Metacomp Technologies participated in the 6th AIAA Propulsion Aerodynamics Workshop held at the 2023 AIAA SciTech Forum and Exposition in National Harbor, MD, USA. The objective of the workshop was to assess the numerical prediction capability of current-generation CFD technology/codes for inlets, diffusers, and nozzles and their propulsion-specific boundary conditions.
The second of two sets of test cases involved modeling the spreading rate of turbulent supersonic nozzle jet plumes emanating from a series of converging-diverging nozzles
The individual cases involve a series of nozzle inflow stagnation conditions, and nozzle geometries, resulting in a range of supersonic jet plumes with varying Mach numbers and characteristics. The experiments were conducted at NASA Glenn Research Center using the Small Hot Jet Acoustic Rig. The exterior of a typical converging-diverging nozzle tested in the experiments is shown in the figure below.
The individual nozzle cases modeled are summarized in Table 1
| Case # | PTot,Nozzle (Pa) | TTot,Nozzle (K) | MNozzle,Jet | Nozzle Geometry |
| 1 | 298832.8 | 715.2 | 1.36 | Mach136 |
| 2 | 440803.2 | 799.4 | 1.63 | Mach163 |
| 3 | 776369.6 | 939.7 | 2.00 | Mach200 |
| 4 | 298832.8 | 715.2 | 1.63 | Mach163 |
| 5 | 440803.2 | 442.1 | 1.63 | Mach163 |
Each of the first three cases listed in Table 1 uses a different nozzle geometry, labeled as “Mach###”. Each geometry and the specific inflow conditions are meant to result in a fully-expanded uniform nozzle jet. For case 4, the prescribed inflow conditions are meant to produce an over-expanded nozzle jet using the Mach163 geometry. In case 5, once again using the Mach163 geometry, the prescribed inflow conditions are again meant to produce a fully-expanded uniform nozzle jet but with a temperature difference of 0 K between the nozzle exhaust and ambient air.
All simulations performed solved preconditioned Navier-Stokes equations on 2-dimensional axi-symmetric grids. The influence of two turbulence models, realizable k-epsilon and cubic k-epsilon, on the predictions was also studied. Also, for both turbulence models, Metacomp’s respective compressibility corrections for wall-bounded flows were employed.
For each case and turbulence model combination, a grid convergence study was performed using a succession of three grids with increasing refinement. In the results that follow, these three grids are referred to as medium, fine, and extra fine. With each refinement level, the average cell-size in the jet core region was halved.
Metacomp contributed data modeled using both the k-epsilon type of turbulence models and Metacomp’s proprietary compressibility corrections. Both sets of data which showed excellent agreement with experimental data, as can be seen in the centerline and radial profiles of axial velocity comparisons shown in Figures 2 and 3.
Figure 2: Centerline Axial Velocity Profiles – RKE – Realizable k-epsilon model; CKE – Cubic k-epsilon model. The labels Medium, Fine, and ExtraFine indicate the mesh refinement level.
Given the quality of CFD++’s predictions without employing more expensive methods (e.g. LES), Metacomp has been invited to write a paper to be presented at the 2024 AIAA SciTech conference.
Figure 3: Radial Profiles of Axial Velocity – RKE – Realizable k-epsilon model; CKE – Cubic k-epsilon model. The labels Medium, Fine, and ExtraFine indicate the mesh refinement level.