Numerical Integration Algorithms for Flows in Turbomachinery and Jet Propulsions



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Bachelor, Master


Turbomachinery plays an important role in large parts of our lives. They are used in in power generation, to power almost all modern aircrafts, or are an important component in process industry plants. In these processes, ever higher demands are being placed on efficiency, emissions and performance. In order to meet these challenges, a deep understanding of the thermodynamics, aerodynamics and structural mechanics of turbomachinery is required.

Today's turbomachinery has reached such a high technological level that improvements in efficiency can only be achieved by using advanced numerical methods. Due to the complexity of the mathematical model, the solution methods require sophisticated knowledge of both analysis and numerics. Therefore it is the aim of the course "Numerical Integration Methods for Flows in Turbomachinery and Jet Propulsion Systems" to provide engineers with the mathematical basics necessary for understanding and developing such numerical solution methods.

The lecture starts with a repetition of the derivation of the conservation laws of fluid dynamics. Based on these laws, the mathematical model is extended to the turbomachinery specific features of a rotating reference system and analyzed with regard to meaningful simplifications. However, the initially chosen vector form of the conservation laws is not easily accessible to numerical solution methods. Tensor calculus is an indispensable basis for the development of solution methods, regardless of the chosen discretization scheme. The engineer is provided with the mathematical tools which are of interest in dealing with the conservation laws of fluid mechanics and their applications. The breadth of the subject area excludes a comprehensive treatment of the solution methods within the scope of one semester. Therefore, the course focuses on a finite-volume approach, which can be regarded as the state-of-the-art method in commercial and scientific programs. This limitation allows on the one hand treatment of the methodology with the appropriate depth and on the other hand provides the most important basics necessary for the study of more advanced models as well as alternative discretization schemes.



  • Finite Volume Method
  • Time Integration Schemes
  • Conservation Laws
  • Tensor Calculus
  • Solver

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