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= Flow in a 3D diffuser =
= Flow in a 3D diffuser =
{{UFRHeader
{{UFRHeader
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relevance. It mimics a  diffuser  situated  between  a  compressor  and  the
relevance. It mimics a  diffuser  situated  between  a  compressor  and  the
combustor chamber in a jet engine.  Its  task  is  to  decelerate  the  flow
combustor chamber in a jet engine.  Its  task  is  to  decelerate  the  flow
discharging from compressor over a  very  short  distance  to  the  velocity
discharging from the compressor over a  very  short  distance  to  the  velocity
field of the combustor section. Typically a uniform inlet profile  over  the
field of the combustor section. Typically a uniform inlet profile  over  the
diffuser outlet is desirable. Such a  flow  situation  is  associated  by  a
diffuser outlet is desirable. Such a  flow  situation  is  associated  by  a
Line 91: Line 90:
[[UFR_4-16_References#7|Cherry  ''et al.''  (2008)]].
[[UFR_4-16_References#7|Cherry  ''et al.''  (2008)]].
See  [[UFR_4-16_Description#figure2|Fig.  2]]  and  the  section
See  [[UFR_4-16_Description#figure2|Fig.  2]]  and  the  section
[[UFR_4-16_Test_Case#Brief_Description_of_the_Study_Test_Case|“Test case description”]]
[[UFR_4-16_Test_Case#Brief_description_of_the_test_case_studied|“Test case description”]]
of  the  present  contribution  for  the  exact  geometry  and
of  the  present  contribution  for  the  exact  geometry  and
dimensions of the diffusers. Both diffuser  flows  are  characterized  by  a
dimensions of the diffusers. Both diffuser  flows  are  characterized  by  a
Line 121: Line 120:
Simulation)  were  comparatively  assessed  (visit  [http://www.ercoftac.org www.ercoftac.org];  under
Simulation)  were  comparatively  assessed  (visit  [http://www.ercoftac.org www.ercoftac.org];  under
SIG15); the comparative analysis of selected results  is  presented  in  the
SIG15); the comparative analysis of selected results  is  presented  in  the
section [[UFR_4-16_Evaluation|"Evaluation"]] of the present contribution.
section [[UFR_4-16_Evaluation#Evaluation_of_the_results|"Evaluation"]] of the present contribution.


===Relevant studies===
===Relevant studies===
Line 130: Line 129:
However, there are neither experimental nor computational studies  performed
However, there are neither experimental nor computational studies  performed
in the past that are relevant to such a  flow  configuration.  All  relevant
in the past that are relevant to such a  flow  configuration.  All  relevant
computational  studies  performed  recently  are  related  to   previously
computational  studies  performed  recently  are  related  to the  previously
described "Stanford 3D Diffuser".
described "Stanford 3D Diffuser".


Line 147: Line 146:
*[[UFR_4-16_References#14|Jakirlić ''et al.'']] (2010a; complementary LES — using  Dynamics  model  of Germano ''et al.'' — and a zonal hybrid LES/RANS method of the Diffuser  1 configuration),
*[[UFR_4-16_References#14|Jakirlić ''et al.'']] (2010a; complementary LES — using  Dynamics  model  of Germano ''et al.'' — and a zonal hybrid LES/RANS method of the Diffuser  1 configuration),
*[[UFR_4-16_References#1|Abe and Ohtsuka]] (2010; complementary LES - using the  mixed-time-scale Subgrid-Scale model of Inagaki et al. - and a  zonal  hybrid  LES/RANS method - utilizing a Non-Linear Eddy-Viscosity Model in the  near-wall region - of the Diffuser 1 configuration),
*[[UFR_4-16_References#1|Abe and Ohtsuka]] (2010; complementary LES - using the  mixed-time-scale Subgrid-Scale model of Inagaki et al. - and a  zonal  hybrid  LES/RANS method - utilizing a Non-Linear Eddy-Viscosity Model in the  near-wall region - of the Diffuser 1 configuration),
*[[UFR_4-16_References#3|Breuer]] (2010; LES — applying different SGS models — and a zonal Hybrid LES/RANS - an Explicit Algebraic Reynolds Stress Model applied in  the near wall region was  coupled  with  the  LES  in  off-wall  region  — simulations of both "Stanford diffuser" configurations)
*[[UFR_4-16_References#3|Breuer]] (2010; LES — applying different SGS models — and a zonal Hybrid LES/RANS — an Explicit Algebraic Reynolds Stress Model applied in  the near wall region was  coupled  with  the  LES  in  off-wall  region  — simulations of both "Stanford diffuser" configurations)
*Jeyapaul and Durbin (2010; Detached Eddy Simulation and different RANS models were  applied  to  Diffuser  1;  furthermore,  an  attempt  was undertaken to computationally find "an optimum diffuser  design"  with respect to pressure  recovery  by  computing  a  family  of  diffusers varying in inlet aspect ratio, but having the same area versus x  were generated).
*[[UFR_4-16_References#16|Jeyapaul and Durbin]] (2010; Detached Eddy Simulation and different RANS models were  applied  to  Diffuser  1;  furthermore,  an  attempt  was undertaken to computationally find "an optimum diffuser  design"  with respect to pressure  recovery  by  computing  a  family  of  diffusers varying in inlet aspect ratio, but having the same area versus x  were generated).
 
A RANS study using some "conventional" Explicit  Algebraic  Reynolds  Stress
Models was performed by
[[UFR_4-16_References#19|Mehdizadeh  ''et al.'' (2012)]].
[[UFR_4-16_References#18|Maduta  and  Jakirlić (2011)]]
have computed the first diffuser by a novel  near-wall  second-moment
closure model coupled with the equation governing the inverse time scale ω.
This model is sensitized to account for the turbulence unsteadiness in  line
with the SAS (Scale-Adaptive  Simulation)  proposal  by
[[UFR_4-16_References#20|Menter  and  Egorov (2010)]].
 
Recently [[UFR_4-16_References#23|Ohlsson ''et al.'' (2009]],
[[UFR_4-16_References#24|2010]])
have performed a  complementary  Direct
Numerical Simulation (DNS) of the diffuser 1  using  a  massively  parallel
high-order  spectral  element  code.  The  3D  diffuser  was  meshed  by
approximately 220 million grid points. In  addition  to  the  mean  velocity
field, all six Reynolds stress components were evaluated,  as  well  as  the
surface pressure distribution and friction factor  distributions  along  the
bottom wall.
 
The interested reader is also referred to the work  of
[[UFR_4-16_References#31|Stock,  Leicher  and Seibert]]
(1988; Zeitschrift fuer Flugwissenschaften und  Weltraumforschung  /
Journal of Flight Sciences and Space Research); see the list of  references)
on a computational investigation of flow separation in a 3d  diffuser  using
a coupled Euler and boundary layer method (the  latter  statement  is  based
only on the manuscript's title; the contributors of this  "Wiki  description
of the flow in a 3D diffuser" are not in possession of this manuscript).
 
====Physical and modelling issues====
Unlike the configurations where separation is fixed by  sharp  corners,  the
flow in a 3D diffuser with asymmetrically diverging walls  is  characterized
by the non-fixed separation  from  a  flat  surface.  In  such  a  case  the
separation onset depends strongly on the  correct  capturing  of  the  shear
stress response to the adverse pressure gradient imposed  by  the  diverging
diffuser walls and consequent flow deceleration. Furthermore,  as  the  flow
recirculation causes non-uniformly strained turbulence, characterized  by  a
more complex mean rate of strain tensor  compared  to  wall-parallel  flows,
the turbulence model's  accurate  representation  of  the  dynamics  of  all
Reynolds stress components becomes particularly important.  Furthermore,  in
the case of the present 3D diffuser,  the  correct  capturing  of  the  flow
structure  in  the  inflow  duct  characterized  by  the  anisotropy-induced
secondary motion is of decisive importance. Accordingly, in addition to  the
eddy-resolving  methods,  such  as  LES-related  ones,  the  most  suitable
statistical models of turbulence are  those  capturing  the  Reynolds-stress
anisotropy.
 
====Reference experimental investigations====
[[UFR_4-16_References#7|Cherry ''et al.'' (2008]],
[[UFR_4-16_References#8|2009]])
provided a detailed reference database  comprising
the three-component mean velocity field within the entire diffuser  sections
in both configurations. Also the streamwise Reynolds stress component  field
within  the  diffuser  sections  of  the  diffuser  1  was  experimentally
determined. In addition the pressure  distribution  along  the  bottom  non-
deflected wall of the diffuser 1 at  different  Reynolds  numbers  was  also
measured. Complementary to the Reynolds number 10000 (for which  the  entire
flow field was measured), two higher Reynolds numbers — 20000  and  30000  —
were also considered.
 
====Test case====
In conclusion, the "Stanford" 3D diffuser represents  a  flow  configuration
of both fundamental importance and industrial relevance.  It  comprises  two
well-documented cases that are particularly suited as test cases
 
*the diffuser geometries with somewhat different divergence causing two completely different separation patterns
*the boundary and inflow conditions, the latter corresponding to fully-developed duct flow
*the comprehensiveness of the  available  database  consisting  of  the fully three-dimensional mean flow and turbulence fields
*a fairly low flow Reynolds number (10000) enabling the computations to be performed at affordable costs
 
The test case study comprises the experimental  database  of  both  diffuser
configurations intended to explore the sensitivity of the  three-dimensional
separation patterns to small geometrical changes. This database  is  further
enriched by a new direct numerical simulation,  the  results  of  which  are
analysed along with the  experimental  data.  Accordingly,  the  present  3D
diffuser configurations represent very suitable  benchmarks  for  turbulence
model validation.


<br/>
<br/>
----
----
{{ACContribs
{{ACContribs
| authors=Suad Jakirli&#x107;
| authors=Suad Jakirli&#x107;, Gisa  John-Puthenveettil
| organisation=Technische Universit&auml;t Darmstadt
| organisation=Technische Universit&auml;t Darmstadt
}}
}}

Latest revision as of 14:38, 12 February 2017

Flow in a 3D diffuser

Front Page

Description

Test Case Studies

Evaluation

Best Practice Advice

References

Confined flows

Underlying Flow Regime 4-16

Description

Introduction/motivation

Configurations involving three-dimensional boundary-layer separation are among the most frequently encountered flow geometries in practice. Accordingly, the methods for simulating them have to be appropriately validated using detailed and reliable reference databases. However, the large majority of the experimental benchmarks being used for validating computational methods and turbulence models relate to two-dimensional internal flow configurations, e.g. the flow in a 2-D diffuser (e.g. Obi et al., 1993), flow over a backward-facing step and a forward-facing step, or flow over fences, ribs, 2-D hills and 2-D humps mounted on the bottom wall of a plane channel. In these examples it is assumed that the influence of the side walls (according to Bradshaw and Wong, 1972, the minimum aspect ratio — representing the ratio of the channel height to channel width — should be 1:10 in order to eliminate the influence of the side walls) is not felt at the channel midplane. Consequently, within a computational framework, the spanwise direction can be regarded as homogeneous which allows the application of periodic boundary conditions (even 2D computations when using the RANS approach). By doing so, the three‐dimensional nature of the flow is completely missed: considerable secondary motion across the inlet section of the channel induced by the Reynolds stress anisotropy — which is, as generally known, beyond the reach of the eddy-viscosity RANS model group, complex 3-D separation patterns spreading over duct corners (corner separation and corner reattachment), etc.

These circumstances were the prime motivation for the recent experimental study of the flow in a three-dimensional diffuser conducted by Cherry et al. (2008, 2009). Such a diffuser configuration is also of a high practical relevance. It mimics a diffuser situated between a compressor and the combustor chamber in a jet engine. Its task is to decelerate the flow discharging from the compressor over a very short distance to the velocity field of the combustor section. Typically a uniform inlet profile over the diffuser outlet is desirable. Such a flow situation is associated by a strong pressure increase.

Review of UFR studies and choice of test case

Here some information about the objectives for investigating the flow in a 3D diffuser and an overview about the works relevant to this flow are given.

Detailed investigations of the flow separating in a three-dimensional diffuser were until recently practically non-existing. The diffuser configurations investigated intensively in the past relate mostly to two- dimensional symmetric (e.g. Xu et al., 1997) and asymmetric plane diffuser geometries, see e.g. the experimental works by Obi et al. (1993), Buice and Eaton (1996, 2000) and Gullman-Strand et al. (2004). Let us shortly recall that the "Obi-diffuser" characterized by an expansion ratio of 4.7 and an opening angle of 10° (in some earlier experimental works this value was regarded as a lower limit below which separation does not take place; this information can be of help when evaluating the computational models applied to the flow in a 3D diffuser) was the test case of the 8th ERCOFTAC SIG15 Workshop on "Refined Turbulence Modelling", Hellsten and Rautaheimo (1999). The first study on the flow in a 3D diffuser aiming at providing a comprehensive database for turbulence model validation was provided by the Stanford University group led by John Eaton, Cherry et  al. (2008, 2009). The objectives were to design a simple but rigorous test for 3D flow separation simulations with well-defined inflow and boundary conditions, to provide the fully 3D mean flow field and to examine the sensitivity of the flow pattern to small geometric changes. The measurements were performed in a recirculating water (ρ=1000 kg/m3 and μ=0.001 Pas) channel using the method of magnetic resonance velocimetry (MRV). Two three-dimensional diffusers with the same fully-developed channel inlet flow but slightly different expansion geometries were considered: the upper-wall expansion angle is reduced from 11.3° (diffuser 1) to 9° (diffuser 2) and the side- wall expansion angle is increased from 2.56° (diffuser 1) to 4° (diffuser 2), Cherry et al. (2008). See Fig. 2 and the section “Test case description” of the present contribution for the exact geometry and dimensions of the diffusers. Both diffuser flows are characterized by a three-dimensional boundary-layer separation, but the size and shape of the separation bubble exhibit a high degree of sensitivity to the geometry of the diffuser.


UFR4-16 figure2.png
Figure 2: Detailed diffuser design: geometry and dimensions. From Cherry et al. (2009)


All these features represent a big challenge for computational models. Therefore, a comparative computational study on both diffuser configurations by using different turbulence statistical (RANS — Reynolds‐Averaged Navier‐Stokes) and SGS (SGS — Subgrid‐Scale models within the LES framework; LES — Large-Eddy Simulation) models was pursued in the framework of the 13th and 14th ERCOFTAC SIG15 Workshops on Refined Turbulence Modelling, Steiner et al. (2009) and Jakirlić et al. (2010b). In addition to different RANS models, the LES and LES-related methods (different seamless and zonal hybrid LES/RANS - HLR - models; DES — Detached Eddy Simulation) were comparatively assessed (visit www.ercoftac.org; under SIG15); the comparative analysis of selected results is presented in the section "Evaluation" of the present contribution.

Relevant studies

The flow in a 3D diffuser represents a very interesting benchmark characterized by a complex, truly three-dimensional separation pattern associated with the corner separation and the corner reattachment, both phenomena encountered frequently in various engineering applications. However, there are neither experimental nor computational studies performed in the past that are relevant to such a flow configuration. All relevant computational studies performed recently are related to the previously described "Stanford 3D Diffuser".

Computational studies

Besides computations for the afore-mentioned workshops, organized by the ERCOFTAC Special Interest Group on Turbulence Modelling (SIG15), a number of studies dealing with this "Stanford-Diffuser" focusing on "modelling and simulation issues" have been performed, most of them inspired by the ERCOFTAC workshops.

The latter studies include the following LES and hybrid LES/RANS calculations

  • Cherry et al. (2006; comparative assessment of LES and several RANS models based on the eddy-viscosity concept by reference to the flow in the diffuser 1),
  • Schneider et al. (2010; LES computations of both diffuser configurations by applying wall functions for the near-wall treatment; see also Schneider et al. 2011, where the possibilities of the flow separation control in a 3D diffuser by manipulating the secondary flow in the inlet duct have been investigated — the latter work was motivated by an experimental investigation due to Grundmann et al., 2011, 2012 who investigated the sensitivity of the secondary currents in the inflow duct to the perturbations induced by dielectric-barrier discharge actuators and vortex-generator devices),
  • Jakirlić et al. (2010a; complementary LES — using Dynamics model of Germano et al. — and a zonal hybrid LES/RANS method of the Diffuser 1 configuration),
  • Abe and Ohtsuka (2010; complementary LES - using the mixed-time-scale Subgrid-Scale model of Inagaki et al. - and a zonal hybrid LES/RANS method - utilizing a Non-Linear Eddy-Viscosity Model in the near-wall region - of the Diffuser 1 configuration),
  • Breuer (2010; LES — applying different SGS models — and a zonal Hybrid LES/RANS — an Explicit Algebraic Reynolds Stress Model applied in the near wall region was coupled with the LES in off-wall region — simulations of both "Stanford diffuser" configurations)
  • Jeyapaul and Durbin (2010; Detached Eddy Simulation and different RANS models were applied to Diffuser 1; furthermore, an attempt was undertaken to computationally find "an optimum diffuser design" with respect to pressure recovery by computing a family of diffusers varying in inlet aspect ratio, but having the same area versus x were generated).

A RANS study using some "conventional" Explicit Algebraic Reynolds Stress Models was performed by Mehdizadeh et al. (2012). Maduta and Jakirlić (2011) have computed the first diffuser by a novel near-wall second-moment closure model coupled with the equation governing the inverse time scale ω. This model is sensitized to account for the turbulence unsteadiness in line with the SAS (Scale-Adaptive Simulation) proposal by Menter and Egorov (2010).

Recently Ohlsson et al. (2009, 2010) have performed a complementary Direct Numerical Simulation (DNS) of the diffuser 1 using a massively parallel high-order spectral element code. The 3D diffuser was meshed by approximately 220 million grid points. In addition to the mean velocity field, all six Reynolds stress components were evaluated, as well as the surface pressure distribution and friction factor distributions along the bottom wall.

The interested reader is also referred to the work of Stock, Leicher and Seibert (1988; Zeitschrift fuer Flugwissenschaften und Weltraumforschung / Journal of Flight Sciences and Space Research); see the list of references) on a computational investigation of flow separation in a 3d diffuser using a coupled Euler and boundary layer method (the latter statement is based only on the manuscript's title; the contributors of this "Wiki description of the flow in a 3D diffuser" are not in possession of this manuscript).

Physical and modelling issues

Unlike the configurations where separation is fixed by sharp corners, the flow in a 3D diffuser with asymmetrically diverging walls is characterized by the non-fixed separation from a flat surface. In such a case the separation onset depends strongly on the correct capturing of the shear stress response to the adverse pressure gradient imposed by the diverging diffuser walls and consequent flow deceleration. Furthermore, as the flow recirculation causes non-uniformly strained turbulence, characterized by a more complex mean rate of strain tensor compared to wall-parallel flows, the turbulence model's accurate representation of the dynamics of all Reynolds stress components becomes particularly important. Furthermore, in the case of the present 3D diffuser, the correct capturing of the flow structure in the inflow duct characterized by the anisotropy-induced secondary motion is of decisive importance. Accordingly, in addition to the eddy-resolving methods, such as LES-related ones, the most suitable statistical models of turbulence are those capturing the Reynolds-stress anisotropy.

Reference experimental investigations

Cherry et al. (2008, 2009) provided a detailed reference database comprising the three-component mean velocity field within the entire diffuser sections in both configurations. Also the streamwise Reynolds stress component field within the diffuser sections of the diffuser 1 was experimentally determined. In addition the pressure distribution along the bottom non- deflected wall of the diffuser 1 at different Reynolds numbers was also measured. Complementary to the Reynolds number 10000 (for which the entire flow field was measured), two higher Reynolds numbers — 20000 and 30000 — were also considered.

Test case

In conclusion, the "Stanford" 3D diffuser represents a flow configuration of both fundamental importance and industrial relevance. It comprises two well-documented cases that are particularly suited as test cases

  • the diffuser geometries with somewhat different divergence causing two completely different separation patterns
  • the boundary and inflow conditions, the latter corresponding to fully-developed duct flow
  • the comprehensiveness of the available database consisting of the fully three-dimensional mean flow and turbulence fields
  • a fairly low flow Reynolds number (10000) enabling the computations to be performed at affordable costs

The test case study comprises the experimental database of both diffuser configurations intended to explore the sensitivity of the three-dimensional separation patterns to small geometrical changes. This database is further enriched by a new direct numerical simulation, the results of which are analysed along with the experimental data. Accordingly, the present 3D diffuser configurations represent very suitable benchmarks for turbulence model validation.




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

Front Page

Description

Test Case Studies

Evaluation

Best Practice Advice

References


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