Radial inflow turbines for turbocharging - Modelisation

When sizing a centripetal supercharger turbine, experience shows that the most critical component is the volute, which accounts for more than half of the total energy loss—and this is without taking into account the heat transfer it causes. For this reason, a one-dimensional approach to flow in the volute has been detailed in order to derive the expression for the velocity components at the impeller inlet.

The flow in the volute is not adiabatic, and a similarity law is proposed for the entire turbine. These dimensionless numbers provide engineers with a simple, approximate method for transposing results to different test and operating conditions.

Using simplifying assumptions and estimates for certain modeling coefficients (losses, effects of angle of attack and angular deflection, etc.), a quick calculation is presented, followed by a numerical application, aimed at satisfying the conditions encountered at a nominal operating point. The results obtained make it possible to sketch out the machine’s geometry and thus ensure the feasibility of using a centripetal turbine. Based on the resulting geometry, a one-dimensional model of the entire turbine assembly is developed to predict its characteristic curves. The results from the proposed models are compared with experimental results provided by the manufacturers. The prediction of overall performance proves to be very satisfactory and sufficient for the preliminary design stage.