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
- Turbulence modelling
- Transition modelling
- Near-wall modelling
- Other modelling
Application Uncertainties
Summarise any aspects of the UFR model set-up which are subject to uncertainty and to which the assessment parameters are particularly sensitive (e.g location and nature of transition to turbulence; specification of turbulence quantities at inlet; flow leakage through gaps etc.)
Recommendations for Future Work
Propose further studies which will improve the
quality or scope of the BPA and perhaps bring it up to date. For example,
perhaps further calculations of the test-case should be performed
employing more recent, highly promising models of turbulence (e.g Spalart
and Allmaras, Durbin's v2f, etc.). Or perhaps new experiments should be
undertaken for which the values of key parameters (e.g. pressure gradient
or streamline curvature) are much closer to those encountered in real
application challenges.
Contributed by: Suad Jakirlić, Gisa John-Puthenveettil — Technische Universität Darmstadt
© copyright ERCOFTAC 2024