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This thesis presents a Lagrangian formulation of the Euler equations for subsonic flows. A special coordinate transformation is used to define the Lagrangian coordinates, namely the stream function and the Lagrangian distance, in function of the Cartesian coordinates. This Lagrangian formulation introduces two new geometry state variables, and a Lagrangian behavior parameter defining a pseudo-Lagrangian time used during the iteration procedure to obtain the solution for subsonic flows. / The eigenstructure and characteristics analysis for the new system of equations is based on a linear Jacobian matrix-mapping procedure, which starts from the well-known eigenstructure and characteristics in the Eulerian plane and uses the coordinate transformation to find their counterparts in the Lagrangian plane. This analysis studies the basic properties of the Euler equations in the Lagrangian formulation, such as hyperbolicity, homogeneity and rotational invariance. The Riemann problem in the Lagrangian plane is also studied. Those elements are used to construct the numerical scheme for solving the Euler equations in the Lagrangian formulation. / The numerical scheme is constructed using first and second-order dimensional-splitting with hybrid flux operators, based on flux vector splitting and Godunov methods, which include a 2-D Riemann solver in the Lagrangian plane. The numerical method is validated by comparing the present solutions with the results obtained with an Eulerian formulation for several internal flows. / This numerical method based on a Lagrangian formulation has also been extended for the solution of unsteady subsonic flows by using a dual time approach. The method validation in this case has been done by comparison with the Eulerian formulation solutions for several internal subsonic flows with oscillating boundaries.

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Thesis (M.S. in Aeronautical Engineering)--Naval Postgraduate School, September 2002. / Thesis advisor(s): Kevin D. Jones, Max F. Platzer. Includes bibliographical references (p. 61). Also available online.

Thesis--Auburn University, 2009. / Abstract. Vita. Includes bibliographical references (p. 53-55).

Thesis (Ph.D.) - University of Queensland, 2003. / Includes bibliography.

Thesis (M.S.)--West Virginia University, 2005. / Title from document title page. Document formatted into pages; contains xiv, 86 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 73-76).

<p> Rising costs and volatility in aviation fuel and increased regulations resulting from climate change  concerns have driven gas turbine engine manufacturers to focus on reducing fuel consumption.  Implementing centrifugal compressors as the last stage in an axial engine architecture allows for  reduced core diameters and higher fuel efficiencies. However, a centrifugal compressor's  performance relies heavily on its stationary diffusion system. Furthermore, the highly unsteady  and turbulent flow field exhibited in the diffusion system often causes CFD models to fall short of  reality. Therefore, rapid validation is required to match the speed at which engineers can simulate  different diffuser designs utilizing CFD. One avenue for this is through the use of additive  manufacturing in centrifugal compressor experimental research. This study focused on implementing a new generation of the Centrifugal Stage for Aerodynamic  Research (CSTAR) at the Purdue Compressor Research Lab that utilizes an entirely additively  manufactured diffusion system. In addition, the new configuration was used to showcase the  benefits of additive manufacturing (AM) in evaluating diffusion components. Two diffusion  systems were manufactured and assessed. The Build 2 diffusion system introduced significant  modifications to the diffusion system compared to the Build 1 design. The modifications included changes to the diffuser vane geometry, endwall divergence, and increased deswirl pinch and vane  geometries. The Build 2 diffusion system showed performance reductions in total and static  pressure rise, flow range, and efficiencies. These results were primarily attributed to the changes  made to the Build 2 diffuser. The end wall divergence resulted in end wall separation that caused  increased losses. The changes to the diffuser vane resulted in increased throat blockage and lower  pressure rise and mass flow rate. In addition to the experimental portion of this study, a computational study was conducted to study  the design changes made to the Build 2 diffusion system. A speedline at 100% corrected rotational  speed was solved, and the results were compared to experimental data. The simulated data matched  the overall stage and diffusion system performance relatively well, but the internal flow fields of  the diffusion components, namely the diffuser, were not well predicted. This was attributed to  16 using the SST turbulence model over BSL EARSM. The BSL EARSM model more accurately  predicted the diffuser flow field to the SST model.  </p>