Academia.eduAcademia.edu

Figure 1 – uploaded by Florian Menter

See full PDFdownloadDownload figure
Table 2: Grids for periodic channel flow at different Reynolds number using WMLES The simulations were carried out on grids with the characteristics given in Table 2. The domain size was LX=16h, LY=2h, LZ=3h (h being half the channel height — this corresponds approximately to the boundary layer thickness for wall boundary layers). The main characteristics of WMLES is clearly visible from Table 2, the non- dimensional values for AX+ and AZ+ are far beyond the limits of standard LES methods (AX+=40, AZ+=20). For WMLES, one only has to ensure a minimum number of cells per boundary layer volume 5x6x6. In the current formulation the minimum resolution per boundary layer volume is of the order of 10x40x20 cells (streamwise, normal and spanwise). The grid for Boundary Layer test case has the parameters given in Table 3.

Table 2 Grids for periodic channel flow at different Reynolds number using WMLES The simulations were carried out on grids with the characteristics given in Table 2. The domain size was LX=16h, LY=2h, LZ=3h (h being half the channel height — this corresponds approximately to the boundary layer thickness for wall boundary layers). The main characteristics of WMLES is clearly visible from Table 2, the non- dimensional values for AX+ and AZ+ are far beyond the limits of standard LES methods (AX+=40, AZ+=20). For WMLES, one only has to ensure a minimum number of cells per boundary layer volume 5x6x6. In the current formulation the minimum resolution per boundary layer volume is of the order of 10x40x20 cells (streamwise, normal and spanwise). The grid for Boundary Layer test case has the parameters given in Table 3.

Related Figures (15)

Table 1: Estimate of CPU resources for RANS and wall-resolved LES for a single turbine blade It is instructive to compare the numerical effort required for a RANS and a LES simulation for the flow over a relatively limited geometry, like a single turbine blade in a gas turbine at a Reynolds number of Re~10° (see e.g. Michelassi et al. 2003). If all physical effects like laminar-turbulent transition and the complete 3D geometry with hub and shroud portions are included the estimates are given in Table 1: Of course, details depend on numerics and code specifics etc., but the estimate shows that routine application of LES for industrial, wall-bounded flows is out of reach for several decades, even for relatively simple geometries and moderate Reynolds numbers. One could argue that this is an extreme case as laminar-turbulent transition needs to be resolved, however, estimates at higher Re numbers as provided by Spalart (1997, 2000) are not more favorable. For this reason, pure LES will not become a standard industrial tool for most applications for several decades.
Table 1: Estimate of CPU resources for RANS and wall-resolved LES for a single turbine blade It is instructive to compare the numerical effort required for a RANS and a LES simulation for the flow over a relatively limited geometry, like a single turbine blade in a gas turbine at a Reynolds number of Re~10° (see e.g. Michelassi et al. 2003). If all physical effects like laminar-turbulent transition and the complete 3D geometry with hub and shroud portions are included the estimates are given in Table 1: Of course, details depend on numerics and code specifics etc., but the estimate shows that routine application of LES for industrial, wall-bounded flows is out of reach for several decades, even for relatively simple geometries and moderate Reynolds numbers. One could argue that this is an extreme case as laminar-turbulent transition needs to be resolved, however, estimates at higher Re numbers as provided by Spalart (1997, 2000) are not more favorable. For this reason, pure LES will not become a standard industrial tool for most applications for several decades.
Figure 1: Turbulent structures for flow over periodic hill with SST-SAS model. Left: Small time step (CFL~ 1), Right 4x larger time step. Color: ratio of eddy-viscosity to molecular viscosity.
Figure 1: Turbulent structures for flow over periodic hill with SST-SAS model. Left: Small time step (CFL~ 1), Right 4x larger time step. Color: ratio of eddy-viscosity to molecular viscosity.
Figure 2: Velocity profiles for the SAS simulations with different time steps for periodic hill flow in comparison with reference LES and SST-RANS solution Figure 2 shows the velocity profiles computed with the SAS model using the two different time steps in comparison with the reference LES (Temmerman and Leschziner, 2001) and the SST-RANS solution. It can be seen that even the large time step leading to the structures seen in the right side of Figure | gives a significant improvement in the velocity profiles compared to the steady state solution (this case is known to be challenging for RANS models due to its large separation zone and periodic conditions).
Figure 2: Velocity profiles for the SAS simulations with different time steps for periodic hill flow in comparison with reference LES and SST-RANS solution Figure 2 shows the velocity profiles computed with the SAS model using the two different time steps in comparison with the reference LES (Temmerman and Leschziner, 2001) and the SST-RANS solution. It can be seen that even the large time step leading to the structures seen in the right side of Figure | gives a significant improvement in the velocity profiles compared to the steady state solution (this case is known to be challenging for RANS models due to its large separation zone and periodic conditions).
Figure 3: Flow over generic airplane configuration FA-5. Left - flow structures. Right - comparison of exp. and SAS axial flow component. (Geometry and data are Courtesy of EADS Deutschland) Air flow past a 3-D rectangular shallow cavity was calculated in order to test the SAS models ability to predict correct spectral information for acoustics applications. The cavity geometry and flow conditions corresponding to the M219 experimental test case of Henshaw (2000). The experiment investigates the noise generation due to turbulent structures forming from the front lip of the cavity and interacting with the cavity walls.
Figure 3: Flow over generic airplane configuration FA-5. Left - flow structures. Right - comparison of exp. and SAS axial flow component. (Geometry and data are Courtesy of EADS Deutschland) Air flow past a 3-D rectangular shallow cavity was calculated in order to test the SAS models ability to predict correct spectral information for acoustics applications. The cavity geometry and flow conditions corresponding to the M219 experimental test case of Henshaw (2000). The experiment investigates the noise generation due to turbulent structures forming from the front lip of the cavity and interacting with the cavity walls.
Figure 4: Resolved turbulent structures for cavity flow: iso-surface (Q22-S2=5-105 s-2. Figure 4 shows the turbulent structures, produced by the SST-SAS model (iso-surface Q-criterion). The power spectral density (PSD) of the transient pressure signals calculated and measured by sensors on the cavity bottom near the leading and the downstream wall respectively is plotted in Figure 5. These plots show that the PSD levels are captured in good agreement with the data. Similar agreement was achieved for the other experimental locations (not shown here) Kurbatskii et al (2011).
Figure 4: Resolved turbulent structures for cavity flow: iso-surface (Q22-S2=5-105 s-2. Figure 4 shows the turbulent structures, produced by the SST-SAS model (iso-surface Q-criterion). The power spectral density (PSD) of the transient pressure signals calculated and measured by sensors on the cavity bottom near the leading and the downstream wall respectively is plotted in Figure 5. These plots show that the PSD levels are captured in good agreement with the data. Similar agreement was achieved for the other experimental locations (not shown here) Kurbatskii et al (2011).
Figure 5: Power spectral density of the transient wall pressure signals on the cavity bottom: left — sensor K20 located close the front wall, right — sensor K29 located close to the rear wall. In Egorov et al. (2010) the SAS model is described in detail and is applied to a wide variety of generic and industrial-like flows.
Figure 5: Power spectral density of the transient wall pressure signals on the cavity bottom: left — sensor K20 located close the front wall, right — sensor K29 located close to the rear wall. In Egorov et al. (2010) the SAS model is described in detail and is applied to a wide variety of generic and industrial-like flows.
Figure 7 shows the turbulent structures for a wall boundary layer flow using the WMLES option. Again the oute: part is covered by LES and the near wall part by RANS. The flow is also computed with ANSYS-Fluent 13 and the turbulence at the inlet is generated by the Vortex Method (Mathey et al. 2006). The turbulence is well maintained a: can be seen from Figure 7. In Figure 8 the wall shear stress is displayed. The WMLES recovers quickly from the synthetic turbulence and maintains a proper wall shear stress downstream.
Figure 7 shows the turbulent structures for a wall boundary layer flow using the WMLES option. Again the oute: part is covered by LES and the near wall part by RANS. The flow is also computed with ANSYS-Fluent 13 and the turbulence at the inlet is generated by the Vortex Method (Mathey et al. 2006). The turbulence is well maintained a: can be seen from Figure 7. In Figure 8 the wall shear stress is displayed. The WMLES recovers quickly from the synthetic turbulence and maintains a proper wall shear stress downstream.
Figure 6: Velocity profiles in logarithmic scale for periodic channel flow using WMLES for various Reynolds numbers.
Figure 6: Velocity profiles in logarithmic scale for periodic channel flow using WMLES for various Reynolds numbers.
Figure 7: Turbulence structures for wall boundary layer flow using the WMLES option and the vortex method to generate synthetic turbulence at the inlet. Right Reg=1000, Left Reg=10000.
Figure 7: Turbulence structures for wall boundary layer flow using the WMLES option and the vortex method to generate synthetic turbulence at the inlet. Right Reg=1000, Left Reg=10000.
Figure 8: Wall shear stress coefficient for wall boundary layer flow using the WMLES option and the vortex method to generate synthetic turbulence at the inlet. Right Reg=1000, Left Reg=10000.
Figure 8: Wall shear stress coefficient for wall boundary layer flow using the WMLES option and the vortex method to generate synthetic turbulence at the inlet. Right Reg=1000, Left Reg=10000.
Figure 9: Channel flow. Viscosity ratio on iso-surfaces of Q-criterion (-500).
Figure 9: Channel flow. Viscosity ratio on iso-surfaces of Q-criterion (-500).
Figure 10: Fully developed channel flow. Mean velocity values inside LES zone (left), rms values inside LES zone at x = 1.5+1.5a (right).
Figure 10: Fully developed channel flow. Mean velocity values inside LES zone (left), rms values inside LES zone at x = 1.5+1.5a (right).
A more challenging testcase for ELES in combination with WMLES is has been computed within the EU project ATAAC. It is the flow over a hump with a relatively large separation zone on the leeward side. Figure 11 shows the experimental set-up (Greenblatt et al. 2005). The flow has been computed with ANSYS-Fluent 13.0 using the SST model in the RANS zone, the vortex method at the RANS-LES interface and the WMLES option in the LES zone.
A more challenging testcase for ELES in combination with WMLES is has been computed within the EU project ATAAC. It is the flow over a hump with a relatively large separation zone on the leeward side. Figure 11 shows the experimental set-up (Greenblatt et al. 2005). The flow has been computed with ANSYS-Fluent 13.0 using the SST model in the RANS zone, the vortex method at the RANS-LES interface and the WMLES option in the LES zone.
Figure 12: Left: grid for the NASA hump simulation. Right: turbulent structures in the LES domain (colour spanwise velocity component). The grid for the testcase can be seen in Figure 12 together with a visualization of the turbulent structures in the LES zone. The grid in the LRS zone consists of 200x100x100 cells and is designed to provide 10x40x20 cells in streamwise, normal and spanwise direction per boundary layer volume. The RANS grid is much coarser, especially in the spanwise direction. It should be noted that the momentum thickness Reynolds number at the inlet to the LES domain is relatively high (Reg=7000).
Figure 12: Left: grid for the NASA hump simulation. Right: turbulent structures in the LES domain (colour spanwise velocity component). The grid for the testcase can be seen in Figure 12 together with a visualization of the turbulent structures in the LES zone. The grid in the LRS zone consists of 200x100x100 cells and is designed to provide 10x40x20 cells in streamwise, normal and spanwise direction per boundary layer volume. The RANS grid is much coarser, especially in the spanwise direction. It should be noted that the momentum thickness Reynolds number at the inlet to the LES domain is relatively high (Reg=7000).
Figure 13: Wall shear stress, cf, and wall pressure coefficients, cp, for NASA hump flow simulations. Comparison of WMLES and WALE LES method in the LES domain.
Figure 13: Wall shear stress, cf, and wall pressure coefficients, cp, for NASA hump flow simulations. Comparison of WMLES and WALE LES method in the LES domain.
Related topics:
EngineeringComputer Science
580 California St., Suite 400
San Francisco, CA, 94104
© 2025 Academia. All rights reserved