### 12.2.3. Stable Flows and Wall Boundary Layers

#### 12.2.3.1. Flow Physics

Stable flows in this context are characterized by a continuous development of the turbulence field. For such flows, the turbulence at a certain location depends strongly/entirely on the turbulence upstream of it. There is no mechanism for quickly generating new turbulence and over-riding the upstream turbulence field. Stable flows in the context of this discussion are essentially wall-bounded flows, which are either attached or have small separation bubbles.

- Generic Flows

  - Channel and pipe flows (attached and mildly separated)

  - Boundary layers (attached and mildly separated)

#### 12.2.3.2. Modeling

For stable flows, the use of embedded or zonal RANS-LES methods with a well-defined interface between the RANS and the LES zone is essential. Synthetic turbulence must be introduced at the RANS-LES interface to ensure a proper balance between the modeled and the resolved content of turbulence. The introduction of resolved/synthetic turbulence allows the balance between RANS and LES turbulence across the interface to be preserved (assuming the synthetic turbulence is of sufficient quality). Neither DDES nor SAS-type models are able to switch from RANS to SRS mode in such stable situations. Even in cases where resolved turbulence is specified at the inlet (or an interface) the SAS model will typically switch back to its underlying RANS mode after some boundary layer thicknesses (for example, Davidson, 2006 [4]). The DDES model does remain in LES mode but with a significant error in the logarithmic layer. The SBES model is able to perform in WMLES mode and provide proper velocity profiles downstream of synthetically generated turbulence.

Even an explicit switch from a RANS to a LES model (and the corresponding grid refinement in the LES zone) at the interface without an introduction of synthetic turbulence does not work well. If sufficient resolution is provided in the LES zone, the flow would eventually go through a transitional process and recover the fully turbulent state. However, such a process would require many boundary layer thicknesses, with an entirely unbalanced model formulation in-between. This method is not acceptable in most technical flows and must be avoided.

In such stable flows, the most suitable selection of hybrid RANS-LES models are Embedded- or Zonal models, where the RANS and the LES zones are user-defined and synthetic turbulence is injected at the RANS-LES interface. As mentioned previously, the RANS-LES interface should be placed in a non-critical region of the flow (equilibrium flow), since existing synthetic turbulence generators do not provide realistic turbulent fluctuations for strongly non-equilibrium flows. As a result, placing the interface in such regions results in a too-slow relaxation from synthetic to "real" turbulence (typically, several boundary layer thicknesses).

As an alternative, the RANS and LES simulations can be carried out separately. The RANS domain would include the full geometry whereas the LES solution can be carried out on a smaller portion of the original domain. This separate LES domain would be identical to the LES zone in the equivalent ELES set-up. The information from the larger RANS solution can then be mapped onto the boundaries of the LES domain. Synthetic turbulence should be introduced at the inlet of the LES domain. This approach can be used if you are confident that the physical decoupling has very little or no effect onto the overall flow topology. The advantage of the decoupled method over the ELES approach is that the RANS solution does not have to carry the burden of the excessive temporal resolution that the LES domain would have otherwise required. However, you should be aware that some scripting is required for mapping the results from RANS to LES in the decoupled approach.

The models selected in the RANS and LES zone depend on the flow physics. In the RANS zone, a suitable model for the flow should be selected. In the LES zone, the use of a WMLES formulation is typically recommended for wall boundary layers in order to avoid the unfavorable Reynolds number scaling of classical LES models. For free shear flows, the WALE model should provide optimal performance.

#### 12.2.3.3. Meshing Requirements

Figure 12.34 shows the schematic of an ELES set-up. There is a central area (red), which is the domain of interest (for example, a boundary layer with a separation bubble). This area is not specifically defined in the ELES set-up, but is just used to demonstrate how such a zone would be handled. Clearly, you would not place the LES zone (green) directly at the start of the zone of interest, but extend it upstream and downstream of that region by several boundary layer thicknesses as indicated in Figure 12.34. For fully developed pipe/channel flow, the boundary layer thickness should be estimated as half of the pipe diameter/channel height. The LES zone is then embedded into a larger RANS zone (blue).

The meshing requirements are those of the underlying turbulence models. In the RANS zone typical RANS resolution requirements should be satisfied (20–30 cells across the wall boundary layer with possibly a and 15–20 cells across free shear flows).

In the LES zone, the resolution requirements depend on the details of the LES model formulation and the flow type. For free shear flows, cubic grid cells with a minimum of cells per shear layer thickness should be used. For wall-bounded flows, the resolution requirements are those described in Section 12.1.5.1 for classical LES and in Section 12.1.6 for WMLES.

Figure 12.34: Sketch of embedded LES (ELES) domain

For wall-bounded flows, it is clear that large domains cannot be covered in SRS mode, even when using WMLES. In most cases you would limit the domain size of the LES zone by one or more of the following concepts:

- Use only a limited spanwise domain size.

  - Apply periodic boundary conditions where appropriate. The domain size has to cover a minimum of 3–5 boundary layer thicknesses in the spanwise direction to avoid inaccuracies caused by the spanwise periodicity condition. Care must be taken that this requirement is satisfied for the entire LES domain. In case the boundary layer grows in the streamwise direction, the most downstream location is relevant for the estimate.

  - In cases where no periodicity can be applied, place the spanwise interfaces into a region of limited interest.

- Place the upstream RANS-LES interface economically to reduce the size of the LES domain. However, the interface should be located in a zone of undisturbed equilibrium flow. Place the RANS-LES interface at a minimum of ~3 boundary layer thicknesses upstream of the zone of interest (for example, a separation region). Limit the size of the RANS-LES interface to the shear layer to capture; that is, do not extend the interface far into the freestream, as the code will then generate resolved turbulence in freestream regions where no LES is required. The Vortex Method (VM) would also generate a large number of vortices if the RANS-LES interface were too large.

- Place the downstream LES-RANS interface economically to reduce the size of LES domain. However, do not place the interface immediately downstream of the zone of interest, but place it several boundary layer thicknesses farther downstream to avoid any negative influence of the downstream RANS model (this approach enables the boundary layer to recover several boundary layer thicknesses downstream of a separation before switching back to RANS)

- Limit the height of the LES zone, but allow for some space above the boundary layer. Typically the LES zone should be about twice as thick as the boundary layer.

In order to check the quality of the simulation, sensitive quantities like time-averaged wall shear stress should be plotted across the RANS-LES zones. There should be no large jump in those quantities and the unavoidable disturbance caused by the interface should be recovered before entering the zone of interest.

#### 12.2.3.4. Numerical Settings

Zonal methods typically enable a separate selection of numerical settings in the RANS and LES zones. For very sensitive simulations, you can therefore select a pure Central Difference (CD) in the LES domain, while using an appropriate numerical scheme in the RANS parts. However, you can also select a global scheme, in which case the Bounded Central Difference (BCD) scheme is recommended.

#### 12.2.3.5. Examples

##### 12.2.3.5.1. Periodic Channel

The periodic channel flow is not an ELES, but a WMLES application. This section of the report shows that as WMLES is typically used in the LES portion of ELES/ZLES applications. The entire domain is WMLES and there are no RANS-LES interfaces. Simulations of this flow have been carried out assuming incompressible fluid at several Reynolds numbers based on friction velocity and channel height , Re = 395, 760, 1100, 2400, and 18000. The flow is driven by a constant pressure gradient , where is the pressure and is the density. This pressure gradient is taken into account in the governing equations via a source term in the momentum equations, which allows imposing periodic boundary conditions not only in the spanwise direction , but also in the streamwise direction . Note that within such an approach, the bulk velocity of the flow is not specified and should be obtained as a part of the solution, which means that it could be different with different turbulence models. Alternatively, you can specify the mass flow and the solver will adjust the imposed pressure gradient accordingly.

The size of the computational domain shown in Figure 12.35 is equal to in the streamwise direction and in the spanwise direction. For all considered Reynolds numbers, the computational grid is unchanged in the streamwise and spanwise directions with a uniform grid-spacing of and respectively. This gives 10 cells per channel half width, , ( being the relevant boundary layer thickness) in the streamwise and 20 cells per in the spanwise direction. Different grids have been used in the wall-normal direction. This arrangement provides a sufficient resolution ( near the wall) at different Reynolds numbers. Note, however, that all simulations could have been performed on the finest grid. The non-dimensional time step is , which ensures that the CFL number is in the entire domain. The solution was averaged in time over 5000 time steps. Table 12.3 gives the details of the grids used in the simulations and the resulting non-dimensional grid spacing. Note that classical wall-resolved LES would require values of , , demonstrating the substantial savings that can be achieved with WMLES for higher Re numbers. The range in Table 12.3 covers the range of values in the wall normal direction, with the largest values located at the center of the channel.

Figure 12.35: Computational domain and grid for WMLES of channel flow

Table 12.3: Grid resolution for WMLES channel flow simulations

| Number of Cells | Number of Nodes |  |  |
--- | --- | --- | --- | --- | ---
395 | 384 000 |  | 40.0 |  | 20.0
760 | 480 000 |  | 76.9 |  | 38.5
1100 | 480 000 |  | 111.4 |  | 55.7
2400 | 528 000 |  | 243.0 |  | 121.5
18000 | 624 000 |  | 1822.7 |  | 911.4

Figure 12.36 shows the turbulence structures using the -criterion (). The isosurface is colored by the streamwise velocity.

Figure 12.36: Turbulence structures for WMLES of channel flow at lowest Reynolds number (Q=350 [s-2])

Figure 12.37 shows the flow in a horizontal cut through the domain for the lowest and the highest Reynolds numbers. The thin region of RANS modeling near the wall for the high Reynolds number is indicated by the high eddy-viscosity (note the different scales in the plot for the eddy-viscosity ratio for the different Reynolds numbers). RANS modeling in this context is as described in Section 12.1.6, based on the near-wall mixing length formulation.

Figure 12.37: Flow visualization for WMLES of channel flow (a) Vorticity rate Omega, (b) Absolute value of velocity U, (c) Ratio of eddy-viscosity to molecular viscosity

Results of the WMLES formulation and their comparison with the empirical correlation of Reichardt, 1951 [23] are shown in Figure 12.38. You can see that the WMLES solutions reproduce the logarithmic layer with good accuracy. There is a slight kink at the switch from the RANS to the LES formulation, but it is moderate and does not affect global properties such as the wall shear stress.

The above simulations have been carried out with ANSYS Fluent. Similar results can be obtained with ANSYS CFX where WMLES is the default formulation inside the LES zone of the ZFLES method.

Figure 12.38: Resolved normal stresses, turbulent kinetic energy, and mean velocity profiles for WMLES at different Reynolds numbers

The same test case has been computed with the global hybrid RANS-LES models. In order to push them into unsteady SRS mode, the simulations are started from the WMLES solution above. Please note that the DDES model is not shown because it would produce a severe shift in the logarithmic velocity profile. The IDDES model shown for comparison has been calibrated for WMLES applications; it does however have only limited shielding capabilities and is therefore not suitable for general industrial applications.

As seen from Figure 12.39: Isosurfaces of the Q-criterion colored with the velocity magnitude, all the models provide resolved turbulent structures for both considered Reynolds numbers. The results of SBES (combination of SST and WALE) and IDDES are visually close to each other with a finer resolution provided by the IDDES model. The near wall resolved turbulence is noticeably reduced by SDES for both Reynolds numbers.

As seen from Figure 12.40: Profiles of the eddy viscosity ratio for different models, SDES lacks resolved turbulence near the wall due to a substantially higher peak of the eddy viscosity resulting from a noticeable shift of the RANS-LES interface away from the wall. SBES also yields a noticeably higher eddy viscosity peak than IDDES but much reduced relative to SDES.

Figure 12.39: Isosurfaces of the Q-criterion colored with the velocity magnitude

Figure 12.40: Profiles of the eddy viscosity ratio for different models

Interestingly, the profiles of the mean velocity as shown in Figure 12.41: Profiles of the mean velocity for different models are in good agreement with each other and with the empirical correlation for all models. It should be noted, that, despite SDES yielding the smallest magnitude of the LLM (Figure 12.41: Profiles of the mean velocity for different models), it noticeably underestimates the total turbulence kinetic energy (Figure 12.42: Profiles of the total turbulence kinetic energy for different models) for both Reynolds numbers. This indicates that the wall modeled LES capability of SDES is not optimal for the given meshes. At the same time, the profiles of the total kinetic energy of SBES and IDDES are relatively close to each other, which means that the models have similar wall modeled LES capabilities. The results also indicate that further improvements in terms of WMLES resolution could be obtained by moving the RANS-LES interface slightly closer to the wall.

Figure 12.41: Profiles of the mean velocity for different models

Figure 12.42: Profiles of the total turbulence kinetic energy for different models

##### 12.2.3.5.2. Wall Boundary Layer

The zero pressure gradient wall boundary layer is a benchmark test case that is commonly used for turbulence model investigation due to its geometric and physical simplicity. Unlike the periodic channel test case, the wall boundary layer needs unsteady boundary conditions because there is no periodicity in the streamwise direction. In the current simulations, the Vortex Method (VM) was used for these purposes (Mathey et al., 2003 [15]).

A computational domain for this test case is shown in Figure 12.43. The characteristic length, which determines the geometry, is the plate length, , of 1 [m] in the current study. Dimensions of the computational domain in , , and directions are equal to , , and respectively.

Figure 12.43: Computational domain for a Wall Boundary Layer test case

The simulations have been performed for an incompressible fluid. A summary of physical parameters is presented in Table 12.4.

Table 12.4: Properties for flat plate boundary layer simulations

| 1000 | 10 000
--- | --- | ---
Inlet boundary layer thickness | 0.032 | 0.032
| 0.001 | 0.001
| 1.0 | 1.0

The geometry and the computational grid used for the test case are shown in Figure 12.44. The base grid is uniform in the - and -directions with steps 0.004 [m] and 0.002 [m] respectively. In the wall normal direction the grid was expanded by a factor of 1.15. For all computations the value of is less than 1, which means that the governing equations are integrated to the wall. A complete summary of all used grids is presented in Table 12.5.

Figure 12.44 (b) presents all the boundary condition types used in the simulations. The cyan color shows one of the periodic planes, the red color the no-slip wall boundary, the blue color the outlet boundary, the green color the inlet boundary, and the yellow color the symmetry boundary.

Figure 12.44: Computational grid (a), (c) and applied boundary conditions (b)

Table 12.5: Information on grids for flat plate test case

| Number of Cells | Number of Nodes |  |  |
--- | --- | --- | --- | --- | ---
1000 | 1 085 000 |  | 68.0 |  | 34.0
10 000 | 1 333 000 |  | 680.0 |  | 340.0

Two cases have been computed using the numerical grids with the parameters shown in Table 12.5. They have different inlet Reynolds numbers that are based on the boundary layer momentum thickness ().

The Non-Iterative Time Advancement (NITA) algorithm based on the Fractional Time Step method was applied with the second order scheme for the approximation of time derivatives. The convective terms in the momentum equations have been approximated with the second order Central Difference scheme and the Green-Gauss cell-based method was used for interpolation of variables on cell faces. The Standard option was selected for the pressure interpolation scheme.

Visualizations of the flow at two values of are shown in Figure 12.45. Isosurfaces of the -criterion that are equal to and colored with the velocity magnitude are depicted. It can be seen that the turbulence structures are well-developed and do not show any visual decay or disruption downstream of the inlet. This indicates that the Vortex Method provides sufficiently realistic turbulent content at the inlet boundary.

Figure 12.45: Isosurfaces of Q-criterion (Q=200 [s–2]) colored with velocity for a flat plate at two different Reynolds numbers

Figure 12.46 shows the skin-friction coefficient for the two Reynolds numbers. The results demonstrate that the inlet wall friction provided by the RANS inlet velocity profiles is maintained without any major disruption. This indicates again that the vortex method produces sensible synthetic inlet turbulence. In addition, the models react properly to the Reynolds number variation, suggesting that the WMLES can maintain a boundary layer accurately even at high Reynolds numbers, where standard LES models would fail due to a lack of resolution. Figure 12.46 (a) shows, in part (a), the impact of the pressure interpolation scheme, which has proven to be critical for locally stable flows. It is worth re-iterating that the PRESTO scheme requires slightly more ‘running length’ to recover the correct levels of turbulence and wall shear stress.

Figure 12.46: Skin friction distributions along a flat plate predicted by WMLES at two Reynolds numbers (a) Re theta=1000 with different numerical settings (b) Re theta =10 000

Figure 12.47 shows Reynolds stresses and velocity profiles from the simulations. The figure suggests that, just as for the channel flow, the quality of the simulations is fairly high in terms of both the mean flow prediction (the logarithmic profile is reproduced faithfully) and Reynolds stresses (they are well within the range expected from known DNS studies of the flat plate boundary layer).

Figure 12.47: Profiles of resolved normal and shear Reynolds stresses and mean velocity in the flat plate boundary layer predicted by WMLES at two Reynolds numbers (a) Re theta=1000 with different numerical settings (b) Re theta=10 000 with the second order pressure interpolation

The above simulations have been carried out with ANSYS Fluent. Similar results can be obtained with ANSYS CFX where WMLES is the default formulation inside the LES zone of the ZFLES method.

##### 12.2.3.5.3. NASA Hump Flow

A challenging test case for ELES in combination with WMLES was computed within the EU project ATAAC. The case models the flow over a hump with a relatively large separation zone on the leeward side. Figure 12.48 shows the experimental set-up (Greenblatt et al., 2005). Due to the limited separation zone, this flow would be categorized as a stable flow in the present context.

Figure 12.48: Experimental set-up for NASA hump flow experiment

The flow was computed with ANSYS Fluent 13.0 using the SST model in the RANS zone, the vortex method at the RANS-LES interface and the algebraic WMLES option in the LES zone. The Reynolds number, based on the free-stream velocity, , and hump chord, , is equal to . The simulation was carried out in the full domain, which extends from to (0 corresponds to the hump beginning). In the spanwise direction, the extent of the domain is . The inflow boundary conditions for RANS have been set based on the preliminary flat plate boundary layer computations up to the flow section (), where the parameters of the incoming boundary layer have been measured in the experiment. At the upper wall of the channel, free-slip wall conditions have been specified.

The grid in the LES zone (see Figure 12.49) consists of cells and was designed to provide cells per boundary layer volume in the streamwise, wall normal, and spanwise directions. The RANS grid is much coarser, especially in the spanwise direction. Figure 12.49 also presents a visualization of the turbulent structures in the LES zone that suggests a high resolution provided by the simulation (note that the momentum thickness Reynolds number at the inlet to the LES domain is relatively high ()). In retrospect, the set-up might not be fully optimal, as the RANS-LES interface is placed relatively close to the non-equilibrium/separation zone of the boundary layer. There are only about two boundary layer thicknesses between the interface and the bend of the geometry. A more optimal grid should cover more of the upstream boundary layer and enable the synthetic turbulence to develop over a longer running length.

Figure 12.49: (a) Grid used for the NASA hump simulation (b) Turbulent structures in the LES domain (Q-criterion colored with spanwise velocity component)

Figure 12.50 shows the skin-friction and wall-pressure coefficient distributions from the simulations. It can be seen that the use of ELES combined with the WMLES model in the LES zone results in very close agreement with the data, even though the skin-friction is known to be very sensitive to simulation details. A comparison of the results obtained using WMLES with those obtained using the standard WALE model in the LES zone is shown in Figure 12.50. The results suggest that the latter performs considerably worse than the former. In particular, in the simulations using the WALE model, the wall shear stress drops immediately after the RANS-LES interface to unrealistically small values due to the lack of resolution. The results with this model further downstream are therefore no longer reliable as the wall shear stress has a strong influence on the overall boundary layer development. Further investigations of this flow are on-going, so the results should not be considered final, but are provided to demonstrate the basic concepts.

Figure 12.50: (a) Skin-friction, cf, and (b) Wall pressure coefficients, cp, from NASA hump flow simulations. Comparison of WMLES and WALE LES methods in the LES domain

##### 12.2.3.5.4. T-Junction with Thermal Mixing

The following example is a flow through a pipe T-junction with two streams at different temperatures Westin et al., 2006 [37]. This test case was used as a benchmark of the OECD to evaluate CFD capabilities for reactor safety applications. This flow is not easily categorized in the current framework. It can be placed somewhere between a globally and a locally unstable flow. As shown below, this flow can be modeled with SAS and DDES, but special care must be taken in choosing the numerical settings. (Note that this flow has been computed with SDES and SBES models and the solutions are similar to the SAS and DDES model results.)

The set-up consists of a horizontal pipe for the cold water flow, and a vertically oriented pipe for the hot water flow. The hot water pipe is attached to the upper side of the horizontal cold water pipe. In the experiments, the length of the straight pipes upstream of the T-junction is more than 80 diameters for the cold water inlet, and approximately 20 diameters for the hot water inlet. The flow conditions are listed in Table 12.6.

Table 12.6: Flow conditions for T-Junction test case

| Diameter | Bulk velocity | Mass flow | Temperature | Re number
--- | --- | --- | --- | --- | ---
Hot Pipe |  |  |  |  |
Cold Pipe |  |  |  |  |

A sketch of the domain is depicted in Figure 12.51. The domain dimensions are as follows. The hot leg inlet is located at the section, the cold leg inlet is located at the section, and the outlet is located at , with being the diameter of the cold leg of the pipe. When ELES was used, two additional interfaces have been introduced in the domain, where the synthetic fluctuations generated with the use of the Vortex Method have been specified. These sections have been placed at in the hot leg and at in the cold leg.

The computational grid for this flow is composed of about 4.9 million hexahedral cells (see Figure 12.51). The wall normal grid spacing was set to 0.0001 [m], which yields in the entire domain. The grid spacing in the axial and circumferential directions was set as follows:

- For the cold water pipe where the inlet boundary layer thickness is equal to 0.07 [m], the grid spacing was chosen and , which yields and .

- For the hot water pipe the inlet boundary layer thickness was set to 0.022 [m] and the grid spacing was chosen and , which yields and .

- In wall units, the grid spacing is (, )˜ (195, 80) for the hot water pipe and (, )˜(115, 70) for the cold water pipe, which means that the flow requires near-wall turbulence modeling. The time step was set to 0.001 [s], which leads to CFL~1 in the central mixing zone.

Figure 12.51: Geometry and grid of T-Junction test case with measurement planes

The boundary conditions for this case have been specified as follows. For the inlet boundaries, the precursor simulations of the pipe flow have been performed using the SST model. For the cold water pipe, a fully developed pipe flow was calculated using the SST model and the profiles of velocity and turbulence quantities have been specified at the inlet boundary. For the hot leg and the pipe, the profiles in the experiments were not fully developed. For this reason, a separate pipe flow simulation was conducted using constant inlet values for velocity and turbulence. The inlet profiles for the hot leg have then been extracted from this precursor simulation at the location where they matched the experimental profiles most closely.

It bears repeating that this flow is not easily categorized into one of the three groups described above, but might be described as between globally unstable and locally unstable. It was originally computed with the global SAS and DDES models. Although both simulations turn into a proper SRS mode in the interaction zone of the two streams, the results turned out to be very sensitive to numerical details and solver settings, especially for the SAS model. As an illustration, in Figure 12.52, the turbulence structures are shown as predicted by the SAS-SST model with the use of the CD and BCD numerical schemes. The effect of the scheme on the resolved flow is striking. This effect is an indication that the underlying flow instability is not very strong and can only be represented by the SAS model with the use of a low dissipative numerical scheme such as CD in this particular case. Under such conditions, it is not advisable to apply global methods like SAS (and to a lesser extent, DDES), as will be seen from the temperature distributions later. It is important to emphasize that in more unstable flows, the difference between CD and BCD is not nearly as strong and often barely noticeable.

Figure 12.52: Turbulence structures for SAS-SST model (a) Central Difference (CD) scheme, (b) Bounded Central Difference (BCD) scheme

It is therefore recommended to apply the ELES model with synthetic turbulence specified at predefined RANS-LES interfaces located in both pipes upstream of the interaction zone. Switch from the RANS to LES at these interfaces using the vortex method. In this case, the SST model was employed in the RANS zone and the WMLES approach was used in the LES part of the domain. As seen in Figure 12.53, with this approach resolved turbulence is generated well-upstream of the interaction zone and is then maintained through the interaction zone independent of the numerical scheme (CD or BCD).

Figure 12.53: Vorticity contours for ELES/WMLES simulation (a) CD scheme, (b) BCD scheme

Figure 12.54 shows velocity profiles of different velocity components at different measurement locations (see Figure 12.51). Figure 12.54 (a) shows results for the DDES, ELES/WMLES, and SAS simulations using the CD scheme. All simulations agree well with each other and with the experimental data. Figure 12.54 (b) shows the same models, but computed using the BCD scheme. As discussed, the SAS/BCD model shows marked differences compared to the experimental data, as already expected from Figure 12.52. It stays in URANS mode, which for this case turns out to be inadequate. The other models are less sensitive to the numerical set-up and provide almost identical results when using the BCD and the CD scheme.

Figure 12.54: Comparison of the experimental and computational velocity profiles for T-Junction flow for different turbulence models (a) CD scheme (b) BCD scheme (note that scales of coordinate axes change by large factors between curves)

From an application-oriented standpoint, the most important outcome of these simulations is the thermal mixing and the resulting wall temperature distributions. Results for the different simulations are shown in Figure 12.55 to Figure 12.58. The comparison is depicted for four lines located on the wall of the main pipe downstream of the intersection at the Top (), Front (), Bottom (), and Rear () (see Figure 12.51). One can find significant differences between the global and the ELES formulations, especially on the top wall. The temperature mixing is more accurately predicted with the ELES model because the transitional process between RANS and LES is not well-defined in global models. While the solution of global hybrid models is much better than URANS (not shown here), the details can still be missed in the initial mixing zone. The ELES method is more consistent, as it provides a clear interface where modeled and resolved turbulence are exchanged (RANS-LES interface with synthetic turbulence). Because of that, well-defined resolved turbulence is already present upstream of the junction, thereby avoiding the ambiguities of the formation of resolved turbulence in the interaction zone.

Figure 12.55: Comparison of the experimental and computational wall temperature distributions for T-Junction flow at the Top wall (0 degrees, see Figure 12.51) of the main pipe

Figure 12.56: Comparison of the experimental and computational wall temperature distributions for T-Junction flow at the Front wall (90 degrees, see Figure 12.51) of the main pipe

Figure 12.57: Comparison of the experimental and computational wall temperature distributions for T-Junction flow at the Bottom wall (180 degrees, see Figure 12.51) of the main pipe

Figure 12.58: Comparison of the experimental and computational wall temperature distributions for T-Junction flow at the Rear wall (270 degrees, see Figure 12.51) of the main pipe

Details of the resolved turbulence can be seen in Figure 12.59, which shows the region just downstream of the pipe intersection on the Top wall ( - Figure 12.51) where the temperature predictions between ELES and DDES differ the most (Figure 12.55). ELES shows significantly stronger resolved turbulence activity than DDES, confirming the arguments above. More recent simulations of this flow using the SBES model show similar solutions to DDES, but with smaller resolved turbulence structures.

Figure 12.59: Comparison of turbulence structures on the Top wall downstream of the pipe intersection (a) DDES model (b) ELES model

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