This paper presents a method to balance aerodynamic loading by optimizing the combined efficiencies of co-axial compressors and turbines for engine preliminary design. Relationships between the aerodynamic and dimensional parameters for co-axial compressors and turbines were set up by nonlinear equations. And the boundary conditions of the equations are thermodynamic parameters and Smith Charts of compressors and turbines.

The process of the method includes the initial value guess, reference point determination and aerodynamic optimization. The first step solves approximate stage numbers for co-axial compressors and turbines, and other initial values used in the second step. In the second step, an appropriate solution of the equations determines a reference point on the Smith Chart. The first step is required for a better convergence in the second step due to the nature of the Newton-Raphson solver. In the third step, the combined efficiencies of co-axial compressors and turbines are optimized under the specified constraints.

An optimizing tool was developed based on the proposed method. An example of a core engine was analyzed by using this tool. The results showed the reliability and high fidelity of the method.

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