60069 - One Dimensional Modelling for Pulsed Flow Twin-Entry Turbine 

One-dimensional (1D) modelling is important for turbomachinery unsteady performance prediction and system response assessment. The purpose of this paper is to describe a novel 1D modelling (TURBODYNA) and its applications on twin-entry turbine.
Twin-entry and double-entry turbines are widely applied in turbocharging in order to increase turbocharger transient response and reduce engine exhaust overlap. Due to reciprocating motion of piston engines, for twin-entry or double entry turbine, separated two volute limbs deliver high pressure, high frequency pulsating exhaust gas into the rotor with 1800 pulsating phase difference respectively. Several different time scales are coupled in this complicated process and a strong mixing happens at the rotor inlet. 
This paper introduces a newly developed 1D simulator (TURBODYNA) and applied it on a twin-entry turbine. Different form traditional modelling, the volume of the rotor is considered and meshed. Effects of the rotor are explained as different kinds of 'source terms, including ‘wall friction force', ‘shaft work ,  and ‘virtual cascade'. In addition, a mass flow ‘extraction and injection’ process is included to simulate two limbs’ swallowing capacity difference. To consider the time scale of flow field in the rotor, dynamic equations, for example, lag equation, are applied to describe the inertial effect of the flow field. 
Another challenge for twin-entry 1D modelling is treatment of limb junction. At volute outlet or rotor inlet, there is a junction where two limbs merge together. Traditionally, the pressure at just upstream and downstream of the junction is assumed the same. However, this assumption is not valid once pressure difference in the two limbs are large (at partial admission condition, pressure in one limb can be around 4bar while 1bar in another limb). In TURBODYNA, the mixing process at the junction is assumed to happen within an infinite small length. Rather than adopt constant pressure assumption, Riemann-Solver is directly applied to solver this spatial discontinuity problem due to the infinite small length mixing.
The 1D modelling has applied on a twin-entry turbine to assess turbine performance at different pulsating frequencies and pressure ratio ranges. Comparison of 1D results and validated unsteady 3D CFD suggest that TURBODYNA can correctly model the twin-entry turbine unsteady behaviour under pulsating conditions. Transportation and reflection of pressure waves can be adequately captured.