Some basic design criteria are presented in the excellent book of S.L. Dixon: Fluid Mechanics and Thermodynamics of Turbomachinery" (Chapter 7). The main design parameters are: mass flow and pressure ratio, No of blades and splitter blades relating to the slip conditions at the rotor exit, rotor diameter and
peripheral velocity in accordance to limiting Mach No's, diffuser components and volute system. Other questions are concerned with the selection of rotor material and the mechanical stress level (from steel to titanium) as well the stage stable characteristics (surge limit higher than 10-15% in the operating range).
The good idea is to study some practical design examples presented in some open sources (see: www.slideserve.com/conlan/design-analysis-of-centrifugal-compressors; http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19890013546_1989013546.pdf). The final part of the study should consist an analysis of the flow in 2D/3D modeling methods based on CFD simulation and
mechanical development by using FEM software (ANSYS/CFX/FEM).