Author ORCID Identifier

https://orcid.org/0009-0000-8900-0389

Date Available

10-7-2025

Year of Publication

2025

Document Type

Doctoral Dissertation

Degree Name

Doctor of Philosophy (PhD)

College

Engineering

Department/School/Program

Mechanical Engineering

Faculty

Dr. Sean Bailey

Faculty

Dr. Jack Maddox

Faculty

Dr. Brehm

Abstract

The performance capabilities of rotorcraft have improved significantly in the past decade as both manned and unmanned rotorcraft become a larger part of future transportation systems. Private companies as well as various government offices have worked to develop capabilities ranging from transportation/package delivery to intelligence/surveillance to livestock monitoring. Their practicality in both rural and urban areas, however, is questionable due to the significant tonal and broadband noise which is produced by the rotors. Public acceptance of rotorcraft, namely small Unmanned Aerial Vehicles (sUAVs), in transportation systems is an issue largely associated with the noise generation and it's effect on nearby populations. Understanding the physical mechanisms that influence rotor noise is of the upmost importance in the design of rotors and rotorcraft such that acoustic performance is optimized. In particular, mechanisms that affect generation of noise are important to understand so that they can be avoided in the design of future rotorcraft systems. A key challenge to the future development of these vehicles is understanding broadband noise generated by the rotor blades. Broadband noise is a direct result of turbulence including shedding of turbulent boundary layers past trailing edges, laminar/turbulent separation, and tip vortex blade interaction. Understanding the physical turbulence mechanisms of the blades is the first step to predicting the aeroacoustic performance of these vehicles. To this end, the ultimate goal of the work is to create a high-fidelity Computational Fluid Dynamics (CFD) simulation approach to understand rotorcraft broadband noise generation. The contents of this dissertation are meant to be a stepping stone to this goal. CFD is a field of study which uses computers to solve governing equations which simulate fluid flow. Simulations may be performed for a variety of purposes, including studying fluid physics, or for the purpose of research and design of new products. Simulations may be preferable to experiment due to monetary cost, time requirements, and improved data collection. The CFD solver under development in this dissertation effort is intended for use in the incompressible, high Reynolds number flows of small rotorcraft. The solver itself is a combination of an immersed boundary code solving the incompressible Navier-Stokes equations with a wall stress model. The acoustics are then solved using the linearized perturbed compressible equations, which have been coupled with the incompressible solver. The flow regime for these systems is essentially incompressible (using a Reynolds number based on air as a fluid, wing tip velocity, and chord length, $Re_L < 0.3$ Mach). The use of the immersed boundary method enables the simulations of multiple moving blade/body systems and their interactions without complex meshing capabilities and human input requirements. The use of the wall model enables high-Reynolds number accuracy near the wall, where it is unreasonable to resolve the inner boundary layer fluid dynamics. Wall models have been investigated as tools to economically calculate high Reynolds number boundary layer flows in lieu of fully resolved large eddy simulation or direct numerical simulations. Modeling the boundary layer provides immense cost savings for high Reynolds number flows as the inner boundary layer is the most expensive part of the simulation, scaling the fastest with increasing Reynolds number. The combination of the incompressible Navier-Stokes equations and the linearized perturbed compressible equations enables an acoustic solution at a reduced cost compared to solving the compressible Navier-Stokes equations. The first part of this dissertation effort was improving and validation the existing incompressible Navier-Stokes solver in the Cartesian Higher-order Adaptive Multi-Physics Solver (CHAMPS) numerical solver. Improvements included additional development of the moving boundary capabilities within the existing immersed boundary code and efforts related to simulation stability and robustness. Additionally, a significant effort was made to improve the adaptive meshing capabilities of the immersed boundary code. The validation of these improvements includes cylinder in crossflow test cases with both static and moving boundaries as well as a turbulent channel flow test case. The cylinder in crossflow validation included literature comparisons of lift, drag, Strouhal number, and physical wake dimensions. Each of these data points matched very well with the literature results. The turbulent channel validation compared velocity profiles and Reynolds stresses and showed a good comparison with the literature results, although with some room for improvement. In this effort, a wall stress model was implemented within the incompressilbe CHAMPS solver. The wall model implementation was validated with test cases from the literature including a wall modeled RANS channel and flat plate cases. The results of the validation show good agreement with the literature results including velocity profile comparisons and shear stress comparisons. Two target cases were ultimately tested using the incompressible Navier-Stokes and wall model combination. These cases were a flat plate and a smooth wall separation. Both of these target cases were solved using a large eddy simulation approach. The results of the target cases were compared to the available literature results for both cases, including velocity profiles, Reynolds stresses, and shear stress at the wall. For the flat plate, the results of the present effort yielded a satisfactory comparison for several simulation configurations, while other configurations show need for improvement. In particular, it seems that there is some sensitivity to the angle of alignment of the flat plate and the Cartesian mesh, which is discussed. The results of the smooth wall separation showed a need for improvement in the capabilities of the solver, particularly with regard to predicting the pressure field and flow separation. While the case shows some positive results, the solver fails to predict the expected separation. A discussion on the current limitations of the incompressible solver is included. The last component of this effort was the implementation of the linearized perturbed compressible equations. These equations are loosely coupled with the incompressible Navier-Stokes equations and use the hydrodynamic incompressible solution to solve the associated acoustic field. Validation of this implementation is tested with a Gaussian pulse test case. A pulse initial condition is tracked through the flow field and the acoustic pressure is recorded and compared to the literature results. The comparison shows excellent agreement with existing literature results, however the results fail to perfectly match the analytical solution. While tests of the linearized perturbed compressible equations in a rotorcraft simulation were planned, they ultimately did not come to fruition. Testing of a relatively low Reynolds number airfoil or rotorcraft is the logical next step of this effort.

Digital Object Identifier (DOI)

https://doi.org/10.13023/etd.2025.467

Funding Information

This research was performed under appointment to the Rickover Fellowship Program in Nuclear Engineering sponsored by Naval Reactors Division of the U.S. Department of Energy, 2020-2025

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