Available at: http://digitalcommons.calpoly.edu/theses/1727

#### Date of Award

5-2017

#### Degree Name

MS in Mechanical Engineering

#### Department

Mechanical Engineering

#### Advisor

Russell Westphal

#### Abstract

Because compressibility effects arise in real applications of propellers and turbines, the Actuator Disk Theory or Froude’s Momentum Theory was established for compressible, subsonic flow using the three laws of conservation and isentropic thermodynamics. The compressible Actuator Disk Theory was established for the unducted (bare) and ducted cases in which the disk was treated as the only assembly within the flow stream in the bare case and enclosed by a duct having a constant cross-sectional area equal to the disk area in the ducted case. The primary motivation of the current thesis was to predict the ideal performance of a small ram-air turbine (microRAT), operating at high subsonic Mach numbers, that would power an autonomous Boundary Layer Data System during test flights. The compressible-flow governing equations were applied to a propeller and a turbine for both the bare and ducted cases. The solutions to the resulting system of coupled, non-linear, algebraic equations were obtained using an iterative approach. The results showed that the power extraction efficiency and the total drag coefficient of the bare turbine are slightly higher for compressible flow than for incompressible flow. As the free-stream Mach increases, the Betz limit of the compressible bare turbine slightly increases from the incompressible value of 0.593 and occurs at a velocity ratio between the far downstream and the free-stream that is lower than the incompressible value of 0.333. From incompressible to a free-stream Mach number of 0.8, the Betz limit increases by 0.021 while its corresponding velocity ratio decreases by 0.036. The Betz limit and its corresponding velocity ratio for the ducted turbine are not affected by the free-stream Mach and are the same for both incompressible and compressible flow. The total drag coefficient of the ducted turbine is also the same regardless of the free-stream Mach number and the compressibility of the flow; but, the individual contributions of the turbine drag and the lip thrust to the total drag differs between compressible and incompressible flow and between varying free-stream Mach numbers. It was concluded that overall compressibility has little influence on the ideal performance of an actuator disk.