Solution of the turbocompressor boundary condition for one-dimensional gas-dynamic codes

Nowadays, turbocharged engines are widely used in cars and trucks. Gas-dynamic codes are an important tool in design and optimization of these types of engines. These codes solve the one-dimensional governing equations in ducts for compressible, unsteady and non-homoentropic flow. The ducts are generally solved using finite difference schemes, the volumes are solved by means of filling and emptying models and the connections represent the boundary conditions of the ducts. One important boundary condition is the compressor which connects two ducts. In this junction an increment of momentum and energy is undergone by the flow but depending on its sense the behaviour is different. This paper presents the mathematical base of a compressor model which solves this complex boundary condition. The governing equations of the model have been presented in detail. The solution involves a non-linear equation system that has to be solved iteratively. The Newton–Raphson root-finding method has been chosen to get its solution. Finally, some results of the model have been compared to measurements focusing in surge prediction.