Modeling the Compressor Component, Design and Off-Design

Abstract

As mentioned in Chapter 1, the function of a compressor is to increase the total pressure of the working fluid. According to the conservation law of energy, this total pressure increase requires external energy input, which must be added to the system in the form of mechanical energy. The compressor rotor blades exert forces on the working medium thereby increasing its total pressure. Based on efficiency and performance requirements, three types of compressor designs are applied. These are axial flow compressors, radial or centrifugal compressors, and mixed flow compressors. Axial flow compressors are characterized by a negligible change of the radius along the streamline in the axial direction. As a result, comparison of the contribution of the circumferential kinetic energy difference $(U^2_3 - U^2_2)/2$ to the pressure buildup is marginal. In contrast, the above difference is substantial for a radial compressor stage, where it significantly contributes to increasing the total pressure as discussed in Chapter 5.

During the compression process, the fluid particles are subjected to a positive pressure gradient environment that may cause the boundary layer along the compressor blade surface to separate. To avoid separation, the flow deflection across each stage and thus the stage pressure ratio is kept within certain limits discussed in the following section. Compared to an axial stage, much higher relative stage pressure ratios π _rad /π _ax  > 5 at relatively moderate flow deflections can be achieved by centrifugal compressors. However, geometry, mass flow, efficiency, and material constraints place limits on utilizing radial compressors. Radial compressors designed for high stage pressure ratios and mass flows comparable to those of axial compressors require substantially larger exit diameters. This can be considered an acceptable solution for industrial applications, but is not a practical solution for implementing into gas turbine engines. In addition, for gas turbine applications, high compressor efficiencies are required to achieve acceptable thermal efficiencies. While the die efficiencies of advanced axial compressors have already exceeded 91.5% range, those of advanced centrifugal compressors are still below 90%. Power generation gas turbine engines of 10 MW and above as well as medium and large aircraft engines use axial compressor design. Small gas turbines, turbochargers for small and large Diesel engines have radial impellers that generate pressure ratios above 5. Compact engines for turboprop applications may have a combination of both. In this case a relatively high efficiency multi-stage axial compressor is followed by a lower efficiency centrifugal compressor to achieve the required engine pressure ratio at smaller stage numbers.

Further stage pressure buildup is achieved by increasing the inlet relative Mach number M _2rel. = W ₂/c ₂. In case of subsonic axial flow compressors with M _2rel. < 1, the compression process is primarily established by diffusion and flow deflection. However, in the case of supersonic relative Mach number M _2rel. > 1 that occupies the entire compressor blade height from hub to tip, the formation of oblique shock waves followed by normal shocks as discussed in Chapter 4 substantially contributes to a major pressure increase. However, the increase of stage pressure ratio as a result of compression shocks is associated with additional shock losses that reduce the stage efficiency. To achieve a higher stage pressure ratio at an acceptable loss level, the compressor stage can be designed as transonic compressor stage. In this case, the relative Mach number at the hub is subsonic and at the tip supersonic, with transonic Mach range in between. Transonic compressor stage design is applied to the first compressor stage with a relatively low aspect ratio of high performance gas turbine engines.

In this chapter, we first investigate several loss mechanisms and correlations that are specific to compressor component. Using these correlations, first the basic concept for a row-by-row adiabatic calculation method is presented that accurately predicts the design and off-design behavior of single and multi-stage compressors. With the aid of this method, efficiency and performance maps are easily generated. The chapter is then enhanced to calculate the diabatic compression process where the blade rows exchange thermal energy with the working medium and vice versa. The above methods provide three different options for dynamically simulating the compressor component. The first option is to utilize the steady state compressor performance maps associated with dynamic coupling. The second option considers the row-by-row adiabatic calculation. Finally, the third option uses the diabatic compression process. Examples are presented.