Converging-diverging transonic diffuser

Confined flows

Underlying Flow Regime 4-19

Abstract

Transonic flow in a converging-diverging diffuser is of considerable practical importance as it occurs in supersonic inlets of air breathing systems of missiles and aircraft and in transonic compressor rotor passages. It is therefore important to understand the flow behavior and to be able to predict it. The flow behavior is complex due to the formation of a shock-wave in the diffuser throat, the interaction of this with the boundary layers developing on the diffuser walls, and the adverse pressure gradient in the diverging part behind the shock, which may lead to flow separation depending on the Mach number and boundary conditions. All these features make the accurate representation of the converging- diverging transonic diffuser flow a great challenge for calculation methods and in particular turbulence models.

The UFR in this contribution concerns a particular diffuser studied experimentally by various researchers, e.g. Bogar et al. (1982), Bogar (1985), Salmon et al. (1982), and also by Sajben et al. (1984), whence this is called the “Sajben transonic diffuser”. Two set-ups were examined, one having a higher outlet pressure leading to a weaker shock-wave (called “weak” Mach number case) and a second with a lower outlet pressure having a stronger shock-wave (named “strong” Mach number case). The position of the shock-wave formed in the diffuser throat and the maximum Mach number are different for the two cases studied. Depending on the flow conditions, a recirculation region can be formed in the diverging part of the diffuser. The diffuser geometry is given in fig.1 and a characteristic view of the Mach number contours in fig.2.

The Sajben diffuser has been studied extensively by computations (see review in section “Review of UFR studies”). Some of these are described in detail in the NPARC Alliance CFD Verification and Validation Web site of NASA (http://www.grc.nasa.gov/WWW/wind/valid/archive.html), from where the experimental data used in the current UFR were taken.

The current UFR contribution focuses on additional calculations for the Sajben diffuser with different turbulence models, including two more advanced turbulence models presented in the literature, which are the cubic non-linear eddy-viscosity model of Craft et al. (1996), and the non-linear Reynolds stress model of Craft (1998). These models are also compared with the widely used linear eddy-viscosity model of Launder and Sharma (1974), which serves as a reference base for the comparisons. This simple model has not been used in previous computational studies, found in the literature, for this particular test case. All the models are used in their low-Reynolds number variants in order to resolve the whole boundary layer. The turbulence models are implemented in a pressure-based flow solver basically developed for subsonic flows. However, with some minor modifications to the pressure-velocity coupling scheme, the solver can be applied to the transonic and supersonic flow regime. The effect of the dilatation-dissipation of turbulence is modelled with the use of a simple expression that is provided by Sarkar et al. (1989).