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Large-Eddy Simulation, Detached-Eddy Simulation, and Variants

Traditional CFD for engineering applications solves the Reynolds-Averaged Navier-Stokes (RANS) equations to provide predictions for mean flow variables, like pressure, velocity, and wall stresses from which forces, moments, and other engineering quantities can be extracted. This statistical approach to fluid-flow simulation is rapid and can be accurate for classes of problems for which the underlying turbulence parameterizations are tuned.

The fidelity of a RANS model is sensitive to the flow configuration. For example, it is well known that RANS parameterizations can be very inaccurate for modeling turbulence in flow separations. Also, some engineering applications require information that cannot be directly extracted from RANS solutions. Turbulent boundary layer forcing for acoustics is an example where details of the pressure fluctuations are important, information that is not available from a RANS simulation.

Eddy-resolving simulation techniques are alternatives to RANS that can be accurate for flow classes where RANS models fail. Such models also provide details of the fluctuating turbulence field allowing them to be used for acoustics and other applications where turbulence details are important. Common examples of eddy-resolving CFD approaches are large-eddy simulation (LES) and the related detached-eddy simulation (DES), zonal-detached-eddy simulation (ZDES), and delayed-detached-eddy simulation (DDES) techniques, among others. Figure 1 presents a notional turbulence energy spectrum. Conceptually, an energy spectrum details the average energy per eddy in a turbulent flow. By convention, the energies are plotted against wavenumber, where the wavenumber is proportional to the inverse of the turbulence eddy size. Therefore, large-eddies contribute to the left side of the plot and small eddies to the right side. The energy in the smallest eddies goes to zero because turbulence dissipation sets a lower limit on their size. The energy spectrum shows a peak contribution from the larger turbulence eddies. These eddies are generally caused by flow around some kind of geometry. The spectrum goes to zero at the far left, because infinitely large eddies cannot have considerable energy. In the context of the turbulence energy spectrum, scale ranges can be defined. Shown are 1) the energy-containing range, those turublence motions responsible for most of the turbulent kinetic energy, 2) the inertial range, those turbulence motions responsible for transferring energy from large scales to the smallest scales where dissipation occurs, and 3) the dissipation range, where turbulence energy is removed from the flow.

All CFD methods can be classifed based on how they attempt to resolve the turbulence depicted graphically in the turbulence energy spectrum. If a CFD model resolves all fluid motions, it can yield the exact solution. Such techniques are called direct numerical simulation (DNS). If a model attempts to resolve the largest turublence structures placing the cutoff in the inertial range, the technique belongs to the class of LES methods. DES techniques place the cutoff in the energy-containing range somewhere in the modeled volume. Finally, the cutoff scale for RANS is at the far left, because RANS does not resolve any turbulence directly, choosing to represent turbulence effects in its subgrid model.

In principle, large-eddy simulation is an extraordinarily attractive solution technique. It provides an "exact" solution for the most energetic turbulence motions and incurs model error only for the dynamically less energetic eddies. Relative to RANS, LES can be computationally expensive, requiring about 1000 times greater computational resources (away from walls), however, yielding fidelity solutions for flow configurations where RANS fails. Near walls, however, turbulence eddy sizes are limited to the distance to the wall, so the inertial range of near-wall turbulence is forced to progressively smaller scales. So traditional LES can also become computationally prohibitively expensive, unless special wall models are used to remove the near-wall flow from the LES regime.

DES-type approaches fall into this category. The near-wall flow in an DES approach is modeled using the RANS equation set. Figure 2 shows RANS, LES, and DES models applied to turbulent channel flow. The RANS model, upper left, shows no turbulence fluctuations, because turbulence is modeled. The solution has the highest velocity at the channel center, as expected, and satisfies zero velocity at the channel walls. The turbulence motions in the LES solution, upper right, are unmistakable. The gray vortex tubes visualized in the figure, are a complicted mass of interacting structures. The contour plot of streamwise velocity shows the tendency for higher velocities at the channel core and slower velocities toward the walls and shows the large range of turbulence motions from large eddies to small. The DES solution, lower middle, is clearly a hybrid of the RANS and LES flow fields. The gray vortex tubes are observed, however, are less dense showing that they represent only the large-scale turbulence motions. Further, the contour plot shows similar large scale features but the small scale motions are clearly absent.

CFD research activity at ARL/Penn State actively engages all of the turbulence modeling approaches described above. Hybrid RANS/LES techniques are a particular focus, because of their computational economy. Simulated turbulent flow past a hump in a boundary layer is presented in Figure 3. The geometry is the Glauert-Goldschmied model that was used at NASA/Langley for a flow-control study. The configuration is challenging because the separation on the lee side of the hump is not set by the geometry but by details of the turbulence model near the separation point. In Figure 4, the mean-flow statistics for RANS and DES variants are reported with the experimental values for reference. Clearly the ZDES and DDES models are superior for simulating this flow field.

Other examples of the use of DES at ARL/PSU are turbulent flows around undersea vehicles, through turbomachines, through urban areas, etc.

ZDES of turbulent flow past a model building is presented in Figure 5. This case is the 6m Hoxey cube in an atmospheric boundary layer. The upper panel shows a snapshot of the instantaneous turbulence structures shedding from the cube. The time-averaged flow along the centerline (lower panel), shows recirculations in front of the cube, along its top, and in the wake. Figure 6 compares pressure coefficient profiles along the top centerline for various computational methods with the experimentally measured profile in black (and black arrows). The ZDES solution, marked by the red arrows, is the only method to faithfully reproduce the experimentally observed details.

Application of DES to a model urban environment is presented in Figures 7 and 8. Here the source of urban geometry is a detailed 3D map, left panel of Figure 7. The computational geometry, right panel of Figure 7, was lofted using these data as reference. Other sources of data could be CAD files from appropriate sources, digital terrain data from satellite and aerial overflights, etc. Figure 8 contrasts a RANS prediction for the urban flow field (left panel) against a DES solution (right panel). The presence of large scale turbulence structures are apparent in the DES solution for the urban scape that are not observed in the RANS solution. Although, one cannot judge whether the DES solution is more physical than the RANS solution in the absence of observational data, prior experience with variants of DES for flow in complicated geometry environments (discussed above) motivate the possibility that the DES solution does indeed more faithfully represent the urban flow.

Research in multiphase turbulence and eddy-resolving simulations has been a strong focus in recent years at ARL-PSU.  In cavitation, a turbulent-simulation capability is crucial to the accurate prediction of cavity shapes. An example of the effect is displayed in the time-averaged cavity shapes is displayed in Figure 9 below, where the DES simulation yields a much more agreeable cavity history through time. Animation 3 displays the evolution of the cavity using a DES approach,  which, similar to experiments, the cavity is dynamic. Whereas an unsteady RANS simulation, using a similar mesh and time-step sizes, dampens the cavity motions and essentially yields a static cavity.  Animation 4 displays a comparison of simulations, using unsteady RANS and the DES, of a cavitating, oscillating control surface.  The DES simulation displays added content in the cavity characteristics, which in turn, improve the overall understanding of the oscillatory loads on the control surface.  Such information is imperative in the design of cavitating parts.

Images
View Image (41kb)	Figure 1: Turbulence energy spectrum showing the ranges of turbulence motions simulated by various modeling approaches. RANS resolves no turbulence, parameterizing all of it. LES-type models resolve the largest turbulence motions, parameterizing only dynamically less important small scale motions. Direct numerical simulation (DNS) resolves explicitly all fluid motions, parameterizing nothing.
View Image (188kb)	Figure 2: Description of RANS, LES and DES (and variants).
View Image (166kb)	Figure 3: Detached Eddy Simulation of flow over a bump. Top left, pressure force on the surface plane. Bottom left, vortical structures of the flow. Right, experimental set-up.
View Image (219kb)	Figure 4: Showing relative accuracy of reattachment points in separated flow.
View Image (140kb)	Figure 5: ZDES of turbulent flow past a model building. The upper panel shows a snapshot of the instantaneous turbulence structures shedding from the cube. The time-averaged flow along the centerline (lower panel), shows recirculations in front of the cube, along its top, and in the wake
View Image (36kb)	Figure 6: Comparison of pressure coefficient profiles along the top centerline for various computational methods with the experimentally measured profile in black (and black arrows). The ZDES solution, marked by the red arrows, is the only method to faithfully reproduce the experimentally observed details.
View Image (99kb)	Figure 7: Application of DES to a model urban environment. The source of urban geometry is a detailed 3D map, left panel. The computational geometry, right panel, was lofted using these data as reference.
View Image (130kb)	Figure 8: Contrast of a RANS prediction for the urban flow field (left panel) against a DES solution (right panel).
View Image (123kb)	Figure 9: Summary of unsteady turbulent modeling of naturally cavitating flow over a blunt ogive. a) RANS vs DES: Snapshots of computed flow. Translucent grey isosurface of liquid volume fraction equal to 0.5 and cylinder colored by pressure. DES in upper part of each frame. b) Photographs from water tunnel experiment at approximately the same cavitation index (0.35) and Reynolds number (1.5e5). c) Comparison of decay to theoretical decay.
View Image (137kb)	Figure 10: Comparison of the simulations using various turbulence model approaches and assumptions. The dark-blue and light-blue isosurfaces are at volume fractions of 0.3 and 0.7, respectively.

Animations
View Animation (671kb)	Animation 1: This animation shows turbulent flow from the Glauert Goldschmied bump in a turbulent boundary layer. The modeling approach uses ZDES allowing LES-type turbulence to be simulated in the recirculation zone behind the body retaining RANS statistics elsewhere. Comparisons to data show that the ZDES solution is an improvement over the original DES formulation and over RANS for this case.
View Animation (1.7mb)	Animation 2: Computed unsteady vaporous cavitating flow over a twisted hydrofoil.
View Animation (1.7mb)	Animation 3: The evolution of the cavity (in Figure 9) using a DES approach,  which, similar to experiments, the cavity is dynamic.
View Animation (1.8mb)	Animation 4: A comparison of simulations (using unsteady RANS and the DES) of a cavitating, oscillating control surface