🌀 Chapter 9: Modeling and Setting of Dynamic Compressors and Turbines

Tackling Turbomachinery Complexity

Dynamic compressors and turbines are complex—but this chapter breaks it down!

• Two Main Methodologies:

  • Velocity triangle deformation under varying conditions.
  • Similarity laws with experimental performance maps.

• Fundamentals Covered:

  • Rateau coefficients (power factor μ, flow coefficient δ).
  • Degree of reaction and theoretical characteristics.

• Real-World Modeling:

  • Corrected rotation speed and flow for dynamic compressors.
  • Stodola’s cone rule and Baumann’s efficiency degradation for turbines.

Thermoptim in Action: Practical screens for each machine type—ready for your simulations!

Abstract

This chapter presents models for representing off-design behavior of turbomachinery, including turbines, dynamic compressors, pumps, and fans. The subject poses significant challenges due to limited consensus approaches in scientific literature and engineering practice. Two main methodologies are employed: analyzing velocity triangle deformation under changing operating conditions, and using similarity laws with experimental performance maps. The chapter begins with supplementary material on turbomachinery fundamentals, including detailed velocity triangle analysis leading to Rateau coefficients (power factor μ and flow coefficient δ), degree of reaction relationships, and theoretical characteristics for centrifugal compressors, axial compressors, and turbines. Real characteristics are explained through qualitative analysis of friction and shock losses. Similarity factors (flow factor ϕ, enthalpy factor ψ, specific diameter Δ, and specific speed σ) enable reduced performance map construction and off-design analysis. For pumps and fans, incompressible fluid assumptions significantly simplify modeling, with single reduced curves sufficient for representation. Dynamic compressor performance maps use corrected rotation speed and corrected flow, with various coordinate systems ((ϕ, ψ), (θ, Δ), (σ, Δ)) achieving different degrees of curve consolidation. Turbine modeling relies primarily on Stodola’s cone rule and Baumann’s efficiency degradation rule for wet steam conditions, supplemented by leaving loss calculations based on velocity triangles. Practical implementation through Thermoptim technological design screens is demonstrated for each machine type.