The aim of this test case is to validate the following parameters of compressible steady-state turbulent flow through a de Laval Nozzle subsonic and supersonic flow regimes:
The rhoSimpleFoam solver is used for the subsonic case, while for the supersonic case the sonicFoam solver is employed. The k−ω model was used to model turbulence. Simulaton results of SimScale were compared to analytical results obtained from methods elucidated in . The mesh was created locally using the blockMesh tool and then imported on to the SimScale platform.
A typical configuration of the de Laval nozzle with a non-smooth throat was chosen as the geometry (see Table 1 for coordinates). Since the nozzle is axisymmetric, it was modeled as an angular slice of the complete geometry, with a wedge angle of 18 degrees (see Fig.1.).
A non-uniformly-spaced hexahedral mesh was generated using the blockMesh tool (see Fig.2.). Flow near the nozzle wall was resolved using inflation of y+=30 for the subsonic and 300 for the supersonic case. In order to keep the flow two-dimensional, the mesh was designed to have only one layer in the y direction.
Tool Type : OPENFOAM®
Analysis Type : Compressible Steady-state (Turbulent)
A comparison of the Mach number and pressure variation in the nozzle obtained with SimScale with analytical results is given in Fig.3A and 3B for subsonic and Fig.4A and 4B for supersonic flow.
Fig.3. Visualization of Mach number and pressure (A, B) along the nozzle for subsonic flow
Fig.4. Visualization of Mach number and pressure (A, B) along the nozzle for supersonic flow
The deviation from analytical results exists because the latter is calculated with a one-dimensional hypothesis. Thus, all parameters are assumed to be uniform in the radial direction. Fig.5. shows that this is in fact not the case – there exists radial variation in flow variables. This is one reason why some deviation is seen between the two.
Fig.5. Contours of velocity and temperature in the nozzle. Clearly, there exists radial variation in these parameters.
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