Converging-diverging transonic diffuser

Confined flows

Underlying Flow Regime 4-19

Test Case Study

Brief Description of the Study Test Case

The geometry of the Sajben transonic converging-diverging diffuser and the flow characteristics have been obtained from the Alliance CFD Verification and Validation Archive-NASA website (http://www.grc.nasa.gov/WWW/wind/valid/archive.html). The diffuser geometry and the dimensions are given in fig.4. The flow starts subsonic with M=0.46 at the inlet of the diffuser, accelerates through the throat up to the supersonic region where a shock-wave is formed which abruptly decelerates the flow which is then subsonic in the remaining diverging part of the diffuser downstream of the shock-wave.

The test case geometry configuration has an entrance-to-throat ratio equal to 1.4 and an exit-to-throat ratio equal to 1.5. In the current study, two flow configurations were examined. Based on the Mach number that is reached in the diffuser, the configurations are named as the "weak" and the "strong" case. For the "weak" case, the flow accelerates up to Mach~1.25 and for the "strong" case up to Mach~1.35, is then decelerated by a weak or a strong shock-wave and leaves the diffuser at Mach=0.52 and Mach=0.65 respectively. The different flow development for the two cases is guided by the imposed static pressure at the outlet boundary of the Sajben diffuser and it is characterized by the ratio R, of the outlet static pressure to the inlet total pressure of the flow. The ratio R takes the values of 0.82 and 0.72 for the "weak" and the "strong" Mach number cases respectively. For the weak case, the boundary layer stays attached, while it separates from the upper wall of the diffuser for the "strong" case leading to different flow development in the diverging part of the diffuser. The position of the "weak" and the "strong" shock-waves together with the corresponding recirculation region for the "strong" Mach number case are indicated in fig.4.

Figure 4: Geometry of the Sajben diffuser and schematic representation of the shock-waves position and the recirculation region

The two test case setups regarding all the flow boundary conditions and the general characteristics e.g. Mach number values, total pressure, total temperature, outlet boundary static pressure, are provided in table 2.

The principal measured quantities that are available for the validation of the various computational CFD codes, are basically mean averaged quantities of the pressure distributions along the walls of the diffuser and the velocity distributions at various stations after the shock-wave. Unfortunately, there are no experimental data regarding the turbulent quantities in order to have a more qualitative assessment of the behavior of the adopted turbulent models.

Test Case Experiments

Provide a brief description of the test facility, together with the measurement techniques used. Indicate what quantities were measured and where.

Discuss the quality of the data and the accuracy of the measurements. It is recognized that the depth and extent of this discussion is dependent upon the amount and quality of information provided in the source documents. However, it should seek to address:

How close is the flow to the target/design flow (e.g. if the flow is supposed to be two-dimensional, how well is this condition satisfied)?

Estimation of the accuracy of measured quantities arising from given measurement technique

Checks on global conservation of physically conserved quantities, momentum, energy etc.

Consistency in the measurements of different quantities.

Discuss how well conditions at boundaries of the flow such as inflow, outflow, walls, far fields, free surface are provided or could be reasonably estimated in order to facilitate CFD calculations

CFD Methods

Provide an overview of the methods used to analyze the test case. This should describe the codes employed together with the turbulence/physical models examined; the models need not be described in detail if good references are available but the treatment used at the walls should explained. Comment on how well the boundary conditions used replicate the conditions in the test rig, e.g. inflow conditions based on measured data at the rig measurement station or reconstructed based on well-defined estimates and assumptions.

Discuss the quality and accuracy of the CFD calculations. As before, it is recognized that the depth and extent of this discussion is dependent upon the amount and quality of information provided in the source documents. However the following points should be addressed: