# UFR 4-16 Best Practice Advice

# Flow in a 3D diffuser

## Confined flows

### Underlying Flow Regime 4-16

# Best Practice Advice

## Key Physics

The flow in the present three-dimensional diffuser configurations is extremely complex, despite a simple geometry: namely a "through flow" in a duct — with the cross-section of its "central part" exhibiting a certain expansion and having one clearly defined inlet and one clearly defined outlet. The basic feature of the flow is a complex three-dimensional separation pattern being the consequence of an adverse pressure gradient imposed on the flow through a duct expansion. Two diffuser configurations characterized by slightly different expansion geometry but leading to completely different recirculation zone topology have been investigated. The differences are with respect to the separation onset and reattachment (form and position of the 3D separation/reattachment line) — multiple corner separation and corner reattachment — as well as with the shape and size (length, thickness, fraction of the cross-sectional area occupied by separation) of the recirculation pattern. An important prerequisite for a successful reproduction of the separating flow structure in the diffuser section is the correct capturing of the flow in the inlet duct characterized by intensive secondary currents — being normal to the main flow direction — induced by the Reynolds stress anisotropy.

## Numerical Issues

### Discretization

It is well-known that the accuracy of the spatial and temporal discretization in the LES-framework should be at least of the second-order. DNS results, which we regarded here more as a reference database, were obtained by applying a code with much higher accuracy level. All LES and LES-related simulations were carried out with second-order accurate discretization schemes. The latter simulations imply the application of Hybrid LES/RANS models. These model schemes employ a RANS model, consisting mostly of two additional (for k and ε) equations (e.g., the TUD-HLR model). For the equations governing such turbulent quantities some upwinding can be used by applying the so called "flux blending" technique without noticeable influence on the quality of the results.

### Grid resolution and grid quality

It is interesting to note that virtually the best agreement with the reference experimental database was obtained by applying a relatively coarse grid (1.6 and 2.0 Mio. grid cells in total for diffuser 1 and 2 respectively) whose cells were distributed uniformly over the entire solution domain. In this LES simulation performed by the Karlsruhe group (ITS-LES-SM) the standard Smagorinsky model was applied in conjunction with wall functions for wall treatment. There was no specific refinement in the region of separation and reattachment. This example shows that results of high quality (with respect to the time-averaged quantities) can be obtained on a moderate grid size — for diffuser 2 there was no significant difference to the wall-resolving LES with 42.0 Mio. cells. The much finer resolutions applied by HSU-LES-DSM (up to 18 Mio. cells; Dynamic Smagorinsky model was used — DSM) and TUD-LES-DSM (the geometry was meshed with the grid consisting of up to 4 Mio. cells in total) resulted in a very similar outcome with no noticeable improvement compared to the ITS-LES results. The reasons for that lie in the nature of the flow in the present 3D diffuser (see the discussion in 2.3 and 2.4).

## Computational domain and boundary conditions

### Computational domain

The computational domain follows exactly the
experimentally investigated configuration. The computational domain
comprises a part of the inlet duct (with length up to *5h*), the entire
diffuser section (*15h*) and the straight outflow duct (*12.5h*; the outflow
boundary conditions are applied at the plane coinciding with the transition
to the converging duct). Some computational groups located the outflow
plane "somewhere" in the converging duct, e.g. TUD-LES adopted a solution
domain with the outlet positioned well within the converging duct at length
*9h* (let us recall that its length is *10h* before transitioning to a pipe;
see
Fig. 1 in the Abstract and Fig. 2
in the Description section).

### Inlet

All computations presented, irrespective of the model applied,
started with the velocity and turbulence-quantity profiles corresponding to
a fully-developed duct flow. The latter profiles were the results of
separate/precursor computations of the inflow duct of a certain length —
mostly *5h* in the case of the eddy-resolving methods — using periodic
inlet/outlet boundary conditions and the same model, the diffuser was
consequently computed. It should be noted that the 3D streamwise-periodic
channel of length *5h* used for the inflow generation might be too short,
keeping in mind the spatial extent of the characteristic eddy structures,
which is in general larger (due to the secondary currents) than in a
(nominally 2D) channel flow with the spanwise homogeneity. Furthermore,
Nikitin (2008) argued that an auxiliary streamwise-periodic simulation
might not be suitable since it causes a spatial periodicity, which is not
physical for turbulent flows. Let us recall that the solution domain in the
DNS of
Ohlsson *et al.* (2010)
comprises an inflow development duct of *63h*
length, accounting even for the transition of the initially laminar inflow.
The present simplification of the numerical setup is certainly adequate for
the RANS computations but is also pertinent to the hybrid LES/RANS method,
since its overall aim is to improve the efficiency (lower computational
costs) and applicability to complex geometries. In order to achieve the
same basis for mutual comparison of the presently employed LES and HLR,
both methods used the same inflow conditions, i.e. the same inflow duct
length. In conclusion, the inflow originating from a separate computation
of fully-developed duct flow by using periodic inlet/outlet boundary
conditions is regarded as satisfactory; this is especially valid keeping in
mind that the focus of the present study was found to be on the
time-averaged flow field which was in reasonable agreement with the reference
databases.

### Wall

No-slip conditions along the diffuser walls are to be applied "irrespective" of whether the governing equations are to be integrated to the wall itself — application of the exact boundary conditions corresponding to the viscous sublayer region — or some "bridging" by wall functions for "modelling" the near-wall region is used. The results suggest that the near-wall treatment is not of decisive importance. In this configuration the flow unsteadiness is introduced into the wall boundary layers from the core flow in accordance with the so-called "top-to-bottom" process. This fact justifies the use of the wall functions in conjunction with some models allowing a coarser grid resolution in the near-wall regions. This was confirmed in conjunction with the high Reynolds number Reynolds stress model (TUD-RSM) but also in the LES framework (ITS-LES-SM).

### Outlet

Different groups positioned the outlet plane differently; however,
the outlet plane location was in all cases sufficiently far away from the
"zone of interest", i.e. from the diffuser section. According to the
experimental and DNS reference database the separation bubble ends well
within the first half of the straight outlet duct at about *6h* (the length
of this duct segment is *12.5h*). Some groups located the outlet plane
approximately at the end of the outlet duct (applying both zero-gradient
and convective-outflow conditions) and some of them well within the
converging duct. The ANSYS group extended the straight outlet part up to
*45h* and applied zero-gradient conditions (RANS computations have been
performed). Keeping in mind that in the focus of the evaluation were the
time-averaged mean flow and turbulence quantities one can conclude that the
outlet plane location and associated outlet boundary conditions do not
represent a critical issue.

## Physical modelling

The advice given here follows mainly from the ERCOFTAC workshops, but it is largely supported also by the results obtained in the ATAAC project.

The comparison with the experimental data demonstrated that **DNS and LES** can
reproduce the separated flow in the 3D-diffusers and the geometric
sensitivity of the flow within experimental uncertainties. From an analysis
of the data the following setup recommendations for LES can be deduced:
There is no need to compute the long inlet channel, instead an inflow data
generator suffices. There is also no need to compute the rear contraction,
since an outflow with buffer zone worked well. Averaging statistics over
approximately 100 flow-through times (formed with U_{b} and diffuser length)
is recommended, although smaller flow-through times can also lead to correct
results (see TUD contribution). For LES, the type of SGS model and near-
wall modeling / resolution seems less important than resolving the free
shear layers and the largest coherent structures in the center of the
diffuser. An economical Smagorinsky-type SGS-model in conjunction with wall-
functions and a simple equidistant grid can suffice to predict the complex
separated flow in the two asymmetric diffusers (see ITS Karlsruhe
contribution).

A conclusion on the **hybrid LES/RANS simulations** is that the high degree of
geometric sensitivity found in the experiments can be well reproduced on a
rather coarse grid. The separation regions in both slightly different
diffusers spread as expected which is not natural for RANS. An exception is
the DES method which delivers poor results and thus cannot be recommended
for such internal flows, but note that in the ATAAC project IDDES produced
fairly good results for diffuser 1.
Furthermore, the hybrid methods generally deliver
better agreement of the mean and r.m.s. velocities with the measurements
than several LES predictions even when the latter were carried out on a
much finer grid. Consequently, Hybrid LES/RANS approaches in general are a
promising tool but still need further evaluation.

The linear **eddy-viscosity RANS** models show no sensitivity to changes in the
geometry of the diffuser section, and generally poor performance.
The results obtained for both diffusers
indicate almost identical flow topology. The reason for that must be
primarily sought in the models' incapability to account for the Reynolds
stress anisotropy governing the secondary currents in the inflow duct. The
results obtained by the models based on the anisotropy-resolving
**RSM concept** (both differential and algebraic) offer a much more differentiated
picture of the flow field in reasonable agreement with the experimental
data, but less so than LES and Hybrid methods as
deviations still exist. This is a consequence of the
incapability of RANS models in general (an unsteady computation brings no
improvement) to account for any spectral dynamics associated with the large
energetic eddies dominating the separated shear layers.

## Application Uncertainties

The configuration considered is confined by rigid walls and has one inlet (with prescribed inflow) and one outlet positioned sufficiently far away from the diffuser section (see discussion associated to the outlet boundary conditions, Section 2.3.4); at both planes there is an entirely positive through flow characterized by a fairly uniform velocity profile over the most of the cross-section. One can say that the present geometry represents a non-ambiguously defined flow configuration. Accordingly, there is not much room for any uncertainty with respect to the flow geometry, operating and boundary conditions.

## Recommendations for Future Work

The corner separation is a flow phenomenon of great industrial importance:
it is relevant to all junction-shaped geometries in general; a prominent
example is the junction between an aircraft wing and its fuselage. However,
in such cases of practical relevance the Reynolds number is usually large
while in the diffuser flows considered here the Reynolds number (Re=10000)
is fairly low, i.e. not really industrially relevant. The case originators
extended their investigation up to a Reynolds number of 30000;
unfortunately only the surface pressure development along the flat bottom
wall was measured (
Cherry *et al.*, 2009).
Hence, investigations at a higher,
more industrially-relevant Reynolds number (even up to a Million) would be
desirable.

Contributed by: **Suad Jakirlić, Gisa John-Puthenveettil** — *Technische Universität Darmstadt*

© copyright ERCOFTAC 2019