Post on 22-Dec-2015
description
Accepted Manuscript
LES and DES of Strongly Swirling Turbulent Flow through a Suddenly Ex-
panding Circular Pipe
Ardalan Javadi, Håkan Nilsson
PII: S0045-7930(14)00444-7
DOI: http://dx.doi.org/10.1016/j.compfluid.2014.11.014
Reference: CAF 2735
To appear in: Computers & Fluids
Received Date: 14 June 2014
Revised Date: 14 October 2014
Accepted Date: 7 November 2014
Please cite this article as: Javadi, A., Nilsson, H., LES and DES of Strongly Swirling Turbulent Flow through a
Suddenly Expanding Circular Pipe, Computers & Fluids (2014), doi: http://dx.doi.org/10.1016/j.compfluid.
2014.11.014
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LES and DES of Strongly Swirling Turbulent Flow through a
Suddenly Expanding Circular Pipe
Ardalan Javadi, Håkan Nilsson
Department of Applied Mechanics, Chalmers University of Technology, Gothenburg, SE-
412 96, Sweden
Corresponding author. Tel.:+46(31)772 52 95, Fax: +46(31)18 09 76, Email address:
ardalan.javadi@chalmers.se (Ardalan Javadi).
Abstract
A detailed numerical study is undertaken to investigate the physical processes that are
engendered in the strongly swirling turbulent flows through a suddenly expanding circular pipe.
The delayed DES Spalart-Allmaras (DDES-SA), improved DDES-SA (IDDES-SA), a dynamic
k-equation LES (oneEqLES), dynamic Smagorinsky LES (dynSmagLES) and implicit LES with
van Leer discretization (vanLeerILES) are scrutinized in this study. A comprehensive mesh
study is carried out, and the results are validated with experimental data. The results of different
operating conditions from LES and DES are compared and described qualitatively and
quantitatively. The features of the flows are distinguished mainly on the basis of different levels
of the centrifugal force for different swirls. The numerical results capture the vortex breakdown
with its characteristic helical core, the Taylor-Görtler vortices and the turbulence structures.
Further features are addressed because of the excellent agreement between the numerical and
experimental data. The hybrid behavior of DDES-SA and IDDES-SA is discussed. The results
confirm that LES and DES are capable of capturing the turbulence intensity, the turbulence
production and the anisotropy of the studied flow fields.
Keywords: Swirling Flow, Vortex Breakdown, Sudden expansion, LES, DES
1. Introduction
Confined turbulent swirling flows are encountered in many industrial applications, such as
hydraulic turbines, gas turbine combustors and internal combustion engines. A key feature of the
strongly swirling flows is vortex breakdown. Vortex breakdown is an abrupt change in the core
of a slender vortex and typically develops downstream into a recirculatory “bubble” or a helical
pattern (Leibovich, 1984; Shtern and Hussain, 1999). The vortex breakdown may be beneficial,
e.g. increasing heat transfer or the combustion rate in heat exchangers and combustors, or
detrimental, e.g. yielding pressure pulsations in hydraulic turbines. The characteristics of various
breakdown states (or modes) in swirling flows depend on the swirl number (Sr),
Sr=�
�
� �������
�
� ������
�
, (1)
the Reynolds number (Re),
�� � ��
�, (2)
and geometry-induced axial pressure gradients in the flow. Here R is the radius and r is the radial
position, W and U are the axial and tangential velocities, respectively, Wb is the bulk velocity,
D=50.78×10-3 m is the inlet diameter, ρ is the density, and μ is the dynamic viscosity. Gupta et
al. (1984) observed experimentally that the vortex breakdown for turbulent flows at low swirl
numbers is dominated by large-scale unsteadiness due to the onset of a slowly precessing helical
vortex core. The precessing vortex core is related to the oscillatory motion of non-turbulent
coherent structures, yielding the dominant frequency of the energy spectrum. It is known that, as
the swirl number increases, the oscillatory motion of the coherent structure becomes more
pronounced (Wang et al., 2004). For non-swirl flow, the jet can rotate in either direction, while
Nomenclature
D inlet radios [m]
f frequency [1/s]
k turbulent kinetic average [m2.s-2]
R radius [m]
r, θ radial and tangential position [m]
Re Reynolds number [-]
Sr swirl number [-]
Sr* modified Swirl number [-]
U, W tangential and axial mean velocity [m.s-1]
u'rms, w'rms tangential and axial velocity root
mean square [m.s-1]
Wb inlet bulk velocity [m.s-1]
x, y, z coordination directions [m]
PN, Pshear normal and shear production of
turbulence [m2.s-3]
Puu, Pww tangential and axial components of
production of turbulence [m2.s-3]
Puw shear component production of
turbulence [m2.s-3]
Greek Symbols
δ boundary layer thickness [mm]
δij Kronecker delta [-]
μ dynamic viscosity [kg.s-1.m-1]
ρ density [kg.m-3]
υ kinematic viscosity [m2.s-1]
υt turbulent viscosity [m2.s-1]
when a slight swirl is included, the precessing vortex counter-rotates to the direction of the swirl
(Guo et al., 2002). Several modes of precession are predicted as the swirl intensity increases, in
which the precession, as well as the spiral structure, reverses direction (Zohir et al., 2011). When
the swirl increases to Sr=0.5, a central recirculation zone occurs, which is a typical manifestation
of vortex breakdown (Guo et al., 2002). This central reversed flow is the result of a low-pressure
region created by the centrifugal force. For swirling flow in a straight circular pipe at a fixed Re,
it is well known that, above a threshold swirl number, a disturbance develops along the vortex
core, characterized by the onset of a limited region of reversed flow along the axis. This marks
the transition from a supercritical to a subcritical swirling flow state (Escudier, 1987). As the
swirl number increases to moderate levels, the flow is known to become more axisymmetric with
an on-axis recirculation, marking the onset of bubble-type vortex breakdown.
The first analysis of sudden-expansion pipe flows was made by Borda (1766) and the literature
has since been concerned with confirming his expression for the overall loss. Turbulent swirling
flow through a sudden axisymmetric expansion possesses several distinctly different flow
regimes, such as separation, one or two recirculation regions, high turbulence levels, and
periodic asymmetries under some conditions. The diverging nature of sudden-expansion flow is
known to initiate and lock the location of the precession and flow instabilities. Many researchers
have reported experimental (Wang et al., 2004), flow visualization (Mak and Balabani, 2007),
analytical (Gyllenram et al., 2007) and numerical investigations (Nilsson, 2012) of swirling
flows. However, this flow is still not well understood, especially for strongly swirling flow,
where the swirl number is about unity. There are only a handful of detailed numerical studies
that treat the coherent structures and vortex breakdown (Gyllenram et al., 2006) of the incident
flow. At elevated swirl intensities (Sr ≥ 0.6), the swirling jet emanating from the expansion is
deflected towards the wall, the secondary recirculation region close to the corner contracts and
reversal of the flow becomes evident near the centerline of the expansion (Dellenback et al.,
1988). The global frequency of the flow field belongs to the precessing helical vortex, which
oscillates about the centerline basically in a symmetrical fashion in spite of the instantaneous
asymmetry. The vortex core precession has been experimentally (Dellenback et al., 1988) and
numerically (Guo et al., 2002) observed to be both co-rotating and counter-rotating with the
mean swirl direction. Dellenback et al. (1988) reported that the precessing vortex core vanishes
for Sr~0.4, that there is a bubble-type vortex breakdown for Sr<0.6 and that there is a strong on-
axis tube of recirculating flow for higher swirl numbers. Thus, there is a maximum swirl number
beyond which no precessing vortex core will occur. Dellenback et al. (1988) also reported that
the precession frequencies appear independent at large Reynolds numbers (Re>105) but follow a
slowly decreasing function of Re at lower Reynolds numbers.
Numerical simulation is a very important tool for gaining in-depth knowledge of fundamental
flow physics. Experiments are often limited to a few discrete positions and thereby do not often
provide a complete view of the flow. Numerical results that are validated by experimentally
available data extend the available information and make it possible to draw further conclusions.
Numerical simulation of turbulent swirling flows is however still a challenging tas. Swirling flow
in sudden-expansions has been studied using conventional unsteady Reynolds-averaged Navier–
Stokes (URANS) models (Nilsson, 2012). Such models are primarily useful for capturing large-
scale flow structures, while the details of the small-scale turbulence eddies are filtered out in the
averaging process. In many cases the large-scale structures are also damped by the URANS
modeling, which is formulated to model all the turbulence. The quality of the results is thus very
dependent on the underlying turbulence model. Better approaches should be used to handle the
anisotropic and highly dynamic character of turbulent swirling flows. One approach is the large-
eddy simulation (LES) technique. Only a limited number of LES results of swirling flows are
reported in the literature. Gylleram et al. (2006) used LES to study the swirling flow in the
sudden-expansion of Dellenback et al. (1988), at Re=4.0×104 and Sr=0.6. It was shown that the
frequency of the numerically predicted processing vortex core is not sensitive to the choice of
discretization scheme. Schlüter et al. (2004) performed LES of the swirling flow in a sudden-
expansion studied by Dellenback et al. (1988) for different inlet boundary conditions, and Wang
et al. (2004) performed LES of swirling flows in the sudden expansion-contraction. Most of
these simulations focus on confined flows at moderate Reynolds numbers (Re ~104) and with a
coarse resolution, especially close to the walls. An approach with hybrid URANS-LES is well
suited for such flow configurations. Detached-eddy simulation (DES) is a promising hybrid
URANS-LES strategy capable of simulating internal flows dominated by large-scale detached
eddies at practical Reynolds numbers. The method aims at entrusting the boundary layers with
URANS while the detached eddies in separated regions or outside the boundary layers are
resolved using LES. DES predictions of massively separated flows, for which the technique was
originally designed, are typically superior to those achieved using URANS models, especially in
terms of the three-dimensional and time-dependent features of the flow (Spalart, 2009).
According to Peng (2005), the hybrid techniques can be sub-divided into flow-matching and
turbulence-matching methods. In the flow-matching methods, the spatial location of the interface
between URANS and LES is explicitly defined, and the flow parameters (velocities and
turbulence kinetic energy) are matched at the interface. A serious weakness of this approach is
that it is difficult to define the URANS-LES interface for complicated flow geometries. In the
framework of the turbulence matching method, a universal transport equation is solved in the
entire computational domain. The stress terms in this equation are treated in different ways in the
LES and URANS regions, and the transition between the two modeling approaches is smooth.
There are two recently developed major improvements of DES. The first one, called delayed
DES (DDES), has been proposed to detect the boundary layers and to prolong the URANS
mode, even if the wall-parallel grid spacing would normally activate the DES limiter (Spalart,
2009). The second one, called improved DDES (IDDES), solves the problems with modeled-
stress depletion and log-layer mismatch (Spalart, 2009). Other versions of the turbulence
matching methods using different blending functions to switch the solution between LES and
URANS modes were proposed by Peng (2005), and Davidson and Billson (2006). Nilsson
(2012) evaluated a hybrid turbulence model that was developed by Gyllenram and Nilsson
(2008), limiting the modeled turbulence scales according to the local mesh resolution and CFL
number.
The present work investigates the strongly swirling turbulent flow in the sudden-expansion of
Dellenback et al. (1988). The study scrutinizes the ability of modern highly resolved turbulence
models to capture the rich flow physics. Five operating conditions are investigated, with
Reynolds numbers varying from 3.0×104 to 105, and swirl numbers varying from 0.6 to 1.23.
Such wide range of strong swirl numbers and high Reynolds numbers has received less attention
in the literature. Three LES sub-grid approaches are used: an implicit LES, dynamic
Smagorinsky (Germano et al., 1991) and a dynamic k-equation (Kim and Menon, 1995) model.
Two hybrid RANS-LES models are also evaluated: DDES-SA (based on the Spalart-Allmaras
RANS model, Spalart et al., 2006) and IDDES-SA (Shur et al., 2008). The present work is
original in diverse facets: The turbulent swirling flow in a sudden-expansion is studied using
three highly resolved LES sub-grid approaches. The applicability of hybrid methods for these
flow features is validated by comparing with LES results. An advanced and in-depth exploration
is conducted of hybrid methods in circumstances with a variety of flow dynamics. To investigate
the physical aspects of the flows, the various vortex breakdown states along the axis, and the
associated large-scale instabilities of the flow along the pipe wall, are emphasized. The
turbulence structures and the state of anisotropy of the flow fields are thoroughly discussed to
accentuate the rich unsteady features of strongly swirling flows.
2. Numerical Methods and Turbulence Modeling
The governing equations are the filtered (LES), or ensemble averaged (URANS), continuity and
Navier-Stokes equations for incompressible flow. Applying the filtering operation to the Navier-
Stokes equations yields,
�����
� 0,
������ ���� ����
� � � � 1
���̂�
� ������ �� � �� �
�� . �3�
The last term on the right-hand side includes the turbulent stress due to velocity correlations,
given by:
� � � ����� � ��� ��� . (4)
The closure of the governing equations requires modeling of the turbulent stress tensor. The
equations are discretized using a general finite-volume method with a fully collocated storage,
using the pimpleFoam solver of the OpenFOAM-2.1.x CFD code. The code is parallelized using
domain decomposition and the Message Passing Interface (MPI) library. The simulations are
performed using an AMD Opteron 6220 super computer, using160 cores.
Two convection schemes are studied using a dynamic k-equation LES model, the second-order
central differencing scheme and the second-order van Leer total variation diminishing (TVD)
scheme (van Leer, 1979). The temporal discretization is done using the implicit second-order
backward and Crank-Nicolson schemes. In agreement with Gyllenram et al. (2006), the results
are reasonably independent of the discretization method and therefore the results of the implicit
second-order backward are only shown here. The local turbulence eddy-viscosity is given by
each of the adopted turbulence treatments, listed here.
• The dynamic Smagorinsky LES model (hereafter: dynSmagLES) (Germano et al., 1991).
The dynamic model coefficient, C, is determined as a part of the simulation, based on the
assumption that local equilibrium prevails, i.e. Pksgs-εksgs=0. Negative values of the
effective viscosity are removed by clipping to zero.
• A dynamic k-equation model (hereafter: dynOneEq) (Kim and Menon, 1995). An
important feature of this model is that no assumption is made concerning the local
balance between the subgrid-scale energy production and the dissipation rate is made. A
dynamic localization procedure is used to determine the dissipation and the diffusion
model coefficients.
• An implicit LES method using van Leer damping (van Leer, 1979) (hereafter:
vanLeerILES). The sub-grid scale turbulence is not explicitly modeled but is given by the
numerical diffusion of the convection discretization scheme.
• The hybrid DDES method (Spalart et al., 2006) with Spalart-Allmaras RANS closure
(Spalart and Allmaras, 1994) (hereafter: DDES-SA). This method detects the boundary
layer thickness and prolongs the RANS region compared with the original DES. This
method is less sensitive to wall-parallel grid spacing compared with the original DES,
and, in terms of massive separation, LES mode takes over RANS, which is self-
perpetuating (Spalart et al., 2006).
• The hybrid IDDES method (Shur et al., 2008) with Spalart-Allmaras RANS closure
(Spalart and Allmaras, 1994) (hereafter: IDDES-SA). The DDES functionality of IDDES
becomes active only when the inflow conditions do not have a turbulent content. An
inflow with turbulent content activates wall-modeled LES.
For the presently investigated cases, with high Reynolds numbers and high levels of
anisotropy, turbulence models that do not assume a local balance between the energy production
and the dissipation rate have a much better potential for correctly modeling the sub-grid stresses
(Kim and Menon, 1995). Backscatter of energy from the sub-grid scales to the resolved scales
may occur if the sub-grid scales have energy-containing eddies. Studies show that backscatter
may occur over a significant portion of the cells (Piomelli et al., 1991). Backscatter appears as
negative values of the turbulence production term.
DES is designed to treat the entire boundary layer using a RANS model and to apply an LES
treatment to separated regions. While the original DES method is straightforward and simple in
its definition, it is nevertheless one of the more difficult models to use in complex applications. It
not only requires a fundamental understanding of the model behavior but also a relatively
intricate mesh generation to avoid undefined simulation behavior at the interface between RANS
and LES. An artificial flow separation was reported by Menter and Kuntz (2004) for an airfoil
simulation when the maximum cell edge length (hmax) inside the wall boundary layer was refined
below a critical value of hmax /δ < 0.5-1, where δ is the local boundary layer thickness. This
effect was termed Grid Induced Separation (GIS), as the separation depends on the grid spacing
and not the flow physics. GIS is obviously produced by the effect of a sudden grid refinement
that changes the DES method from RANS to LES, without balancing the reduction in eddy-
viscosity by resolved turbulence contents. Spalart (2009) coined the term Modeled Stress
Depletion (MSD), which refers to the effect of reduction of eddy-viscosity from RANS to LES
without a corresponding balance by a resolved turbulent content. In other words, GIS is a result
of MSD. MSD is essentially a result of insufficient flow instabilities downstream of the switch
from the RANS to the LES model formulation. Spalart et al. (2006) proposed a more generic
formulation of the shielding function, which depends only on the eddy-viscosity and the wall
distance. It can therefore, in principle, be applied to any eddy-viscosity based DES method. The
resulting formulation was termed DDES. The IDDES model features several rather intricate
blending and shielding functions, which allow this model to be used in both DDES and wall-
modeled LES mode (Gritskevich et al., 2012) based on the inflow (or initial) conditions used in
the simulation. The fact that several variants of the DES method, such as DDES and IDDES, are
proposed with rather different characteristics makes the selection of the method and
interpretation of results challenging.
3. Flow Configuration
The case studied in the present work is the swirling flow through a sudden 1:2 axisymmetric
expansion that was experimentally examined by Dellenback et al. (1988). The origin is located
on the centerline at the expansion. The experimental inlet Reynolds number was varied between
3.0×104 and 105, and the swirl number was varied between 0 and 1.2. Measurements of mean and
RMS velocities were made with a laser Doppler anemometer at some cross-sections. For more
details about the validation of the flow in the downstream, see Javadi and Nilsson (2014a). The
present work is devoted to strongly swirling flows, and thus includes only high swirl numbers
(Sr≥0.6). Five highly swirling conditions are thus studied in the present work, see Table 1. The
swirl number is calculated based on the inlet radius and the applied axial and tangential velocity
at inlet boundary condition. Equations (1) and (2) give the details of swirl and Reynolds
numbers, respectively.
Table 1. Studied operation conditions
Reynolds number Swirl number
105 1.23
105 0.74
6.0×104 1.16
3.0×104 0.98
3.0×104 0.6
a)
b) c)
Fig.1. a) experimental cross-sections, (z/D=0.25, 0.5,1 ,2 ,4) b) mesh configuration at expansion,
c) mesh configuration at z/D=1
4. Computational Domain and Mesh Resolution
The experimental study of Dellenback et al. (1988) proved the existence of very large-scale
motions in the form of short regions of outer-layer streamwise fluctuations. Figure 1a shows the
computational domain. The experimental results are available at z/D=0.25, 0.5,1 ,2 ,4. The
computational domain is extended 2D upstream of the expansion and 10D downstream of the
expansion, to reduce the influence of the inlet and the outlet boundary conditions. Gyllenram et
al. (2006), Nilsson (2012) and Javadi and Nilsson (2014a) used the same domain, and the
validation in the downstream raises the least concerns about the viability of the result. Figures 1
b-c show the configuration of the mesh. Table 2 lists the three different mesh resolutions used.
The finest resolution is used only for vanLeerILES. Two different O-grid configurations were
studied to investigate the influence of grid skewness on the first and second invariants, with the
conclusion that the effect is negligible. The maximum aspect ratio of a cell is kept below 200.
The mesh resolutions after the expansion, see Table 2, are comparable with Wu and Moin (2008)
and Jung and Chung (2012), who performed DNS and LES of a turbulent pipe flow, respectively.
Wu and Moin (2008) reported Δz+=8.37 and Δ(Rθ)+=7.01 while Jung and Chung (2012) reported
Δz+=61, Δ(Rθ)+= 23.95 and ymax+=12.2. The mesh resolution units are defined as
Δz+=���
��
�
� Δz, Δ(rθ)+=� ��
�����
�
� Δ (rθ) (5)
where υ is the kinematic viscosity and θ is the tangential position. The y+ is defined as
y+=u*y/υ , u*=(τw/ρ)1/2 , τw=μ(∂u/∂y) (6)
where u* is the friction velocity and τw is the wall friction stress.
The present case is a sudden-expansion with a free-stream shear layer. Therefore the
maximum value of Δ(rθ)+ does not necessarily occur at the wall. Due to the flow configuration,
the maximum y+ value occurs in the moving reattachment point. The maximum CFL number in
average 0.03, with a local maximum of 2. The time steps used for the different mesh resolutions
are given in Table 2.
Table 2 Mesh resolutions and near-wall metrics for the case with Re=105, Sr=1.23
No. Cell
(M)
No. Cells before
expansion*
No. Cells after
expansion*
ymax+, ymin
+ Δzz/D<1+, Δzmax
+ Δ(rθ)max+ core Δt (sec)
8 15,000×90 26,650×248 8, 0.12 15, 20 15 96 10-5
10.4 15,000×150 26,650×306 6, 0.08 13, 15 15 128 7×10-6
12.6 18,500×150 32,000×306 20, 0.06 15, 20 27 160 10-6
*The given number is Ncross-section× Nz
5. Boundary Conditions
The inlet boundary condition for the mean velocity is constructed by spline curves based on the
data measured at z/D=-2. A boundary layer based on the log-law is added between the radially
outermost measuring point and the wall, as suggested by Gyllenram et al. (2006) and used by
Javadi and Nilsson (2014a). Earlier investigations of the same case by Schlüter et al. (2004)
showed that the turbulence level of the inlet boundary condition has strong effects on the mean
velocity profiles if the swirl level is low. However, in the present study, the swirl level is high
enough for high turbulence production and a fast transition to turbulent flow. The results for the
flows under consideration were thus found to be quite insensitive to fluctuations at the inlet,
especially for the higher swirl numbers (Schlüter et al., 2004). The no-slip condition is applied
on the walls and the homogenous Neumann for all boundaries of ksgs. A series of outlet boundary
conditions were evaluated, and the combination of inletOutlet for velocity and homogenous
Dirichlet for pressure was finally found to have the least effect on the upstream flow. The
inletOutlet applies a homogenous Neumann condition but with a limitation of the backflow.
6. Results and discussion
All the studied turbulence treatments are scrutinized for a single condition (Re=105, Sr=1.23),
which has the smallest turbulent structures. For brevity only the result of DDES-SA are
presented for the rest of the operating conditions. The flow parameters are normalized with the
inlet diameter, D, and the inlet bulk velocity, Wb, corresponding to different Reynolds numbers.
6.1. Mean velocity
a) b)
Fig. 2. Mean axial (a) and tangential (b) velocity distributions at cross-section z/D=0.25 for the
case with Re=105, Sr=1.23. The same legend applies for both figures.
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.2 0.4 0.6 0.8 1
W/W
b
r/D
Measured8M-DDES-SA
dynOneEqdynSmagLES
10M-DDES-SA10M-IDDES-SA
vanLeerILES
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.2 0.4 0.6 0.8 1
U/W
b
r/D
a) b)
c) d) e)
Fig. 3. Mean axial (W) and tangential (U) velocity distributions at cross-section z/D=0.25 for
DDES-SA a) Re=105, Sr=1.23, b) Re=105, Sr=0.74, c) Re=6.0×104, Sr=1.16, d) Re=3.0×104,
Sr=0.98, e) Re=3.0×104, Sr=0.6.
Figure 2 validates the mean axial and the tangential velocity distributions of different
turbulence treatments for the case with Re=105, Sr=1.23. For brevity, only the results at cross-
section z/D=0.25 are presented here, while the downstream flow is discussed qualitatively.
Javadi and Nilsson (2014a) compared and discussed results at the downstream cross-sections.
The averaging is conducted for at least 50 vortex core precession periods. To avoid redundancy,
only the flow features that are not discussed in the literature are clarified. All the numerical
simulations are capable of capturing the main flow features with acceptable accuracy. For the
axial velocity, almost all turbulence treatments predict a similar qualitative behavior of the on-
axis recirculation region (r/D<0.5). In the outer region, vanLeerILES predicts a slightly different
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.2 0.4 0.6 0.8 1
(U,W
)/W
b
r/D
Measured WMeasured U
DDES-SA WDDES-SA U
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.2 0.4 0.6 0.8 1
(U,W
)/W
b
r/D
Measured WMeasured U
DDES-SA WDDES-SA U
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.2 0.4 0.6 0.8 1
(U,W
)/W
b
r/D
Measured WMeasured U
DDES-SA WDDES-SA U
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.2 0.4 0.6 0.8 1
(U,W
)/W
b
r/D
Measured WMeasured U
DDES-SA WDDES-SA U
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.2 0.4 0.6 0.8 1
(U,W
)/W
b
r/D
Measured WMeasured U
DDES-SA WDDES-SA U
behavior than the other turbulence treatments. The DDES-SA (and IDDES-SA) using eight
million cells underestimates the on-axis recirculation, while the corresponding simulations using
10.4 million cells perform qualitatively well. The difference between these two mesh resolutions
is the streamwise (wall-parallel) number of cells. Furthermore, to keep the same maximum
aspect ratio of a cell (~200), the wall-normal spacing is decreased. According to its definition,
the DDES functionality of IDDES should become active only when the inflow conditions do not
have a turbulent content (Shur et al., 2008), while the investigation shows that the IDDES-SA
results differ from those of DDES-SA. This can be related to a high level of recirculation and
production of turbulence in the flow field, which activates the wall-modeled LES mode. It is
worth mentioning that dynOneEq and dynSmagLES predict the flow features reasonably well
using eight million cells and give the same results as with 10.4 million cells.
Figure 3 shows the mean axial and tangential velocity distribution at z/D=0.25 for DDES-SA
for all operating conditions. For all cases, the peak of the axial velocity is at r/D=0.5 and
z/D=0.25, which is right downstream of the edge of the expansion, and the magnitude is
W/Wb~1.3. Comparing Sr=1.23 with 0.74, a higher swirl with the same Re leads to a stronger
backflow on the centerline, i.e. if the swirl intensifies the backflow moves upstream. Dinesh et
al. (2010) also confirm that the vortex breakdown bubble shifts towards the inlet plane with
increased swirl number. Generally, the rate of entrainment of the ensuing jet increases with the
swirl, which gives rise to centrifugal forces and a decrease of the reattachment length. As the
swirl increases from zero to its maximum value, the flow reattachment point moves upstream
from 9 to 2 step heights. The reattachment length is an important parameter in sudden-expansion
flows as it defines the extent of the recirculation and depends on a number of parameters such as
the Re number, the expansion ratio, the free stream turbulence initial and downstream conditions
(Dellenback et al.,1988). A comparison of Sr=1.23 with 0.74 and Sr=0.98 with 0.6 shows that,
as the swirl increases, the recirculation region has a steeper bubble shape. The downstream flow
reveals an on-axis recirculation region that grows longer as the swirl number is reduced. It
reaches about z/D=2.0 for Sr=0.74 and about z/D=1.5 for Sr=1.23. There is a similar trend for
Sr=0.98 and Sr=0.6. Furthermore, since the recirculation region is wider at higher swirl numbers,
it has a steeper cone shape. An interesting observation is that the velocity profiles of Sr=1.23 and
Sr=1.16 are very similar, i.e., for swirl numbers greater than unity, the mean velocity profiles are
even less dependent on the Reynolds number. The on-axis recirculation flow, which onsets the
bubble-type vortex breakdown, increases with the Reynolds number, i.e. the case with Sr=1.23
has a wider bubble than the cases with Sr=1.16 and 0.98. The axial velocity downstream of the
bubble increases to the end of the domain as the axial velocity profile is flattening out.
Furthermore, the static pressure drops at the expansion, and the drop grows as the Reynolds
number increases. The main difference between Sr=0.98 and the profiles of the very similar
conditions of Sr =1.23 and Sr=1.16 is that the axial velocity close to the wall, r/D>0.8, is not as
steep. This can be related to lower amount of mass flux, with respect to the pressure gradient.
Moreover, at the high swirl levels, the flow at the centerline is in the same direction as the mean
flow. The tangential velocity peak at r/D=0.4 is U/Wb~1.2 for three higher swirls.
The most accepted definition of the swirl number is cumbersome insofar as the swirl number
is not known a priori but must be found by integration of the mean velocity profiles according to
eq. (1). Furthermore, Gyllenram et al. (2006) argued that the common definition of the swirl
number is inappropriate for recirculating flow because it results in a lower swirl number for a
given tangential velocity profile, as compared to a non-recirculating flow. Because of the square
in the denominator, only the integrand in the numerator will change sign when backflow occurs.
Thus, Gyllenram et al. (2006) used absolute velocity values in the formulation, hereafter denoted
as Sr*, given by
Sr*=�
�
� ��|��|���
�
� ������
�
. (7)
In cases with an inlet swirl number of about unity, i.e. Sr=1.23, 1.16 and 0.98, the swirl
reduces to Sr~0.4 (Sr*~0.7) directly after the expansion and then increases to Sr~1.5 (Sr*~1.55)
at z/D=1. The swirl number continues to increase to Sr=Sr*~2.1 at z/D=3, and then decreases
further downstream. Generally, this behavior can be related to the bubble type vortex breakdown
that occupies a remarkable part of the cross-section. Due to the vortex breakdown, the axial and
the tangential velocity vanish and appear in the radially same points, see Fig. 3, which leads to a
higher swirl number. The difference between Sr* and Sr in z/D<1 in the recirculation region is
remarkable. For this reason, in term of the features of the flow with a swirl number without the
absolute value in the numerator, the current definition should be treated with caution.
a) b)
Fig. 4. Axial and tangential velocity root mean square distributions at cross-section z/D=0.25 for
the case with Re=105, Sr=1.23.
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Wrm
s/W
b
r/D
MeasureddynOneEqDDES-SA
IDDES-SAvanLeerILES
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Urm
s/W
b
r/D
MeasureddynOneEqDDES-SA
IDDES-SAvanLeerILES
a) b)
c) d) e)
Fig. 5. Axial and tangential velocity root mean square distributions at cross-section z/D=0.25 for
cases a) Re=105, Sr=1.23, b) Re=105, Sr=0.74, c) Re=6.0×104, Sr=1.16, d) Re=3.0×104, Sr=0.98,
e) Re=3.0×104, Sr=0.6.
6.2. Turbulence intensity
Figures 4 and 5 show the root mean square of the axial, w'rms, and tangential, u'rms, velocity
fluctuations at cross-section z/D=0.25. Javadi and Nilsson (2014a) compared and discussed the
velocity fluctuations at the downstream cross-sections. The dynOneEq treatment predicts a
slightly higher level of turbulence intensity compared to the other treatments. The accuracy of
the vanLeerILES treatment is promising for this kind of flow, even close to the wall where the
mesh resolution should be on the coarse side for an implicit LES. The hybrid methods generally
predict a lower peak compared to LES, which can be related to the switching between RANS and
LES, see Fig. 4 . The double-peaked profiles of u'rms are predicted reasonably well, although the
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1(U
rms,
Wrm
s)/W
b
r/D
Measured WrmsMeasured Urms
DDES-SA WrmsDDES-SA Urms
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
(Urm
s,W
rms)
/Wb
r/D
Measured WrmsMeasured Urms
DDES-SA WrmsDDES-SA Urms
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
(Urm
s,W
rms)
/Wb
r/D
Measured WrmsMeasured Urms
DDES-SA WrmsDDES-SA Urms
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
(Urm
s,W
rms)
/Wb
r/D
Measured WrmsMeasured Urms
DDES-SA WrmsDDES-SA Urms
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
(Urm
s,W
rms)
/Wb
r/D
Measured WrmsMeasured Urms
DDES-SA WrmsDDES-SA Urms
on-axis peak is lower and the off-axis peak, which caused by the shear layer, is higher than what
is suggested by the experiment. The flow presents a double- or triple-peaked in w'rms, see in
particular Fig 5b. The first peak is arises from the same physics as that in confined jet flow. The
second peak is due to the turbulence generated by the separation at the expansion edge, similar to
the flow over a backward facing step. The third peak is the wall-effect. The experiment does not
distinctly capture the second peak, although there is a clear tendency. The velocity fluctuation
levels of the turbulent flow are highest in the core region. These fluctuations are apparently
induced by the high velocity gradients in the core, and the very weak motion of the core
(Derksen, 2005). As the swirl number increases to about unity, the first two peaks merge, see
Fig. 5 for Sr=1.23, 1.16 and 0.98, while the third peak goes closer to the wall and becomes
stronger. As the swirl number decreases, the first peak moves closer to the centerline due to the
narrower on-axis recirculation. It shows that the jet emanates closer to the centerline when the
swirl decreases. The main fluctuations of the tangential velocity component occur along the
centerline and in the shear layer emanating from the edge of the sudden-expansion. It is worth
mentioning that the experiment suggests that the second peak is closer to the main stream, while
it is numerically predicted closer to the wall. Furthermore, the magnitudes of the peak are still
independent of the Reynolds number but intensified with an increased swirl. All simulations
predict the turbulent fluctuations qualitatively well.
Having established good agreement of the numerical results with the experimental
measurements of Dellenback et al. (1988), these can be used to elaborate on the physics of the
flow fields by visualizing the instantaneous coherent structures of the flow. The highly swirling
flow can be categorized as an extremely turbulent flow because of the sudden jump in the
turbulence intensity. In case Sr=1.23, the turbulence intensity ascends to 67% after the
expansion and then descends. Dellenback et al. (1988) reported that the turbulence intensities at
the highest swirl levels were found to reach 60%. The confinement and the separating nature of
the expansion flow are known to intensify the helical precession and the flow instabilities. In
Sr=0.74, the turbulence intensities are augmented to 48% at z/D=0.5 and then reduced. The
turbulent intensity of the flow is, similar to the other quantities, a function of the swirl but less a
function of the Reynolds number. As reported above, the swirl, and consequently the turbulent
intensity still is intensified after the expansion due to the vortex breakdown. The diffusion rates
are elevated with high levels of turbulence kinetic energy, and the thickness of the viscosity-
dominated sublayer is reduced.
6.3. Instantaneous Flow Features
Figure 6 shows the viscosity ratio, υt/υ , of DDES-SA, for the case Sr=1.23 and for two mesh
resolutions. The high ratio region corresponds to where URANS is prominent and the low ratio
region corresponds to where LES is used. The DDES is developed from DES with the purpose of
extending the RANS modeling further away from the viscous sub-layer, while the LES mode
takes over in massive separation regions (Spalart et al., 2006). Javadi and Nilsson (2014b)
studied the hybrid methods in a flow generated by a swirl generator. They showed that the
DDES-SA switches to LES still very close to the wall. However, the results show that this
behavior is followed in neither the coarse nor the fine mesh resolution. Although the results of
the coarse and the fine resolution are different for the case of Sr=1.23, the hybrid methods are
less mesh dependent at other operating conditions. In other word, LES is still more robust than
DES for certain flow conditions. To confirm Spalart et al. (2006), DDES-SA is still sensitive to
the wall-parallel resolution for certain flow conditions, see Table 2 for details on the mesh
resolutions.
Figure 7 shows the streamlines at z/D=0.5 for two cases, Sr=1.23 and Sr=1.16. The flow is
divided to an inner part, which is the swirling jet flow, and an outer part which is the primary
recirculation region caused by the separation from the edge of the expansion. For Sr=1.23, the
on- and off-axis recirculation regions are stronger. There are smaller coherent structures adjacent
to the wall, which these structures are a special kind of streak called Taylor-Görtler vortices
(Escudier et al., 1988). The Taylor-Görtler vortices form on the tube wall, mix up the fluid
outside the core, and result in a relatively uniform stable distribution of vorticity in this outer
region. These streaks are presumably related to the centrifugal force of the flow along the
concave wall boundary layer. The issuing of Taylor–Görtler vortices as also observed by
Escudier (1987) for a related swirling flow experiment in a straight pipe geometry. These
structures are well captured although occurring in the region where RANS modeling is
prominent.
Figure 8 shows the q-criterion for different cases. For a swirl number about unity, the flow
downstream of the expansion is more organized and is characterized by the onset of a large-
scale, full-length, columnar vortex along the pipe centerline, which rotates in the mean flow
swirl direction and becomes intertwined. Salas and Kuruvila (1989) reported that near the inflow
the solutions become independent of Reynolds number. The emergence of the large-scale on-axis
vortex at high swirl numbers is obviously related to the on-axis, elongated pocket of the
recirculating flow on the tube centerline. For high swirl numbers, the on-axis vortical structure
strengthens, Figs. 8a and b, and its bend and the adverse longitudinal pressure gradient are
intensified. Dellenback et al. (1988) reported that, at high Reynolds numbers, the vortex
bre
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a) b)
Fig. 7. Swirling flow visualized by instantaneous streamtraces z/D=0.5 for cases a) Re=105,
Sr=1.23 and b) Re=6.0×104, Sr=1.16.
a) b)
c) d
Fig. 8. Vortex breakdown visualized by instantaneous iso-surface of q-criterion (=10000) for the
case a) Re=105, Sr=1.23, b) Re=6.0×104 Sr=1.16, c) Re=3.0×104, Sr=0.98, d) Re=3.0×104,
Sr=0.6.
6.4. Energy Spectrum
Large-eddy simulation is ordinarily addressed using a spatial filtering but without explicitly
stating the associated time filtering (Pope, 2005). Although there is no reference to determine
what timescales are well resolved numerically and physically, we tried to apply fine time steps to
mask the issue. Figure 9 shows the power spectra density captured at (r/D, z/D)=(0.5, 0.25). The
energy spectrum shows that the dominant frequency depends on the swirl number. The study of
the iso-surface of the pressure in successive timesteps shows that the flow pulsations (lashes)
caused by the on-axis recirculation which occupies a considerable portion of the cross-section,
see Fig. 3. Theses lashes increase at higher Reynolds numbers. The power spectrum at the point
shows that the flow is characterized by the existence of the vortex breakdown with dominant
frequencies of about 0.75, 0.86, 1.47 and 1.71, respectively for Sr=1.23. The dominant frequency
varies with the configuration of the inlet, presumably related to differences in the initial shear-
layer of the jet, often characterized by the boundary-layer displacement thickness. In the
downstream, the flow looks like a well developed turbulent flow, with most of its power in its
harmonics. All the spectral components indicate a strong dissipation and a reduction in the total
turbulent kinetic energy while the rate is higher for larger swirls and is generally like an isotropic
turbulence, see subsection 6.6 for more details. It can be seen that the slope changes similarly
from energetic to inertial range in all cases. Commonly, LES somewhat overestimates the energy
content at large-scales and gives a plateau; however, as the structures break down, the energy
content rapidly loses energy fast and the slope increases. This can be related to the frequency of
the SGS filtering and an attempt is made to mask this by fine resolution (Sagaut, 2002). With
regard to the accuracy, this type of finding should nonetheless be treated with caution because
the conclusions may be reversed if we bring in an additional parameter, which is the numerical
scheme or higher advanced solution, DNS. As the cell size decreases, the diffusion decreases and
the model resolves smaller flow structures. Nonetheless, at this stage, we tried to use a self-
adaptive subgrid models that is able to tune induced dissipation so that the sum of the numerical
and subgrid dissipation will reach the required level to obtain physical results.
a) b)
c) d)
Fig. 9. Power spectra at a selected streamwise location (r/D, z/D)=(0.5,0.25), for the case a)
Re=105, Sr=1.23, b) Re=6.0×104 Sr=1.16, c) Re=3.0×104, Sr=0.98, d) Re=3.0×104, Sr=0.6.
An implicit LES technique is also scrutinized because DNS of the current test case is hard to
afford. Interestingly, the same change of the slope at high frequency is observed in all cases,
which shows the energy transfer from large- to small-scales. This transfer rate of the energy
cascade from the large to small-scale motions is accelerated downstream.
6.5. Turbulence Production
For a three-dimensional incompressible turbulent flow, the production terms in the transport
equations for the Reynolds shear stress and turbulent kinetic energy are given by
-Production=�������/��� � ����/�������
� ���/�� � ����/�������
�������������������������
+� ��/�� � � ��/�� � ����/�������
� ����/�� � ���/�� � ���/�������������������������������������������������������
(8)
where uiuj are the Reynolds stresses and ∂Ui/∂xj are the velocity gradients. All terms normalized
by W3b/D are shown in Fig. 10. Since the distribution of the RMS velocity is reasonable, the
different terms of the turbulent kinetic energy equation should be mimicked fairly plausibly
(Javadi, 2013). Two cases with, Sr=1.23 and 0.74 and the same Reynolds number, are discussed
here to exclude the Reynolds number effects. The normal production terms, Puu and Pww, and the
shear term, Puw , are depicted individually and in total, PN and Pshear , to shed light on the physics
of turbulence in the incident flow. Primarily, the comparable level of the production before and
after the expansion confirms what was said earlier about the independence of the simulation from
the inlet, i.e. the flow features at the separation edge are characterized by the turbulence that is
generated. Secondly, the studied flows before and after the expansion are rather different for
various cases. The level of increase of the production after the expansion for Sr=0.74 is large,
which is the reason for the augmentation of the turbulent intensity in the near downstream after
the expansion (z/D<0.5), see section 6.2. Figures10a and b show the production of turbulence
before the expansion. Most of the turbulence is produced by Puu and Pww before the expansion
while Puu is primarily responsible for the backscatter. For Sr=0.74, most of the turbulence is
produced about the axis, while, for Sr=1.23, it is distributed more along the radius. This can be
related to a larger centrifugal force in Sr=1.23. The ∂W/∂z is negative except in the near wall
region where the helical vortex forms a locally high velocity region. This can be the reason for
backscatter.
The dominant shear term is Puw which is distributed more along the radius. The Puw of Sr=1.23
is twice as large as that of Sr=0.74. Regardless of the Reynolds and swirl numbers, the PN is
negligible compared to Pshear, which shows the rich turbulent nature of the flow.
Figures 10c and d show the production after the expansion for the two cases. There is a free
shear layer caused by the separation The shear layer has two edges; the former is a high velocity
edge and the latter is a low velocity edge. These two edges play important roles in the turbulence
nature for strongly swirling flows. The dominant normal terms are still Puu and Pww but hey have
an opposite sign, which naturalizes PN in Sr=0.74. In other words, the amount of the cascade and
the backscatter are the same. In Sr=1.23, Pww is still larger than Puu. Most of the Pww occurs
along the high velocity edge while Puu is on the low velocity edge. This trend is the reverse for
the operation conditions Sr=0.98 and 0.6.
The only shear production term after the expansion is Puw, which is influenced by the free shear
layer of the separation at the edge. The level of Puw compared with normal terms is remarkably
larger. For Sr=1.23, the high velocity edge is larger than the other edge. This is the reverse for
Sr=0.74. The production is almost negligible further downstream (z/D>1). At mid-downstream,
redistribution plays a more important role, and far downstream, dissipation is escalated.
a) b)
c) d)
Fig. 10. Radial distributions of the production terms in the transport equations for the Reynolds
normal and shear stress normalized by W3b/D , Re=105 , Sr=1.23 (blue lines), Re=105 , Sr=0.74
(red lines), before expansion at z/D=-0.5 plane (a-b) and after expansion at z/D=0.5 (c-d).
6.6. Anisotropy-invariant investigations
The state of turbulence is analyzed by the amount of anisotropy in the flow (Lumley and
Newman, 1977). Only the anisotropy components, aij , are effective in transporting momentum
(Saguat, 2002). The nondimensional anisotropy tensor is defined as
ij
ji
ij k
uua δ
3
1
2−= , (9)
with the turbulent kinetic average k and the Kronecker delta δij . The anisotropy of a flow can be
derived from the Reynolds stresses τij=-ρ‹uiuj› by subtracting the isotropic part from τij and
normalizing with τss=-ρ‹usus› . This leads to the nondimensional anisotropy tensor. The
nondimensional anisotropy tensor, aij, is previously defined in (10). Tensor aij has three scalar
invariants
aii=0 , II=aijaji , III=aijajkaki . (10)
By cross-plotting II and III, the state of turbulence in a flow can be analyzed with respect to its
anisotropy. The isotropic turbulence is found at the origin where II = III = 0. Figure 11 shows the
states of turbulence at z/D=0.25 and 0.5, where the most anisotropy may occur. It is found that
large degrees of turbulent anisotropy occur in the region that is dominated by the oscillating
vortex core. Further downstream, the degree of turbulent anisotropy is almost negligible. As
expected, the present swirling jet is highly anisotropic. If the scalar invariants II and III are
evaluated for the case of a two-component turbulence, i.e. one component of the velocity
fluctuations is negligibly small compared with the other two, this leads to II = 2/9 + 2III. Doing
the same for the axisymmetric turbulence, i.e. two components are equal in magnitude, yields II
= 3/2(4/3|III|)2/3. Hence, if these relations are cross-plotted, as done in Fig. 11, they define a
narrow region called the anisotropy-invariant map. All physically realizable turbulence has to lie
within this small region. However, different states of turbulence are represented by different
parts of the map.
The left branch of the map (III < 0) describes axisymmetric turbulence, in which one
component of the velocity fluctuations is smaller than the other two. The simplest example of
this type is the passage of grid turbulence through an axisymmetric contraction, which also
happens in the current flow field. Due to the on-axis recirculation, the streamwise velocity
fluctuation is smaller than the other two on the centerline at z/D=0.25, see also Figs. 4a and b. In
Fig. 11, the points at the centerline and the wall are denoted by ‘C’ and ‘W’, respectively. In
contrast, the axisymmetric turbulence on the right side (III > 0) is characterized by one
fluctuating component that dominates over the other two. This holds for grid turbulence through
an axisymmetric sudden-expansion, which the streamwise velocity fluctuation is considerable in
0.2<r/D<0.6, see Figs. 4a and 11. The third boundary line on the top of the map is the limiting
case of a two-component turbulence, as it can be found in the direct vicinity of walls (Javadi and
El-Askary, 2012). Here, the radial component of the velocity fluctuations tends towards zero,
leaving only the wall-parallel components, while the streamwise velocity fluctuation is larger
than the tangential velocity fluctuation, see Fig. 4. The wall points tend to the right part of the
graph. It must be noted that, taking the entire flow into account, all states indeed lie within the
invariant map, as is required by realizability constraints. The wall end point of the profiles lies at
the two-component limit, and the centerline end point lies at axisymmetric contraction limit for
all cases. The state of turbulence tends quickly to isotropy due to the high level of redistribution
after the expansion.
a) b)
Fig. 11. Anisotropy-invariant mapping in two streamwise planes, for the case with a) Re=105,
Sr=1.23 b) Re=105, Sr=0.74. ‘C’ and ‘W’ denote centerline and wall points of the trace,
respectively.
7. Conclusion
The strongly swirling turbulent flow through an abrupt expansion was explored using LES and
DES. The LES captures main features of the flow in a plausible manner. The applicability of
hybrid RANS-LES methods are also scrutinized, the DDES-SA is capable of capturing the
physics of the flow with reasonable accuracy while still being sensitive to wall-parallel
resolution. To predict a certain flow condition with DDES-SA (Re=105, Sr=1.23) with the same
level of accuracy as LES, a finer resolution is needed. The IDDES-SA behaves as wall-modeled
LES in the flows with a high recirculation level, even though no turbulent content is applied at
the inlet.
The key feature of the high swirl flow is the vortex breakdown and the on-axis recirculation
region. The distribution of the on-axis recirculation region varies with different Re and Sr. The
intertwined nature of the coherent structure due to the vortex breakdown is broader and steeper
for higher Re and Sr. The dominant frequency, the precessing helical vortex, of the flow is
insensitive to Reynolds number for a swirl number of about unity. The level of the turbulence
and the turbulence production increases remarkably with the swirl number, while the state of
isotropy is not susceptible to Re and Sr. The flow is anisotropic immediately after expansion,
while it rapidly becomes isotropic due to the redistribution between velocity fluctuations.
Acknowledgement
The research presented was carried out as a part of the ‘‘Swedish Hydropower Centre –
SVC’’. SVC is established by the Swedish Energy Agency, Elforsk and Svenska Kraftnät
together with Luleå University of Technology, The Royal Institute of Technology, Chalmers
University of Technology and Uppsala University, www.svc.nu.
The computational facilities are provided by C3SE, the center for scientific and technical
computing at Chalmers University of Technology, and SNIC, the Swedish National
Infrastructure for Computing.
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Highlights
The strongly swirling flow through a sudden expanding circular pipe is studied.
High swirl number causes vortex breakdown and on-axis recirculation region.
The on-axis recirculation region is wider and steeper for higher swirl number.
Hybrid RANS-LES is a robust method for predicting highly swirling flows.
The flow is highly anisotropic after expansion while quickly becomes isotropic because of
redistribution.