# Several Cases for the Validation of Turbulence Models Implementation
## 4 Results
### Two-Dimensional Backward-Facing Step  
The backward-facing step is a case proposed by [PERSON] and [PERSON] [23] to test how well the turbulence model simulates separated flows. The backward-facing step case is a challenging problem as turbulence models generally have difficulty modeling separated flows.  
The test configuration had a 100 cm long \(\times\) 15.1 cm wide \(\times\) 10.1 cm high rectangular inlet duct followed by a backward-facing step of \(H\) = 1.27 cm. The geometry of the computational domain of the backward-facing step, shown in Figure 17, is defined as a function of the step height, \(H\). The experiment took place at atmospheric total pressure and temperature. The freestream velocity was 44.2 m/s. The Reynolds number based on step height was Re\({}_{H}\) = 36,000. The boundary conditions are also shown in Figure 17. A detail of the mesh near the step is shown in Figure 18.  
Figure 16: Dimensionless turbulent shear stress profiles on [PERSON]’s airfoil: (**a**) Spalart–Allmaras, and (**b**) Shear Stress Transport.  
Figure 17: Backward-facing step geometry and boundary conditions [20].  
Two grids were used for this test case: (1) the second coarsest and (2) the finest grid provided by the NASA Turbulence Modeling [20]. The results generated with the UNS3D-SEQ and UNS3D-PAR codes were compared against those generated with the NASA FUN3D and CFL3D codes which used the finest grid. The sets of results presented herein include velocity profiles, turbulent shear stresses, skin friction coefficients, and reattachment points.  
Figure 19 compares the measured and predicted velocity profiles at four locations downstream from the step: \(x/H=1\), 4, 6, and 10. The velocity profiles were calculated using the UNS3D-SEQ, UNS3D-PAR, and CFL3D codes with the Spalart-Allmaras and Shear Stress Transport models. There was a good agreement among the results of the three codes, for both turbulence models. The Shear Stress Transport model matched the experimental data better than the Spalart-Allmaras model near the step, at \(x/H=1\). Away from the step, at \(x/H=4\), 6, and 10, the Spalart-Allmaras model captured the velocity profiles better than the Shear Stress Transport model.  
Figure 20 compares the measured and predicted friction coefficients. There is a relatively good agreement among the results produced by the UNS3D-SEQ, UNS3D-PAR, and CFL3D codes, using both Spalart-Allmaras and Shear Stress Transport models.  
The experimental investigation found the reattachment point to be at 6.26 \(\pm\) 0.01 [23]. The predicted location of the reattachment point varied depending on the turbulence model. The Spalart-Allmaras model predicted an earlier reattachment, while the Shear Stress Transport model predicted a delayed reattachment. The predicted locations of reattachment point are summarized in Table 5.  
Figure 21 compares the measured and predicted turbulent shear stresses at four locations downstream from the step. The results predicted using the Shear Stress Transport model matched the turbulent shear stresses better than the Spalart-Allmaras model.  
Figure 19: Velocity profiles on backward-facing step: (**a**) Spalart–Allmaras, and (**b**) Shear Stress Transport.  
Figure 20: Coefficient of friction on backward-facing step: (**a**) Spalart–Allmaras, and (**b**) Shear Stress Transport.