FW-H Steady Model

The Ffowcs Williams-Hawkings Steady model is based on the convergent steady-state RANS approach for aerodynamic computation of propeller blade loads for a single or multiple rotating reference frames with the FW-H Acoustic Analogy Model. It is for three-dimensional simulations with impermeable FW-H surfaces. It cannot be used for non-rotating cases.

This method deals with the case where an unsteady motion problem is converted to a steady-state RANS problem by imposing a rotating frame of reference on a static mesh. The FW-H Steady acoustics model (for convergent steady-state RANS simulations with MRF) uses a single rotating reference frame when all parts selected for an FW-H impermeable surface have an identical rotation rate value. In this case, even though all parts execute an identical rotating movement, different FW-H impermeable surfaces can have different rotation rates. When different parts rotate at different rotation rates, the FW-H Steady model implements multiple rotating reference frames. To see applications of this model refer to [46], [55], [59], [60], and [75].

Thickness surface noise is dependent only on the shape and motion of the blade. Conceptually, the displacement of the air by the rotor blade causes this noise. Loading noise is an aerodynamic adverse effect due to the acceleration of the force distribution on the air around the rotor blade due to the blade passing through it. Brentner and Farassat [46] listed various sound generation mechanisms. However, steady-loading noise and blade-displacement noise are perceived as the major contributions in the absence of installation effects.

The thickness and loading noise from relations of the FW-H acoustics model are computed from steady-state computation of the pressure field.

The steady formulation allows prediction of an unsteady pressure time signal from a steady simulation by defining an artificial unsteady time-step. Specify this artificial time-step in the Number of Time Steps Per Revolution and the Number of Revolutions properties of the FW-H Steady solver.

Previous aeroacoustic results for a few propeller cases show good agreement with experimental measurements for high rotational speed (over 2500 rpm) and larger under-prediction of the noise at low rotational speed. Thus it is not possible to predict vortex noise at low tip Mach numbers (low rotational speed). For low tip Mach numbers, it is suggested to choose accurate simulations such as a transient LES simulation with rotating motion, to simulate all transient features and broadband noise.

If the boundary is part of the region where motion is stationary and the reference frame is rotating, then the model uses the rotating reference frame properties to compute the rotating movement of the FW-H Impermeable Surface. The reference frame properties are: origin, direction, and rotation rate. To determine the position of the blade on rotating movement, the face centroid of the blade and the surface area of the blade are evaluated at each artificial unsteady time-step.

Periodic domain is considered in the same way as in the On-The-Fly FW-H model for rotating motion.