In this method, both generation and propagation of sound waves are directly computed by solving the appropriate fluid dynamics equations. Prediction of sound waves always requires time-accurate solutions to the governing equations. Furthermore, in most practical applications of the direct method, one has to employ governing equations that are capable of modeling viscous and turbulence effects, such as unsteady Navier-Stokes equations (that is, DNS), RANS equations, and filtered equations used in LES and hybrid RANS-LES models.

The direct method is therefore computationally difficult and expensive inasmuch as it requires highly accurate numerics, very fine computational meshes all the way to receivers, and acoustically nonreflecting boundary conditions. The computational cost becomes prohibitive when sound is to be predicted in the far field (for example, hundreds of chord-lengths in the case of an airfoil). The direct method becomes feasible when receivers are in the near field (for example, cabin noise). In many such situations involving near-field sound, sounds (or pseudo-sounds for that matter) are predominantly due to local hydrodynamic pressure, which can be predicted with a reasonable cost and accuracy.

Since sound propagation is directly resolved in this method, you would normally solve the compressible form of the governing equations (for example, compressible RANS equations, compressible form of filtered equations for LES). Only in situations where the flow is low subsonic and the receivers in the near field sense primarily local hydrodynamic pressure fluctuations (that is, pseudo sound) can incompressible flow formulations be used. But this incompressible treatment will also not allow you to simulate resonance and feedback phenomena.

For predictions of mid- to far-field noise, the methods based on Li's acoustic analogy  [87] offer viable alternatives to the direct method. In this approach, the near-field flow obtained from appropriate governing equations such as unsteady RANS equations, DES, SAS, SDES, SBES, or LES are used to predict the sound with the aid of analytically derived integral solutions to wave equations. The acoustic analogy essentially decouples the propagation of sound from its generation, allowing one to separate the flow solution process from the acoustics analysis.

Ansys Fluent offers a method based on the Ffowcs Williams and Hawkings (FW-H) formulation [44]. The FW-H formulation adopts the most general form of Lighthill’s acoustic analogy, and is capable of predicting sound generated by equivalent acoustic sources such as monopoles, dipoles, and quadrupoles. Ansys Fluent adopts a time-domain integral formulation wherein time histories of sound pressure, or acoustic signals, at prescribed receiver locations are directly computed by evaluating a few surface integrals.

Time-accurate solutions of the flow-field variables, such as pressure, velocity components, and density on source (emission) surfaces, are required to evaluate the surface integrals. Time-accurate solutions can be obtained from unsteady Reynolds-averaged Navier-Stokes (URANS) equations, large eddy simulation (LES), or hybrid RANS-LES models as appropriate for the flow at hand and the features that you want to capture (for example, vortex shedding). The source surfaces can be placed not only on impermeable walls, but also on interior (permeable) surfaces, which enables you to account for the contributions from the quadrupoles enclosed by the source surfaces. Both broadband and tonal noise can be predicted depending on the nature of the flow (noise source) being considered, turbulence model employed, and the time scale of the flow resolved in the flow calculation.

The FW-H acoustics model in Ansys Fluent allows you to select multiple source surfaces and receivers. It also permits you either to save the source data for a future use, or to carry out an “on the fly” acoustic calculation simultaneously as the transient flow calculation proceeds, or both. Sound pressure signals therefore obtained can be processed using the fast Fourier transform (FFT) and associated postprocessing capabilities to compute and plot such acoustic quantities as the overall sound pressure level (SPL) and power spectra.

One important limitation of Ansys Fluent’s FW-H model is that it is applicable only to predicting the propagation of sound toward free space. Therefore, while the model can be legitimately used to predict far-field noise due to external aerodynamic flows, such as the flows around ground vehicles and aircraft, it cannot be used for predicting the noise propagation inside ducts or wall-enclosed space.

In this hybrid simulation method, which is intended to simulate aeroacoustics of low Mach number flows, the incompressible flow model is used for the calculation of sound sources, while the differential wave equation is used to calculate the propagation of sound generated by these sources. The acoustics wave equation implemented in Ansys Fluent is derived from the acoustics perturbation equations by Ewert and Schroeder [178] under the assumption of constant density flow. The main advantages of this model are:

• Extended applicability compared to the Ffowcs Williams and Hawking integral solver, which can be used only to model the sound propagation in open space (see Integral Method by Ffowcs Williams and Hawkings).

• Simple and convenient workflow of hybrid aeroacoustics simulations, without any data exchange between different software components via disk files, and without the interpolation of sound sources on a different mesh. A transient co-simulation of fluid flow and noise propagation using the same domain and mesh has been chosen for the current implementation.

In many practical applications involving turbulent flows, noise does not have any distinct tones, and the sound energy is continuously distributed over a broad range of frequencies. In those situations involving broadband noise, statistical turbulence quantities readily computable from RANS equations can be utilized, in conjunction with semi-empirical correlations and Lighthill’s acoustic analogy, to shed some light on the source of broadband noise.

Ansys Fluent offers several such source models that enable you to quantify the local contribution (per unit surface area or volume) to the total acoustic power generated by the flow. They include the following:

Considering that one would ultimately want to come up with some measures to mitigate the noise generated by the flow in question, the source models can be employed to extract useful diagnostics on the noise source to determine which portion of the flow is primarily responsible for the noise generation. Note, however, that these source models do not predict the sound at receivers.

Unlike the direct method and the FW-H integral method, the broadband noise source models do not require transient solutions to any governing fluid dynamics equations. All the source models need is what typical RANS models would provide, such as the mean velocity field, turbulent kinetic energy () and the dissipation rate (). Therefore, the use of broadband noise source models requires the least computational resources.