Converging-diverging transonic diffuser

Confined flows

Underlying Flow Regime 4-19

Best Practice Advice

Key Physics

Although the geometry of the Sajben converging-diverging diffuser is relatively simple and can be treated as two dimensional, there are interesting flow features present in the flow and their capturing is a considerable challenge for turbulence models. The key flow characteristics are summarized below:

The primary structure that governs the examined transonic converging-diverging diffuser is the shock-wave that is formed in the transonic diffuser throat.

The shock-wave position and strength strongly depend on the static pressure that is imposed at the outlet of the diffuser as a boundary condition. As the boundary pressure outlet decreases, (by keeping constant the total inlet conditions), a stronger shock-wave is formed in the diffuser throat resulting in an increased Mach number value. In the current UFR study, the two boundary conditions that were examined led to the formation of a “weak” and a “strong” shock-wave, associated with a lower and a higher maximum Mach number.

The pressure after the shock-wave increases and the Mach number decreases. This may lead to boundary layer separation and to the formation of a recirculation region right after the shock-wave in the diverging part of the diffuser near the upper wall. In the current study, this behavior was measured for Mach~1.35 which is the “strong” case. For the “weak” case, Mach~1.25, the boundary layer remains attached along the diverging part of the diffuser.

There is a strong shock-wave/turbulent boundary layer interaction that has to be precisely described by the adopted turbulence models in order to compute with accuracy the flow development and the possible recirculation region after the shock-wave depending on the boundary conditions.

Numerical Modelling

In order to describe the compressibility effects and capture with accuracy the shock-wave when a pressure based solver is used, a compressibility correction algorithm has to be adopted in order to take into consideration the mean density variations.

In case there are stability problems due to high Mach number caused by the low level pressure at outlet, initially a higher static pressure value can be used as a boundary condition, then gradually reducing the pressure at outlet until the desirable value is reached.

As reported in NASA study#2, for obtaining supersonic flow through the diffuser, the pressure initially was kept low at the boundary outlet. After the supersonic flow was achieved, the pressure was raised to the desired value in order to be consistent with the experimental value. This was reported for calculations with fairly simple turbulence models (BL and SA). In the current study such a measure was not necessary.

For the studies in the literature where an unstructured grid was used, as in the NASA study#5, it was shown that for the “strong” Mach number case the recirculation region extended down to the outlet and remained during the iterative procedure in the whole computational area of the upper diffuser wall. This numerical problem was solved by extending the outlet region and fixing the outlet pressure to such a value that the desired pressure at the original outlet position of the diffuser was established. For the structured grid and also the grids that were used in the current study, this problem did not occur.

Grid dependency studies from the current and previous studies showed that there is no specific fine grid resolution needed for capturing the shock-wave and the velocity distributions. However, it is necessary to have a fine grid for stability reasons when using more advanced turbulence models such as non-linear eddy-viscosity models and RSM.

Physical Modelling

Turbulence modelling
Transition modelling
Near-wall modelling
Other modelling

Application Uncertainties

Summarise any aspects of the UFR model set-up which are subject to uncertainty and to which the assessment parameters are particularly sensitive (e.g location and nature of transition to turbulence; specification of turbulence quantities at inlet; flow leakage through gaps etc.)

Recommendations for Future Work

Propose further studies which will improve the quality or scope of the BPA and perhaps bring it up to date. For example, perhaps further calculations of the test-case should be performed employing more recent, highly promising models of turbulence (e.g Spalart and Allmaras, Durbin's v2f, etc.). Or perhaps new experiments should be undertaken for which the values of key parameters (e.g. pressure gradient or streamline curvature) are much closer to those encountered in real application challenges.

Contributed by: Z. Vlahostergios, K. Yakinthos — Aristotle University of Thessaloniki, Greece