significant business needs, the partners are continuing to use the techniques on their own application-specific cases.
Prediction of the noise from a strut in the wake of a jet: velocity vectors.
Radiating noise field (Amplitude of SPL) from the strut at 280 Hz.
The results, using a transient RANS model, are qualitatively consistent with the physical mechanism of noise generation in rotor-stator interaction and the simulation correctly computed the blade-passing frequency. Fan in duct with simple stator - pressure field on the blades.
Courtesy of FIAT Research Center.
Instantaneous velocity field at the bottom of a cyclone, with an isosurface of low pressure, identifying the strong vortex in the cyclone core.
Turbulent structures in the wake of a cylinder. Experimental visualization.
Picture courtesy of FIAT Research Centre.
Turbulent structures in the wake of a cylinder calculated with CFX-5's LES. Axial velocity isosurfaces for a cylinder between two endplates.
Picture courtesy of FIAT Research Centre.