Turbulence -- Mathematical models

This project is intended to demonstrate the current state of knowledge in the prediction of the tonal and broadband noise radiation from a Sevik rotor. The rotor measurements were made at the Virginia Tech Stability Wind Tunnel. Details of the rotor noise and flow measurements were presented by Wisda et al(2014) and Murray et al(2015) respectively. This study presents predictions based on an approach detailed by Glegg et al(2015) for the broadband noise generated by a rotor in an inhomogeneous flow, and compares them to measured noise radiated from the rotor at prescribed observer locations. Discrepancies between the measurements and predictions led to comprehensive study of the flow in the wind tunnel and the discovery of a vortex upstream of the rotor at low advance ratios. The study presents results of RANS simulations. The static pressure and velocity profile in the domain near the rotor's tip gap region were compared to measurements obtained from a pressure port array and a PIV visualization of the rotor in the wind tunnel.

This dissertation will consider the sound radiation from forward-facing steps and a three dimensional cylindrical embossment of very low aspect ratio mounted on a plate. Glegg et al (2014) outlined a theory for predicting the sound radiation from separated flows and applied the method to predicting the sound from forward-facing steps. In order to validate this theory it has been applied to the results of Catlett et al (2014) and Ji and Wang (2010). This validation study revealed that the original theory could be adjusted to include a mixed scaling which gives a better prediction. RANS simulations have been performed and used to support the similarities between the forward-facing step and the cylindrical embossment. The simulations revealed that the cylindrical embossment exhibits a separation zone similar to that of the forward-facing step. This separation zone has been shown to be the dominant source of noise on the forward-facing step in previous works and therefore was expected to be the major source of sound from the cylindrical embossment. The sensitivity of this separation zone to the different parameters of the flow has been investigated by performing several simulations with different conditions and geometries. The separation zone was seen to be independent of Reynolds number based on boundary layer thickness but was directly dependent on the height of the cylinder. The theory outlined in Glegg et al (2014) was then reformulated for use with a cylindrical embossment and the predictions have been compared with wind tunnel measurements. The final predictions show good agreement with the wind tunnel measurements and the far-field sound shows a clearly defined directionality that is similar to an axial dipole at low frequencies.

The numerical method presented in this study attempts to predict the mean, non-uniform flow field upstream of a propeller partially immersed in a thick turbulent boundary layer with an actuator disk using CFD based on RANS in ANSYS FLUENT. Three different configurations, involving an infinitely thin actuator disk in the freestream (Configuration 1), an actuator disk near a wall with a turbulent boundary layer (Configuration 2), and an actuator disk with a hub near a wall with a turbulent boundary layer (Configuration 3), were analyzed for a variety of advance ratios ranging from J = 0.48 to J =1.44. CFD results are shown to be in agreement with previous works and validated with experimental data of reverse flow occurring within the boundary layer above the flat plate upstream of a rotor in the Virginia Tech’s Stability Wind Tunnel facility. Results from Configuration 3 will be used in future aero-acoustic computations.

For aerospace and naval applications where low radiated noise levels are a
requirement, rotor noise generated by inflow turbulence is of great interest. Inflow
turbulence is stretched and distorted as it is ingested into a thrusting rotor which can have
a significant impact on the noise source levels. This thesis studies the distortion of
subsonic, high Reynolds number turbulent flow, with viscous effects ignored, that occur
when a rotor is embedded in a turbulent boundary layer. The analysis is based on Rapid
Distortion Theory (RDT), which describes the linear evolution of turbulent eddies as they
are stretched by a mean flow distortion. Providing that the gust does not distort the mean
flow streamlines the solution for a mean flow with shear is found to be the same as the
solution for a mean potential flow with the addition of a potential flow gust. By
investigating the inflow distortion of small-scale turbulence for various simple flows and
rotor inflows with weak shear, it is shown that RDT can be applied to incompressible
shear flows to determine the flow distortion. It is also shown that RDT can be applied to more complex flows modeled by the Reynolds Averaged Navier Stokes (RANS)
equations.