AD/AG49: Scrutinizing Hybrid RANS-LES Methods for …garteur.org/Technical Reports/AD_AG-49_TP-182_OPEN.… · · 2017-01-03GARTEUR TP-182 FOI-S--4866--SE 1 Sammanfattning Huvudsyftet

S.-H. Peng1, S. Deck2, H. van der Ven3, T. Knopp4, P. Catalano5, C. Lozano6, C. Zwerger7, J. C. Kok3, A. Jirasek1, F. Capizzano5, C. Breitsamter7

1FOI, 2ONERA, 3NLR, 4DLR, 5CIRA, 6INTA, 7TUM

AD/AG49: Scrutinizing Hybrid RANS-LES Methods for Aerodynamic Applications

FOI, Totalförsvarets Forskningsinstitut FOI, Swedish Defence Research Agency

Avdelningen för informations- och aerosystem

Division of Information and Aeronautical Systems

164 90 Stockholm SE-164 90 Stockholm

Titel AD/AG49: Utförlig undersökning av hybrid RANS-LES metoder för aerodynamiska tillämpningar

Title AD/AG49: Scrutinizing Hybrid RANS-LES Methods for Aerodynamic Applications

Rapportnr/Report no GARTEUR TP-182

(FOI-S--4866--SE)

Rapporttyp Report Type

Scientific Report Vetenskaplig rapport

Sidor/Pages 60p

Månad/Month november/November

Utgivningsår/Year 2014

ISSN 1650-1942

Forskningsområde Flygteknik och luftstridssimulering

FoT-område Flygteknik

Projektnr/Project no E3651409

Project Manager Shia-Hui Peng

Scientifically/technically responsible Shia-Hui Peng and Torsten Berglind

ORIGINAL: ENGLISH

GARTEUR TP–182

NOVEMBER 2014

CLASSIFICATION: OPEN

GARTEUR ACTION GROUP (AG) 49

Scrutinizing Hybrid RANS-LES Methods

For Aerodynamic Applications

by

S.-H. Peng1, S. Deck

2, H. van der Ven

3, T. Knopp

4 , P. Catalano

5, C. Lozano

6, C.

Zwerger7, J. C. Kok

3, H., A. Jirasek

1, F. Capizzano

5, C. Breitsamter

7

1FOI,

2ONERA,

3NLR,

4DLR,

5CIRA,

6INTA,

7TUM

GARTEUR aims at stimulating and coordinating cooperation between Research

Establishments, Industry and Academia in the areas of Aerodynamics, Flight

Mechanics, Systems and Integration, Helicopters, and Structures & Materials

AG49 members

Pietro Catalano and Francesco Capizzano, CIRA

Tobias Knopp and Dieter Schwamborn, DLR

Shia-Hui Peng, FOI (Chairman of AG49)

Carlos Lozano Rodriguez, INTA

Harmen van der Ven and Johan C. Kok, NLR

Sébastien Deck, ONERA (Vice-chairman of AG49)

Christian Breitsamter and Christian Zwerger, TUM

GoR Aerodynamics members

Mr. T. Berglind, FOI

Dr. E. Coustol, ONERA

Dr. H. Rosemann, DLR

Dr. G. Schrauf, Airbus Deutschland

Mr. G. Mingione, CIRA

Mr. K.M.J. de Cock, NLR

Mr. F. Monge Gómez, INTA

Dr. P. Weinerfelt, SAAB

Mr. F. Ogilvie, ATI

IPoC of GoR Aerodynamics

Mr. D. Pagan, MBDA-France

Dr. M. Mallet, Dassault Aviation

Dr. N. Wood, Airbus UK

Dr. T. Berens, EADS Deutschland

Dr. N. Ceresola, Alenia Aermacchi

Dr. L.P. Ruiz-Calavera, Airbus Military

Mr. C. Newbold, QinetiQ

GARTEUR TP-182 FOI-S--4866--SE

1

Sammanfattning Huvudsyftet med GARTEUR AD/AG-49 har varit att undersöka och utvärdera utvalda

hybrid RANS-LES metoder beträffande några fundamentala modelleringsproblem på

speciella aerodynamiska tillämpningar. AG-49 har sju deltagare varav sex

forskningsinstitut och ett universitet. Det övergripande målet med verksamheten har

varit att genom ett flernationssamarbete göra en grundlig undersökning av DES och

relevanta hybrid RANS-LES-metoder med avseende på metodernas flexibilitet och

noggrannhet för industriella tillämpningar. DDES-liknande modeller och andra

metoder som HYB0, X-LES och ZDES har blivit utvärderade inom verksamheten av

detta projekt. Arbetet har i AG49 bedrivits i två tekniska delprojekt 1 och 2 baserade på

RANS-LES-beräkningar av fyra testfall och riktlinjer för bästa praxis har

sammanfattats i delprojekt 3.

Fokus i delprojekt 1 var att undersöka tillvägagångssätt för modelleringen genom

beräkningar av fundamentala strömningsfall och validering mot tillgängliga

experimentella mätningar där två grundläggande testfall har studerats, nämligen ett

turbulent blandningsskikt(TC1.1) och strömning över ett bakåtvänt steg(TC1.2). Detta

har möjliggjort noggranna analyser av prestanda för olika hybridmodeller avseende

upplösning av typiska och viktiga aerodynamiska strömningsegenskaper, speciellt

instabiliteten av det fria skjuvskiktet som utgår från det inkommande gränsskiktet

modellerad med RANS och som löses upp av LES-moden. Utgående från resultaten

som beräknats av AG-medlemmarna har korsjämförelser gjorts. Det visade sig att

standard DDES-modeller gav en sämre prediktionsförmåga jämfört med andra hybrid

RANS-LES-metoder i att upplösa initiala skjuvskiktsinstabiliteter. Försämringen

förklaras av begreppet ”grey area” problem, relaterade till omslag från RANS till LES

vilket fördröjer återskapandet av upplöst turbulens. Detaljerade jämförelser med

experiment visar också vikten av prediktionen av det inkommande gränsskiktet.

Delprojekt 2 har koncentrerats på hybrid RANS-LES beräkningar av komplexa

aerodynamiska strömningsfall. Två testfall har studerats, F15 tre-element

höglyftskonfiguration(TC2.1) och VFE-2 deltavingen med rund framkant (TC 2.2).

Inriktningen av delprojekt 2 har varit utvärdering av hybrid RAND-LES-metoder som

använts av AG-medlemmarna för beräkning av aerodynamiska strömningsfall som är

relevanta för industrin. Korsplottning gjordes av resultat gjordes av de involverade

deltagarna. För höglyftsfallet uppmärksammades DDES modellens oförmåga att

hantera mötespunkten där RANS-modellerat gränsskikt och LES-upplöst vak bakom

glipan mellan framkantsklaff och vinge eller mellan vinge och bakkantsklaff. Detta kan

väsentligt påverka prediktionen av gränsskiktsseparationen på bakkantsklaffens

bakkant. För strömningen runt deltavingen är upplösningen av området runt

virvelbildningen och virvlarnas inbördes växelverkan väsentlig för noggranna

prediktioner. Den sekundära virveln verkar svårare att lösa upp i simuleringen än den

primära virveln. Erfarenheterna genom projektarbetet har sammanfattats i delprojekt 3.

Nyckelord: Hybrid-RANS-LES-metoder, utvärdering och värdering av modellering,

skjuvskiktsinstabilitet, strömning över bakåtvänt steg, multielement

höglyftskonfiguration, VFE-delta vinge.


2

Summary The main purpose of the GARTEUR AD/AG49 has been to explore and evaluate

selected hybrid RANS-LES modelling approaches on some fundamental modelling

issues and targeting aerodynamic applications. AG49 consists of seven members, of

which six are from research organizations and one from university. The general

objective of AG49 has been, by means of trans-national collaborative investigation, to

make in-depth assessment of DES and other relevant hybrid RANS-LES methods in

terms of modelling flexibility and accuracy for industrial applications. DDES-type

models and other approaches like HYB0, X-LES and ZDES have been assessed in the

framework of this project. The work in AG49 has been addressed in two technical tasks

(Tasks 1 & 2) based on hybrid RANS-LES computations for four test cases (TC), and

some best-practice guidelines have been summarized in Task 3.

Task 1 focuses on an exploration of modelling approaches through computations of

fundamental flows in validation against available experimental measurements, where

two test cases have been addressed, namely, a turbulent mixing-layer flow (TC 1.1)

and a backward-facing step flow (TC 1.2). This has enabled to make in-depth analysis

of hybrid modelling performance in resolving some typical and important aerodynamic

flow features, in particular, on the free shear layer emanating from incoming RANS-

modelled boundary layer and resolved by the LES mode. With the results computed by

involved AG members, cross comparisons have been conducted. It is shown that the

standard DDES-type models present a degraded predictive capability, as compared to

the other hybrid RANS-LES methods in resolving the initial shear-layer instabilities.

The degradation is mainly attributed to the “grey-area” problem related to the RANS-

to-LES switching with delayed re-establishment of resolved turbulence. Detailed

comparison with the experiment also reveals the importance of the prediction of the

incoming (upstream) boundary layer. Making one step forward, Task 2 focuses on

hybrid RANS-LES computations of complex aerodynamic flows. Two test cases have

been addressed, namely, the F15 three-element high-lift configuration (TC 2.1) and the

VFE-2 Delta wing with a round leading edge (TC 2.2). The emphasis of Task 2 has

been placed on an assessment of hybrid RANS-LES methods used by AG members in

computations of industry-relevant aerodynamic flows. Cross-plotting has been made of

the results contributed by involved partners. For the high-lift flow, the lack of ability in

DDES modelling has been highlighted when dealing with the confluence of RANS-

modelled boundary layer and LES-resolved wakes behind the slat-wing and wing-flap

gaps. This may significantly affect the prediction of the boundary layer separation on

the flap trailing edge. For the Delta-wing flow, the resolution of the primary and

secondary vortex formation and interaction is shown to be an essential issue for

accurate predictions. The secondary vortex seems to be more difficult to be resolved.

The lessons learned and the experience gained throughout the project work have been

summarized in Task3.

Keywords: Hybrid RANS-LES methods, Modelling evaluation and assessment, Shear-

layer instability, Backward-facing step flow, Multi-element high-lift configuration,

VFE-2 Delta wing


3

Contents

1 Introduction 5

1.1 Previous Activities ............................................................................. 6

1.2 Objectives ......................................................................................... 7

1.3 Description of Test Cases ................................................................. 7

1.3.1 Test Case 1.1: Mixing Layer ......................................................... 8 1.3.2 Test Case 1.2: Backward-Facing Step (BFS) flow ....................... 9 1.3.3 Test Case 2.1: LEISA F15 High-Lift Configuration ..................... 10 1.3.4 Test Case 2.2: VFE-2 Delta Wing ............................................... 11

2 Modelling and Simulation Approaches 13

2.1 Hybrid RANS-LES Models .............................................................. 13

2.1.1 DES, DDES and IDDES models ................................................ 13 2.1.2 Zonal Detached Eddy Simulation ............................................... 17 2.1.3 Extra Large Eddy Simulation (X-LES) Models ............................ 19 2.1.4 Algebraic (HYB0) and One-Equation (HYB1) Hybrid Models ..... 19

2.2 Information of CFD Solvers ............................................................. 21

3 Computations of Fundamental Flows 23

3.1 Mixing layer ..................................................................................... 23

3.2 Backward-facing Step Flow ............................................................ 31

4 Complex Aerodynamic Flows 37

4.1 LEISA High-Lift Configuration ......................................................... 37

4.2 VFE-2 Delta Wing ........................................................................... 42

5 Summary and Conclusions 47

5.1 Best-Practice Guidelines ................................................................. 47

5.2 Concluding Remarks ....................................................................... 49

6 References 51


4


5

1 Introduction Simulation of turbulent flows has often been conducted in either of the following three main approaches: Direct

Numerical Simulation (DNS) which resolves all turbulent scales (and thus no turbulence model invoked); Large

Eddy Simulation (LES) which resolves large-scale eddies (larger than a predefined filter width that is usually

proportional to the local grid size) and models the effect of unresolved small eddies (namely, unfiltered subgrid-

scale eddies); and statistical modelling based on Reynolds-Averaged Navier-Stokes equations (RANS). Despite

extensive development, however, none of the above methods has yet emerged as indisputably superior and

applicable to general turbulent flow problems of engineering interest in terms of both computational accuracy and

efficiency. Instead, each method with recognized limitations has its own niche where it offers decisive advantages.

DNS, being the most exact with no needs for modelling, offers a genuinely accurate method to study flow physics,

and is especially useful in providing information intractable by experimental methods. However, its exorbitant

demanding on computing resources has limited its applications only to low Reynolds numbers and very simple

flow configurations. This has indeed largely deterred any applications of DNS to industrially-relevant

aerodynamic flows, which are often featured by high Reynolds numbers and configured with complex geometries.

LES has long been regarded as the most prospective tool, expected to emerge as industrial standard for flow

simulations. Over the years, however, LES has also shown serious shortcomings. Particularly for wall-bounded

flows computing costs increase sharply with the Reynolds number, in association with the need to resolve a large

range of eddy scales. Complex geometries are especially difficult to handle, and the treatment of wall boundaries

remains a major problem, especially when wall friction is in focus. Proper resolution of the wall boundary layer

and capturing inherent energetic streaky structures require a very fine numerical grid not only in the wall-normal,

but also in wall-parallel directions, close to those of a DNS.

At the other end of the pallet are the RANS methods, which have gained a wide range of applications. The

RANS methods have long been the mainstay of industrial CFD, with good prospects to retain this role in the near

future. They are simple to use, computationally affordable and economical, thus appealing to industry for various

applications such as design, optimization, and prediction of off-design performances. Nonetheless, the RANS

approach has also serious limitations. In addition to the lack of universality and unavoidable empiricism, the

major deficiency is in the inability to account for the anisotropy of turbulent stresses, for spectral dynamics and

for unsteady vortex motions, as well as for different scales that characterize turbulence interactions – features that

are naturally captured by DNS and LES. These shortcomings are the main reasons that most RANS models

perform unsatisfactorily in strongly non-equilibrium, fast evolving and separating flows, as well as in flows with

dominant large-scale coherent vortex motions, as being present in many aerodynamic applications.

This has thus over the past decade motivated intensive studies of hybrid RANS-LES methods, being

pioneered by the work on Detached Eddy Simulation (DES) due to Spalart and co-workers [1-3]. A “standard”

hybrid RANS-LES method uses (unsteady) RANS modelling in the near-wall layer coupled with a LES mode

away from the wall. The use of RANS mode in the wall boundary layer enables, to a large extent, to avoid

resolving the near-wall small-scale (yet energetic) structures and, consequently, to alleviate a dense near-wall grid

resolution for wall-bounded flows, which would otherwise be required in full LES. On the other hand, the

advantage of LES may be well-adopted in off-wall regions for flows being detached from boundary layers and

undergoing massive separation with unsteady vortex motions. After the presence of the Spalart-Allmaras DES

(SA-DES) approach, progress has been made on hybrid RANS-LES approaches of different types, which have

demonstrated promising performance in modelling fundamental flow physics and in some emerging industrial

CFD applications. All these approaches have laid intention for predicting high Reynolds number wall-bounded

flows.

The development of hybrid modelling has ranged from two-layer models (see e.g. [4–10]), zonal and/or

embedded LES modelling methods (see e.g. [11, 12]), to other DES-type modelling approaches [13–15] and

further improvement of the SA-DES model [16, 17]. Being a part of the hybrid modelling development, the

RANS-LES interface has been an interesting and significant topic to attain appropriate RANS-LES hybridization

[18–21]. Bearing the same arguments of alleviating the grid resolution in full LES, other interesting methods have

also emerged in recent years, noticeably, the Scale-Adaptive Simulation (SAS) method by Menter [22, 23], the

Limited-Numerical-Scale (LNS) approach by Batten [24], the Partially Integrated Transport Model (PITM) by

Schiestel and co-workers [25, 26] and the Partially-Averaged Navier-Stokes (PANS) model due to Girimaji [27,

28].

The vivid development of different hybrid RANS-LES methods has been motivated and further facilitated by

industrial needs on advanced turbulence modelling in numerical analysis of complex aerodynamic flows.


6

Typically, hybrid RANS-LES modelling requires profound studies on, in particular, RANS modelling and SGS

modelling (in LES) incorporated in the hybridization, the interfacing of these invoked RANS and LES modes and,

inherently, the interaction of different scales over the RANS-LES interfacing zone being defined in the context of

”resolved” and ”modelled” turbulence. Obviously, a hybrid RANS-LES approach rests not only on the LES and

RANS modes incorporated, but more on the interaction of the two modes.

In aeronautic applications, flows around air vehicles are often characterized by turbulent flow separation and

unsteady vortex motions. The main purpose of GARTEUR AG49 has been, by means of close collaboration of the

AG members, dedicated to a systematic investigation of several selected hybrid RANS-LES methods in modelling

and simulation of both fundamental and applied aerodynamic flows and, consequently, to explore the pros and

cons of these approaches in the computation of four different test cases. AG49 consists of six members, including

five research organizations (CIRA, DLR, INTA, NLR, ONERA) and one university, TU-Munich, In the early

stage (for the first 6 months) Cassidian (now Airbus-DS) was also an active member in AG49.

This report summarizes the work performed in AG49. The collaborative work has been conducted in two

main technical tasks, addressing respectively the modelling of fundamental flows and further verification of

modelling for aerodynamic applications. The tasks are test-case-based, which are described below. Cross

comparisons of results obtained with different hybrid RANS-LES models by AG49 members are presented. Based

on the results, as well as the experience gained by AG members in the computation of different test cases, the

conclusions and some guidelines have also been summarized.

1.1 Previous Activities

There have been extensive studies over the past decade on hybrid RANS-LES modelling approaches. One of the

earliest attempts on a combination/hybridization of different modelling approaches was pioneered by Speziale

[29], who proposed to use an empirical function of turbulent length scales of different hierarchy (from RANS to

the Kolmogorov length scale for DNS) to unify the modelling formulation in such a way that a RANS-type model

may approach to DNS via LES with increasing grid refinement. At about the same time, due to Spalart and his co-

workers [1], the first hybrid model (namely, the S-A DES approach based on the Spalart-Allmaras RANS model)

was developed using a similar idea of Speziale’s. Due to its promising performance in aerodynamic applications,

particularly, for massively separating flows with vortex motions, the S-A DES model has been intensively

explored and, alternatively, a number of other hybrid modelling methods have also been developed.

In Europe, a systematic trans-national collaborative research work on DES and hybrid RANS-LES methods

may be marked by the DESider project (2004-2007) in the 6th EC Framework Research Program, which has

covered a wide range of development on advanced URANS (Unsteady RANS), improved DES and hybrid RANS-

LES approaches. Along with several European aeronautic industries (e.g. Alenia, Dassault, EADS and Eurocopter

as partners, Airbus and Bombadier as industrial observers), several organizations in GARTEUR (DLR, FOI, NLR

and ONERA) have actively participated in this project. The project has focused more on fundamental development

and validation of new URANS and hybrid modelling approaches. In the 7th

EC Framework Research Program, the

project, ATAAC (2009-2012), has placed a major part of work dedicated to industry-challenging applications

using hybrid RANS-LES methods. All these activities have formed a profound platform for the work to undertake

by AG49. While an effective platform has set up with these projects, the AG work has focused on in-depth

investigation on some significant problems identified in previous research activities. The AG49 has engaged in an

interaction with the ATAAC project, since several AG49 members are also the ATAAC project partners.

In the framework of GARTEUR programs, DES and other hybrid methods have also gained increasing

applications. In the AG42 project completed recently [30], several partners have employed DES and other hybrid

RANS-LES methods in computations of the subsonic flow around the AG04 missile configuration at a high angle

of attack. It has been demonstrated that the numerical scheme used may play a significant role in the flow

predictions, particularly, when a hybrid RANS-LES method is employed. It is shown that hybrid RANS-LES

methods are able to reproduce some of the damping in the oscillation of the local side force towards the rear part

of the missile observed in the experiment, whereas a RANS method fails to indicate any damping phenomena

towards the end part of the missile. Similarly, in the AG43 project, hybrid RANS-LES methods have been applied

to computations of engine inlets, aiming at a better resolution on the internal flow separation. The modelling of

internal flows, such as flows in an S-duct, using DES or similar methods represents another challenging aspect of

hybrid modelling in terms of, for example, inflow turbulence conditions and grid arrangement. Similar to external

boundary layer separation, hybrid modelling of internal flow separation is rather sensitive to the grid arrangement

and, even more, to the (re-)establishment of upstream turbulence structure. Indeed, while hybrid RANS-LES


7

modelling has shown great potential for accurate and effective simulations of aerodynamic flows, it possesses also

some significant problems and challenges that call for further investigation and improvement. The AG49 work has

targeted to make contributions towards a better understanding, in-depth investigation and improvement of hybrid

RANS-LES modelling for aerodynamic applications.

1.2 Objectives

The activities of AG49 have targeted comprehensive exploration and evaluation of some selected DES and hybrid

RANS-LES methods for both fundamental and industry-relevant aerodynamic flows. The emphasis was placed on

a systematic investigation of some significant modelling problems in predicting typical aerodynamic flow

features, including shear-layer instabilities, boundary layer separation and subsequent detached vortex motion and

vortex breakdown. To resolve appropriately these and other related flow physics, some further investigation and

improvement of the RANS-LES modelling, as well some related numerical issues, have been undertaken.

In summary, the general objectives of AG49 have been

To make comprehensive evaluation, assessment and improvement of DES and other hybrid RANS-LES

methods in modelling both fundamental and industry-relevant flows based on available and detailed

experimental data.

To contribute a database of hybrid RANS-LES approaches in resolving/modelling typical aerodynamic flow

physics, which conventional RANS methods may fail to capture.

To draw some relevant “best practice” guidelines for aerodynamic industries in terms of the pros and cons of

hybrid methods in modelling some important aerodynamic flow problems.

Ultimately, to facilitate the use of hybrid RANS-LES methods in aeronautic industries.

To achieve these objectives, a number of numerical computations have been carried out for several test cases

using several different hybrid RANS-LES methods. Partners have used their own in-house and/or commercial

CFD codes to perform the computational work. The test cases include both fundamental and applied aerodynamic

flows, designated in two tasks, as described below.

1.3 Description of Test Cases

Numerical analyses have been collaboratively conducted for several selected test cases in two technical tasks. The

test cases include both fundamental and applied aerodynamic flows. In Task 1, two fundamental flows have been

considered with two different test cases. The flow configurations of these test cases are relatively simple, yet

possessing complex and relevant flow phenomena that are suitable for an effective and in-depth investigation.

Task 2 aims at an exploration and evaluation of hybrid modelling for industry-relevant aerodynamic flows with

increasing complexity (in terms of the flow physics). In Task 3, some relevant “best-practice” guidelines are

summarized on the basis of the results and experience obtained, and the lessons learned, from the work

undertaken in Tasks 1 and 2. The fundamental test cases in Task 1 provide an effective platform for

comprehensive studies of modelling behavior to highlight existing problems/weakness of hybrid modelling. These

test cases support further modelling improvement with validation against detailed experimental data. The applied

test cases in Task 2 have served for the purpose of overall investigation of modelling performance and to assess

the appropriateness and availability of the improvement/remedies made on the basis of the fundamental TCs in

Task 1 when applied for industry-relevant and complex aerodynamic flows. Over the whole procedure of project

work, the AG members have made close interaction and communications on intermediate results, as well as the

modelling performance, numerical grids and other related issues.

Task 1 is dedicated to scrutinizing the behavior of hybrid RANS-LES modelling in simulation of

fundamental flows characterized by shear layer (or mixing layer) emanating and/or evolving after wall boundary

layer separation. Two test cases, TC 1.1 and TC 1.2, are included in this task. This task concerns itself with the

canonical test case of the spatially developing shear layer. An important issue in DES-type methods is the

development of free shear layers starting from turbulent boundary layers. Even though free shear layers are

intrinsically unstable, computational results may show stable shear layers of lengths that seem unphysical (see, for

example, Spalart [33]).


8

1.3.1 Test Case 1.1: Mixing Layer

In DES-type methods, the turbulent boundary layers upstream of a free shear layer are typically in RANS mode

and therefore do not contain any resolved turbulence. As a consequence, the development of turbulence in the

shear layer will start from the intrinsic instability of the shear layer and will not be forced by turbulence coming

from the boundary layers. This resembles the situation when the upstream boundary layers are laminar. In that

case, however, the distance over which the initial, essentially 2D, Kelvin–Helmholtz instabilities develop into

fully 3D turbulence may be very long (of the order of hundreds of initial displacement thicknesses or more, see

Huang & Ho [32]).

The current test case is a fundamental test case for the investigation of shear layer instabilities: the spatial

shear layer. The experiment is taken from the thesis of Delville [31], as summarized in AGARDograph 345 ([30],

Test identification SHL04). The emphasis of this test case is on the correct development of the instabilities rather

than the meticulous comparison with experiment. The scrutiny of the hybrid RANS-LES methods is in their

capability to predict a turbulent development of the instabilities in the shear layer, rather than a laminar

development.

Figure 1.1: Experimental setup for the mixing-layer test case

The splitter plate is 3mm thick and tapers off to 0.3 mm at the trailing edge (at an angle of ‘about’ 3o over 50

mm). The shear layer develops in a 0.3m × 0.3m square test section of length 1.2m The experimental setup is

shown in Figure 1.1.

The free shear layer starts from the trailing edge of a flat plate with free-stream velocities u1 = 41.54 m/s and u2 =

22.40 m/s at the different sides of the flat plate. The freestream turbulence level is 0.3% in the longitudinal

velocity. At the trailing edge, the turbulent boundary layers are fully developed (boundary layers are tripped) with

the momentum and displacement thicknesses equal to θ1 = 1.0 mm and δ*1 = 1.4 mm at the high-speed side and θ2

= 0.73 mm and δ*2 = 1.0 mm at the low-speed side. The θ -based Reynolds number at the high-speed side is Reθ 1

= 2900 at the trailing edge. A self-similar flow with fully developed turbulence is reached well within the test

section.

The experimental data base, containing raw data is stored in the ERCOFTAC data base, of which turbulent

statistics are taken and saved in the database of the AGARDograph. Measured at various locations, the turbulent

statistics for the mixing layer include:

- averaged velocity

- Reynolds stress

- third order moments

- spectra

- dissipation terms from spectra

- turbulent kinetic energy balance

A complete set of Reynolds stresses is available at six downstream stations. Single wire measurements for the

streamwise normal stress are available at 24 downstream locations.

NLR has generated a block-structured grid [35], which can be used by other partners. A description of the mesh is

as follows. The splitter plate is modelled as a flat plate with zero thickness. A computational domain is used with

a width of 0.15m (z-direction) and a height of 0.3m (y direction). To capture the correct boundary-layer profiles at


9

the trailing edge, the flat plate has a length of 0.5 m on the high-speed side and 0.3m on the low-speed side and

fine-tuning has been done by varying the transition locations.

Figure 1.2: Block topology and boundary conditions for the spatial shear layer; black: splitter plate; green:

inflow; red: outflow; purple: slip wall. The grid dimensions shown are for the fine mesh G2.

The boundary conditions and principal grid dimensions are shown in Figure 2. At the inflow (green faces in the

figure) a constant velocity profile is prescribed, with magnitude equal to the respective experimental freestream

velocities. Also, the freestream temperature of 20oC is prescribed at the inflow. No turbulence is introduced at the

inflow. For NLR’s combination of the TNT k–ω turbulence model and numerical scheme, transition is specified

0.468 m upstream of the trailing edge on the upper side of the splitter plate, and 0.274 m upstream of the trailing

on the lower side. At the outflow (red faces in the figure) static pressure is prescribed, equal to the freestream

static pressure. The upper and lower walls of the computational domain (purple faces in the figure) are modelled

with the slip boundary condition. In the span direction, periodic boundary conditions are imposed.

The grid is stretched in the y-direction to capture the boundary layers with approximately y+ = 1 for the first grid

cell. At the trailing edge, the number of cells in the wall normal direction in the boundary layer (momentum

thickness) is in the order of 30. A computational ‘test section’ is defined with a length of 1m after the trailing edge

and with a uniform grid in the x- and z-directions, followed by a buffer zone of 1m length with a stretched grid in

x-direction.

Two grid levels are available, G1 and G2, with 1.29 and 10.3 million grid cells. Grid G2 has a uniform

distribution of 96 cells in z-direction and a uniform distribution of 640 cells in x-direction in the computational

test section, giving a uniform mesh size h = 1.5625mm in both directions (similar to Tenaud [39]). The filter width

is set equal to this mesh size. For grid G1 the mesh sizes and the filter width are all doubled compared to G2.

1.3.2 Test Case 1.2: Backward-Facing Step (BFS) flow

The chosen test case is a channel flow separating downstream from a backward facing step, see Figure 1.3. This

configuration represents the A3C combustion chamber which has been experimentally used to study the

separation of inert and reactive flows downstream from the step [49].

Figure 1.3: Sketch of the BFS flow


10

This test case allows assessing the following issues.

• Shielding of the incoming boundary layer (I)

• Damping of the growth of instabilities through advection of RANS viscosity (II)

• Possible delay in the formation of instabilities in the free shear layer (III)

• Recovery of the reattached boundary layer (IV)

The same flow conditions have been used by all partners involved. The inlet state is defined by a mean flow

velocity of 50 m/s, a static temperature of 520 K and a static pressure of 99990 Pa. At the outlet, it is

recommended to impose a pressure equal to 100400 Pa. Finally, a no slip adiabatic condition is applied at the

walls as well as lateral periodic conditions.

The proposed “common” grid is the same as the one used by Sainte-Rose et al. [49]. The extent of the

domain upstream of the step is equal to 34h to ensure a boundary layer thickness of 13mm at the separation point.

The structured multi-block mesh has four domains and the total number of grid points is Nxyz =3.76 106 and Nz=36

points are used in the spanwise direction.

Figure 1.4 Dimension of the computational domain.

A view of the grid is further shown in Figure 1.5. One can notice that particular attention has been paid to the

shear layer development of the vortical structures.

Figure 1.5: Visualisation of the grid (Nxyz=3.76 106)

1.3.3 Test Case 2.1: LEISA F15 High-Lift Configuration

The DLR F15 three-element airfoil was studied experimentally in the DLR project LEISA (Low noise exposing

integrated design for start and approach, 2005-2008) [54, 55]. The underlying contour is a wing section of the

FNG wing by Airbus. The wind tunnel data are from the low-speed wind tunnel at DLR Braunschweig (NWB).

The wind tunnel model has a retracted chord length C = 0.6 m, a span of S = 2.8 m, and thus the aspect ratio span

to chord is 4.66. We note that the slat chord Cslat is around 20%C. The deflection angles are 28.8o for the slat and

38.3o for the flap. The trailing edges of all three elements of the WT model are blunt and given by straight lines.

The lower edge of the slat is sharp. This configuration is called “OptV2“, since the flap position is optimized in

the sense that the flow remains attached on the flap at high Reynolds numbers relevant for flight conditions. This


11

case is of interest as the flow separates on the flap for small Reynolds numbers typical for wind-tunnel conditions.

For incidence angles α smaller or equal α = 9o, the flow remains attached on the wind tunnel side walls until the

position on the flap where separation occurs. Therefore the correction of the angle of attack for 2D numerical

simulations is expected to be less than α = 1o. The inflow conditions are Ma = 0.15 and Re = 2.1 million. The

uncorrected incidence angle is 7.05o. Experimental data cover mean pressure coefficient Cp in three spanwise

sections at positions η = y/S = 0.5 (mid span), η = 0.11, and η = 0.89, where S denotes the model span and y is the

span-wise coordinate.

This case is of considerable interest from the viewpoint of industrial aerodynamics. On the one hand, the aim is to

study the behavior of hybrid RANS-LES methods for the confluent boundary layers on the flap with the wake

flow of the main wing element and the flow separation on the flap. Moreover, we focus on the unsteady flow field

in the region of the slat cove, where classical RANS models fail to predict the turbulent kinetic energy

distribution, which is of great importance for a proper prediction of noise generation and the underlying

mechanisms.

1.3.4 Test Case 2.2: VFE-2 Delta Wing

The VFE-2 delta wing has been used within the NATO RTO task group AVT-113 for extensive experimental and

theoretical investigations. It has a sweep angle of 65º and can be equipped with four different leading edges (LE):

sharp (S), rounded with small radius (SR), rounded with medium radius (MR), and rounded with large radius

(LR). The geometry of the VFE-2 Delta wing is illustrated in Figure 1.6.

Figure 1.6: Geometry of delta wing [RTO-TR-AVT-113, Chapter 25]

With increasing angle of attack, α, the flow around the wing undergoes three major regimes [56], which are

further affected by the leading-edge (L.E.) shape of the delta wing, as tabulated in Table 1.1.

Table 1.1: Highlight of flow regimes with increasing AoA, .

AoA =13o =18

o

=23o

Flow features Onset of vortical flow separated flow without

vortex breakdown

separated flow with vortex

breakdown

Sharp L.E. separated flow separated flow separated flow

Medium radius

rounded L.E.

partly attached, partly separated

flow separation and vortex motions

intensive flow separation and vortex motions


12

Within the GARTEUR AG49 work, hybrid RANS-LES computations have been undertaken to investigate the

flow physics for different angles of attack and leading edge geometries. Experimental data are available from

wind tunnel tests conducted at TUM [79, 80].


13

2 Modelling and Simulation Approaches In this section, the modelling and simulation approaches used in the computations by AG members are presented.

The hybrid RANS-LES models are usually those that have been incorporated in respective in-house CFD solvers.

Some of the models have been developed by the partners themselves.

2.1 Hybrid RANS-LES Models

The hybrid RANS-LES models used in the computations include the SA (Spalart-Allmaras) model based DES and

improved variants (DDES and IDDES), the X-LES, the ZDES, the HYB0 and the HYB1 model. Below, these

modelling approaches are briefly introduced.

2.1.1 DES, DDES and IDDES models

Using the Spalart-Allmaras RANS model as base model, the so-called “Detached Eddy Simulation (DES)” has

been formulated [1]. Following this development, two improved DES variants, DDES (Delayed DES) and IDDES

(Improved DDES), have been further proposed [16, 51]. These models have been used in the computations by AG

members, and are thus briefly described here.

In the Spalart-Allmaras model [50] the eddy viscosity is computed through a partial differential equation for

a working variable related to the eddy viscosity through the relation

1 ,t vf (1)

where is the ratio

,

(2)

( is the fluid´s kinematic viscosity), and

3

1 3 3

1

v

v

fc

(3)

is a damping function. The working variable ~ is computed from the following field equation:

2 1 2

Pr

2

211 2 12

1( ) (1 )

,

b b t

Convectionoduction

Diffusion

bw w t t

Trip

Destruction

u c c f St

cc f f f U

d

(4)

where u

is the velocity vector of the fluid. The production term is defined using the following functions:

22 2,v

w

vS S f

d (5)

2

1

1 ,1

v

v

ff

(6)


14

where wd is the distance to the closest wall, is Von Karman´s constant and S u is the magnitude of

the vorticity. The destruction term is built from the functions:

1/ 66

3

6 6

3

1,w

w

w

cf g

g c

(7)

6

2 ( ) ,wg r c r r (8)

2 2.

w

vr

d S (9)

The function ft2 is introduced into the production and destruction terms in order to make v~ = 0 a stable solution to

the linearized problem. It is defined as:

2

2 3 4exp( )t t tf c c (10)

Finally, the trip term is given by the following function:

22 2 2

1 1 1 2exp ( )t

t t t t w t tf c g c d g dU

(11)

where dt is the distance to the nearest trip point, t is the vorticity at the wall at the trip point, U is the norm of

the difference between the velocity at the trip point (zero if the wall is stationary) and the field point under

consideration, and gt = min(0.1, U / t x) where x is the grid spacing along the wall at the trip point. The trip

term allows one to specify explicitly the turbulent transition points. Many implementations of the SA model

ignore the ft2 term, which was a numerical fix in the original model in order to make zero a stable solution to the

equation with a small basin of attraction (thus slightly delaying transition so that the trip term could be activated

appropriately). It is argued that if the trip term is not used, then ft2 is not necessary. The equations are the same as

for the "standard" version (SA), except that the term ft2 does not appear at all.

The different constants in the model take the values:

1 2

1 21 2 32

1

1 2 3 4

0.1355, 0.622 ,

2 / 3, 0.41 ,

1, 0.3, 2 ,

7.1, ,

1, 2, 1.2, 0.5 .

b b

b bw w w

v

t t t t

c c

c cc c c

c

c c c c

(12)

Detached-eddy simulation (DES-97) [1] is a non-zonal hybrid RANS-LES model that can be based on all

common RANS models. DES is obtained by replacing the original turbulent length scale in the dissipation term of

the underlying RANS-model (which is the one-equation Spalart-Allmaras (SA) model in this section) by a new

length scale DES

, resulting in an LES-like behavior away from the wall. To be more precise, the production and

destruction terms P and D in the SA-RANS model are:

2

11 2 1 22(1 ) , b

b t w w t

w

cP c f S D c f f

d

(13)

Here is the Spalart-Allmaras viscosity, S is a modified vorticity, 2 and t wf f are model functions, 0.41

is the von Kármán constant and 1bc and

1wc are model constants. The turbulent length scale in the destruction

term D , which is given by the wall distance wd in Eq. (13), is then replaced by:


15

maxmin( , ), max[ , . ], 0.65 .DES w DES DESd C h x y z C (14)

Near a wall DES

equals wd , ensuring normal SA-RANS mode. Farther away from a wall

DES DESC ,

leading to

(15)

which is analogous to a LES-Smagorinsky model.

Delayed Detached-Eddy Simulation (DDES). As a potential shortcoming in the DES-97 model described above,

the filter ∆ is only based on grid properties, but not on the actual flow field. If a fine grid is used in streamwise

and wall-normal direction, the LES region of the DES model can be shifted into the boundary layer. This may

lead to grid-induced separation resulting from modelled-stress depletion, which is especially undesirable when

dealing with airfoil stall. Moreover, grid-dependent flow solutions can occur, making a grid convergence study

virtually impossible.

In order to address these issues, the Delayed DES (DDES) [16] has been introduced. Here the RANS-LES

switch is also based on local flow properties, thereby eliminating most disadvantages of the original DES model.

The length scale DDES

in DDES is given by:

3

2 2

, ,

max(0, ) ,

1 tanh (8 ) ,

.

DDES w d w DES

d d

td

i j i j w

d f d C

f r

rU U d

(16)

Here is the molecular viscosity, t is the kinematic eddy viscosity and ,i jU are the velocity gradients. Within

a boundary layer 0df , leading to DDES wd and thereby ensuring normal SA-RANS-mode. Outside the

boundary layer 1df , resulting in min( , )DDES w DESd C , which is the original DES model introduced

above.

The term in Eq. (16) is a low-Reynolds correction required to obtain Smagorinsky-like behaviour in the

LES branch at locally low eddy-viscosity levels [51]:

22 1 2 2 2 1

2 1

1 ( (1 ) ) /( )

(1 )

b t t v w w

t v

c f f f c f

f f

(17)

Here 1 2 2, , , and v v t wf f f f are functions and constants from the SA-RANS model. The original formulation in

Spalart et al. includes the function 2

2 3 4exp( ( / ) )t t tf c c which is introduced into the production and

destruction terms in order to make 0v a stable solution to the linearized problem.

Improved Delayed Detached-Eddy Simulation (IDDES). Besides classical applications of the detached-eddy

simulation, where the LES region is usually strictly limited to separated flows, a DES can in principle also act as a

wall-modelled LES (WMLES). Here, the large outer part of an attached boundary layer is treated in LES mode,

whereas only a thin near-wall region is modelled via RANS. However, it was found that in both DES and DDES,

the modelled and the resolved parts of the logarithmic layer are mismatched and lead to wrong skin friction

predictions. This defect has been addressed with a new version called Improved DDES (IDDES) [52].

The first key element in IDDES is a redefinition of the subgrid length-scale, since the classical length-scale ∆ in Eq. (14) was found to require different subgrid-model constants when applied to wall-bounded turbulence and

free turbulent flow, respectively. Therefore, suited length-scale definitions for the two limiting cases are derived to

construct a linear blending which satifies both demands in a single subgrid length-scale:

max maxmin(max( , , ), )w w w wnC d C h h h (18)


16

It involves the wall distance wd , the wall-normal grid spacing

wnh and an empirical constant 0.15.wC

The second element is the definition of a new hybrid length-scale IDDES

to be inserted in the turbulence model’s

destruction term instead of the DDES length-scale DDES

from Eq. (16). It acts much like DDES in unresolved,

attached boundary layers (RANS mode) and free turbulent flow (LES mode), respectively, but quite differently in

boundary layers containing resolved turbulence (WMLES mode) in order to avoid the log-layer mismatch. For

this purpose, two empirical functions, stepf and

restoref , are introduced to properly control the blending between

the RANS length-scale RANS wd for the SA model and the LES scale LES DESC in the WMLES branch

as:

(1 ) (1 )WMLES step restore RANS step LESf f f (19)

Eq. (19) includes the low-Reynolds correction term Ψ from Eq. (17) to ensure consistent behaviour at very low

modelled turbulence levels. Here, stepf is to provide a more rapid switching from RANS to LES mode with

increasing wall distance

2

maxmin 2exp( 9 ),1.0 , 0.25 / ,step wf d h (20)

whereas the “elevating-function” restoref locally increases the modelled Reynolds stresses near the RANS-LES

interface to correct the log-layer mismatch:

max ( 1),0 .restore hill ampf f f (21)

The functions hillf and ampf read:

2

2

2exp( 11.09 ) , 0 and 1 max( , ) .

2exp( 9 ) , 0hill amp t lf f f f

(22)

Whilehillf serves to guide the elevation of the modelled stresses only based on grid properties, the function ampf

contains flow field information divided in turbulent (tf ) and laminar (

lf ) parts as:

2 3

2 2 10

, ,

tanh ( ) with ,max ,10

tt t dt dt

w i j i j

f c r rd U U

(23)

2 3

2 2 10

, ,

tanh ( ) with .max ,10

l l dl dl

w i j i j

f c r rd U U

(24)

ampf ensures that the elevation of modelled Reynolds stresses is limited to the case, where the IDDES operates in

WMLES mode. The empirical constants are 1.63tc and 3.55lc for Spalart-Allmaras as the RANS

background model.

The remaining blending of the WMLES length-scale, Eq. (19), with the DDES length-scale, Eq. (16), can be

written as

(1 ) (1 )IDDES hyb restore w hyb DESf f d f C (25)

Here, hybf is a blending function

max(1 , )hyb dt stepf f f (26)

with 31 tanh (8 )dt dtf r , which is the turbulent part of the DDES delay function,

df , shown in Eq. (16)


17

DES-type methods have also been proposed using the SST model as base model. The DES formulation of the k-ω

SST turbulence model can be obtained by changing the turbulent length scale defined as

*

2/1

tL in the

following way:

),min(~

DESt CLL (27)

where Δ is a measure of the grid spacing and * and CDES are constants.

The length scale L~

is used in the dissipation term of the ω equation of the SST model that in DES

formulation reads as:

LD ~

2/3 (28)

The constant DESC is computed as the other constants of the SST model through a blending function F1

DESDESDES CFCFC 11)1( (29)

The values of the two constants are 0.61 and 0.78 respectively.

The formulation described above has been modified in order to prevent the activation of the DES limiter

inside the boundary layer and avoid possible grid-induced separations. To this aim the blending function F1 is

employed and the DDES formulation of the κ-ω SST model is obtained. The destruction term of the ω equation is

then written as

DESFD * (30)

with

1,1 1F

C

LMaxF

DES

tDES

(31)

2.1.2 Zonal Detached Eddy Simulation

Zonal Detached Eddy Simulation (ZDES) has first been proposed in Refs [42,43] and a generalized formulation

including implementation details have recently been proposed in [39]. ZDES differs from DES97 or DDES by the

fact that within ZDES, the user has to select individual RANS and DES domains as well as the hybrid length scale

corresponding to the problem of interest (problem of category I, II or III, see Figure 2.1.

Figure 2.1: Classification of typical flow problems. I: separation fixed by the geometry, II:separation induced by

a pressure gradient on a gently-curved surface, III: separation strongly influenced by the dynamics of the

incoming boundary layer.

In the frame of ZDES, a sensor named mode (mode =0, 1, 2 or 3 chosen according to the category of the

problem as previously defined) is introduced to select the proper hybrid length scale.

The ZDES length scale reads as:


18

3mod~

2mod~

1mod~

)(0mod

~

eifd

eifd

eifd

RANSieeifd

d

III

DES

II

DES

I

DES

w

ZDES

(32)

In practice, the formulas of ZDES differ from those of DES97 or DDES in the definition of the ZDES length

scale, the subgrid length scale and the treatment of the near wall functions in the LES mode as detailed in the

following.

mode I of ZDES (mode = 1), location of separation fixed by the geometry:

I

DESDESw

I

DES Cdd ~

,min~

(33)

mode II of ZDES (mode = 2), location of separation unknown a priori:

II

DESDESwdw

II

DES Cdfdd ~

,0max~

(34)

mode III of ZDES (mode = 3), Wall-Modeled LES (WMLES):

otherwised

ddifdd

I

DES

erface

wIII

DESw

~~

int

(35)

Concerning this latter mode devoted to WMLES (see Sec. 5.1), the switching into LES mode occurs at a given

altitude erface

wd intprescribed by the user. In this mode (see Ref. [45]), the solution has to be fed with turbulent

inflow content.

A second important ingredient of ZDES is the definition of the subgrid length scale ~

entering Eqs. (33),

(34) and (35). Indeed, analogous to the classical LES exercise ~

controls which wavelengths can be resolved as

well as the eddy viscosity levels. Though physically justified in the frame of DES97/DDES [46] aimed to shield

the attached boundary layer from MSD, the slow delay in the formation of instabilities in free shear layers of

DDES has been partly attributed to the use of the maximum grid extension max =max (x,y,z) as subgrid

length scale. The use of the cubic root of the cell volume vol = (xyz)1/3

decreases dramatically the level of

predicted eddy viscosity because this latter value is proportional to the square of the filter width. Chauvet et al.

[44] proposed an efficient flow-dependent definition based on the orientation of the vorticity vector

aimed at

solving the slow LES development in mixing layers. A generalization of Chauvet et al. subgrid length scale has

been proposed in [43] and may read as:

S (36)

where S is the average cross section of the cell normal to

. More precisely; it introduces the notion that at

any spatiotemporal point, if the vorticity is not zero, there exists one particular direction indicated by the vorticity

.

Figure 2.2: Definition of the subgrid length scale S . S is the average cross section of the cell normal

to the vorticity vector

.


19

Finally, the subgrid length scale is defined in a zonal manner according to the problem of interest (see [39]). The

subgrid length scale that enters Eq. (2) and Eq. (3) is respectively given by:

andUzyx volji

I

DES ,,,,~

(36)

and

0

0max~

dvol

ddII

DESffifor

ffif

(38)

II

DES~

clearly borrows ideas from DDES in the sense that the fd sensor is employed to determine whether max or

vol (or ) is used. Eqs. (37) and (38) are not a minor adjustment in the DES framework since the modified ~

length scales depend not only on the grid but also on the velocity and eddy viscosity fields. It is important to

emphasize that the shielding of the boundary layer is still ensured by Eq. (34) which behaves as standard DDES

( = max) as long as fd < fd0. The improvement lies in (or vol) becoming the new subgrid length scale when fd

> fd0 which solves the delay in the formation of instabilities (see [39]).

2.1.3 Extra Large Eddy Simulation (X-LES) Models

In the X-LES method [34], as in similar DES-type methods, a single set of turbulence-model equations is used to

model both the Reynolds stresses in RANS zones and the subgrid stresses in LES zones. The X-LES method in

particular is based on the TNT k–ω model. The method switches to LES when the RANS length scale (l = k1/2

/ω)

exceeds the LES length scale (C1Δ, with Δ the filter width and C1 = 0.05). The RANS length scale is then replaced

by the LES length scale in the expression for the eddy viscosity (νt = k1/2

l) as well as in the expression for the

dissipation of turbulent kinetic energy (ε = β k3/2

/l, with β = 0.09). The filter width Δ is defined at each grid point

as the maximum of the mesh size in all directions.

To improve the capturing of free shear layers, two modifications have been added to the X-LES method. The first

modification consists of a stochastic SGS model [35], in which a stochastic variable ξ = N(0,1) is introduced in the

expression for the eddy viscosity in LES mode, by multiplying the eddy viscosity with ξ2. At each time step, a

new value of ξ is drawn for every grid cell. The stochastic term is not included in the turbulent dissipation.

The second modification consists of a high-pass filtered (HPF) SGS model [36]. In order to avoid high SGS

stresses in the initial shear layer, the SGS stresses are computed from the velocity fluctuations u' instead of the

instantaneous velocity. The velocity fluctuations u' are obtained by applying a temporal high-pass filter to the

velocity field. This high-pass filter consists of subtracting the running time average of the velocity from the

instantaneous velocity.

2.1.4 Algebraic (HYB0) and One-Equation (HYB1) Hybrid Models

Two other models used in the AG work are the hybrid RANS-LES modelling based, respectively, on an algebraic

(zero-equation) formulation (HYB0) [8,9] and a one-equation formulation (HYB1) [8]. With the HYB0 model for

both incompressible and compressible flows, the turbulent stress tensor, ij , is modelled using the eddy viscosity

concept for both RANS and LES modes in the form of

kkijkkijijhij SS 3

1

3

12

(39)

where μh is the hybrid eddy viscosity and Sij is the strain rate tensor. Note that, for incompressible flows, the

isotropic part of the stress tensor is usually absorbed into an effective pressure, and the trace for the strain rate

tensor is zero due to continuity. For compressible flows, the isotropic part in the LES mode may be modelled as 222 SCIkk , where is the LES filter width and |S| is the magnitude of the flow strain rate tensor. For the

near-wall RANS mode, the turbulent kinetic energy, k, may be estimated by 2 lk h , where lμ is a turbulent


20

length scale. Based on a number of calibrations, we have set CI = 0. In addition, for modelling compressible flows,

the transport equation for the total energy, E, is solved, in which a model for the turbulent heat flux vector is

incorporated. We have adopted the eddy diffusivity model for both the RANS and LES modes, namely,

kh

hk

x

Th

Pr

(40)

where Prh is the turbulent Prandtl number and Prh = 0.4. This value is commonly used as the SGS Prandtl number

in LES for turbulent thermal convection flows. For the near-wall RANS mode, the mixing-length concept is used

to formulate the eddy viscosity by Slt

2~~ , where the length scale, lμ, is proportional to the wall distance d,

reading dfl ~

and = 0.418 being the von Karman constant. To avoid the awkwardness of using wall-shear

related parameters in the formulation when modelling separating flows, the empirical damping function fμ is

formulated in the form of 5.2tanh 3/1

tRf as a function of the RANS turbulent Reynolds number, ttR ~ .

In the LES region, the Smagorinsky SGS model is employed, viz. SCssgs

2 , where 12.0sC

and 223/22

max V . Note that V is the local control volume, max is the local maximum cell size,

zyx ,,maxmax, or the local maximum edge size for unstructured grids. The matching between the RANS

and LES modes is accomplished by modifying the RANS length scale into sfll

~ so that Slt

2

for the

RANS mode, where sf is a function of

sgstsR /~ and

5.2exp

75.4exp

2

13.075.0

sss

RRf (41)

The use of the function, fs, is to achieve a smooth transition for the RANS-LES length-scale adaptation, which

makes the near-wall RANS mode produce interfacing turbulence that is comparable to the resolve-turbulence in

order to attain a realistic matching with the LES mode. The eddy viscosity for the HYB0 model, h , is computed

by sgsh if l

~, and

th otherwise.

In AG49, FOI has further worked on an improved LES modelling formulation by introducing energy backscatter

into the SGS model in combination with the original SGS eddy viscosity model [61, 62]. Instead of taking the

conventional formulation of a similarity SGS model, the backscatter part has been cast in a formulation based on

velocity gradients by means of a Leonard expansion [61]. The addition of the energy backscatter part to the LES

mode has been motivated to better resolved the so-called “grey area” arising usually in hybrid RANS-LES

computations where the RANS-modelled boundary layer is detached (or separated) and is further evolving into a

free shear layer that is to be treated by the LES mode. This has actually been investigated by other AG49

members in the computations of the test cases, particularly, for the mixing -layer and backward-step flows. The

energy-backscatter formulation has been calibrated in combination with the HYB0 model (forming the HYB0M

model). It is noted here that the energy-backscatter function can actually incorporated into any other SGS eddy

viscosity model with appropriate modelling calibration.

In the HYB1 model [61], the transport equation for the turbulence kinetic energy, k, is used in the hybrid one-

equation model, reading

hj

h

jj

iij L

kCx

k

xx

u

Dt

kD

2/3

(42)

where ,3

22 ijijhij kS and kLC hkh with 07.0kC and 6.0C . The two length scales, hL

and hL , are determined in the RANS mode by, respectively, yCCl 4/3 with 09.0C and 418.0 ;

and kCyfCl /4/1

, where 90exp1 yy RRf and ykRy . In the LES region the filter size,

3/1

,, Vll sgssgs . The length scales in the HYB1 model are then determined by, respectively,

rh llL ,max,min and rh llL ,min,min , where lllr .


21

2.2 Information of CFD Solvers

In the computations of test cases, several in-house CFD source codes have been used, in which the modelling

approaches have been well implemented and calibrated in previous activities. Below a brief introduction of each

CFD solvers used by the AG members is provided.

CIRA has used two in-house CFD solvers, UZEN (Unsteady Zonal Euler Navier-Stokes), and SIMBA

(Simulation system based on IMmersed Boundary Approach). Both codes are based on the RANS equations and

have been validated on several benchmarks.

The UZEN solver is a multi-block well assessed tool for the analysis of complex configurations in the

subsonic, transonic, and supersonic regimes [61]. The equations are discretized by means of a standard cell-

centered finite volume scheme with blended self-adaptive second and fourth order artificial dissipation. The

pseudo time-marching advancement is performed by using the Runge-Kutta algorithm with convergence

accelerators such as the multi-grid and residual smoothing techniques. The turbulence equations are weakly

coupled with the RANS equations and solved only on the finest grid level of a multi-grid cycle. A time-accurate

version of the flow solver has also been developed [63]. The time integration is based on the dual-time stepping

method where a pseudo steady-state problem is solved at each physical time step.

The SIMBA simulation system is composed of the mesh generation module SIMBA_MESH and the flow

solver module SIMBA_FLOW [64]. The whole method is aimed to simplify and speed up the pre-design process

of aerodynamic-type configurations. The mesh is based on a Cartesian method. A fully unstructured data

management is adopted to allow a robust and automatic grid refinement procedure. The flow solver is based on a

finite-volume Cartesian method coupled with an Immersed boundary technique. The differential equations are

solved by a cell-centered finite volume method based on a second-order central difference for the convective

terms with added artificial dissipation to damp the oscillatory nature of the scheme. The integration procedure is

obtained by using Runge-Kutta pseudo-time relaxation. Local time stepping is performed in each cell to accelerate

convergence together with enthalpy damping. Euler and low-Reynolds number flows can be studied simply

solving the Navier-Stokes equations coupled with the IB technique near wall surfaces. The RANS equations and a

proper wall modelling make affordable the simulation of high Reynolds number flows in the engineering

approximation field [65]. The immersed boundary methodology is applied by a discrete forcing approach. The

body force that mimics the effect of the body on the flow is obtained by the imposition of a direct boundary

condition. The face-center quantities can be reconstructed by using different interpolation schemes involving

surrounding known values (cell centers, wall points) and the IB local unit normal vector.

DLR and INTA have conducted the simulations with the DLR TAU code [49], which is a compressible

finite-volume flow solver for unstructured and hybrid meshes. The solver uses an edge-based dual-cell approach,

i.e. the method is of cell-centered type with respect to the dual-mesh cells. Viscous fluxes are discretized using

central differences. To ensure low numerical diffusion all DES computations employ second-order central

discretization with matrix-based artificial dissipation. Low-Mach number preconditioning was not used, since we

found that the standard low-Mach number preconditioning implemented in TAU, which was developed for

steady-state problems, suffered from convergence problems in case of small physical time steps which are typical

for hybrid RANS-LES simulations. For the time discretization, a second-order backward differencing formula is

used together with the dual time stepping approach. Within each time step, the nonlinear problems are solved

using either a semi-implicit lower-upper symmetric Gauss-Seidel (LU-SGS) or a low-storage explicit Runge-

Kutta scheme together with a multigrid scheme of full approximation scheme type and residual smoothing for

convergence acceleration.

FOI has used the in-house Navier-Stokes solver, Edge, and an additional solver, CALA-LES, for

incompressible flows. The Edge solver, used to compute the two applied test cases (namely, the F15 high-lift

configuration and the VFE-2 Delta wing) in the AG49 work, is a node-based Euler/Navier-Stokes solver for the

compressible flow equation system using finite volume method. An edge-based formulation and a preprocessor

that translates element-based information into edge-based information allow the system to handle structured,

unstructured and hybrid grids seamlessly. Both the convective and viscous fluxes are approximated with the

second-order central scheme. A dual time-stepping method is employed, in which the physical time is advanced

using a second-order implicit scheme, while at each time step the governing equations are integrated toward

convergence with a 3-stage Runge-Kutta scheme based on local time steps and using implicit residual smoothing.

The convergence is accelerated with agglomeration multigrid where finer control volumes are fused to coarser

control volumes. An injection operator is used for prolongation, and its transpose for restriction. It should be noted


22

that the Edge solver has a local preconditioning approach incorporated for low-speed flow computations, which is

thus able to handle low-speed subsonic flow. It was observed, however, due to the density-based scheme inherent

in this compressible solver, it requires several times of sub-iteration numbers at each time step to reach

convergence as compared with an incompressible solver. This has thus motivated in the AG work the use of an

incompressible solver for the two fundamental TCs. This compressible solver was described in details by Eliasson

[67].

The incompressible, finite volume code, CALC-LES [68]. The numerical procedure is based on an implicit,

fractional step technique with a multigrid pressure Poisson solver [69] and a non-staggered grid arrangement. For

the momentum equations, second-order central differencing is used in space and the semi-implicit second-order

Crank-Nicolson scheme is used for time advancement.

NLR’s in-house flow solver ENSOLV employs a cell-centred finite-volume method to solve the

compressible Navier–Stokes equations on multi-block structured grids. For hybrid RANS–LES computations, a

fourth-order low-dispersion symmetry-preserving finite-volume method [37]is used. A central (instead of upwind)

discretization is used, so that the method contains no numerical dissipation. For large-eddy simulations, it is

important to prevent numerical errors from interfering with the sub-grid scale (SGS) model. For this purpose, the

method has two key features. First, the skew symmetry of the convection operator is preserved, so that kinetic

energy is only dissipated by the SGS stresses and not by numerical errors. Second, the numerical dispersion at

high wave numbers has been minimized, so that the numerical accuracy is high at small wave lengths close to the

filter width, where the SGS model does its work. The finite-volume method maintains its key properties (fourth-

order accurate, low numerical dispersion, no numerical dissipation) on non-uniform, curvilinear grids.

The equations are integrated in time by the 2nd

-order implicit scheme. The non-linear set of equations per

time step are solved by a multi-grid scheme, using Runge–Kutta pseudo time stepping with implicit residual

averaging as relaxation operator. Sixth-order artificial diffusion is added to ensure rapid convergence of the multi-

grid scheme in the RANS regions (typically the boundary layers), while maintaining fourth-order accuracy. An

appropriate level of the artificial diffusion for the LES regions is given in [36].

ONERA has used, for all applications, the in-house FLU3M code which solves the compressible Navier-

Stokes equations on multiblock structured grids. The time integration is carried out by means of the second-order-

accurate backward scheme of Gear. Temporal accuracy of the calculation was checked during the inner-iteration

process (typically four Newton-like inner-iterations are used to reach second order time accuracy). A decrease of

the inner-residuals of at least one order is obtained. The time step used for the calculation will be given for each

test case. The spatial scheme is a modified AUSM+(P) scheme. Further details concerning the numerical method

and implementation of turbulence models can be found in references [47, 48]. The accuracy of the solver for DNS,

LES and ZDES has been assessed in various applications.

TUM uses their CFD solver, INCA, a general-purpose multi-physics CFD solver, suitable for DNS and LES.

It can handle compressible and incompressible flows, single- and multi-phase systems with multiple species, real

or ideal fluid properties, phase changes and chemical reactions. For complex geometries, a semi-automatic built-in

routine can generate locally refined grids. Flow boundaries (stationary and moving) are represented by cut-cell

methods and it is possible to conduct simulations with moving frames of reference. As mentioned in the previous

subsection, INCA uses an implicit SGS-model based on ALDM and different wall models can be employed to

facilitate LES of high Reynolds number engineering flows. INCA is massively parallel, using OpenMP and MPI,

and can be run on thousands of CPUs [57].


23

3 Computations of Fundamental Flows In this Section, the results computed for the two fundamental test cases are presented. Cross comparisons have

been conducted of the computations by partners using different hybrid RANS-LES models.

3.1 Mixing layer

Simulations have been performed by FOI, INTA, NLR and ONERA. The details of the computational settings by

partners are summarized in Table 3.1.

Table 3.1: Computational information for the mixing layer

Partners Models XY-Domain / mesh Zmax / Nz t (sec) Time for statistical

analysis (sec)

FOI

HYB0

HYB0

LES-Smag.

3m×0.3m / 424×144

0.15m / 80

0.15 m / 40

0.15 m / 80

5 ×10-6

1 ×10-5

5 ×10-6

0.065

0.596

0.060

INTA

SA-DDES (lam)

SA-DDES

SA-DDES

SA-IDDES

Grid G2 0.15 m / 96

3.75 ×10-5

3.75 ×10-5

3.75 ×10-6

3.75 ×10-5

0.15

0.3

0.1875

0.48

NLR Zonal model

X-LES Grid G1 0.15 m / 48 9.6 ×10

-6 0.2

ONERA SA-DDES

ZDES Ref [39]

1.0m/96

Ref [39]

10-6

Ref [39] Ref [39]

It is further noted here that, in the computations

- The XY-mesh at the FOI mesh has 424×144 structured cells over a domain, which consists of the whole

flat plate (1 m in length).

- The SA-DDES (lam) by INTA used a laminar upper incoming boundary layer by activation of ft2. Only

the results corresponding to this simulation have been shown in the cross-plotting. The other three

simulations are not significantly different from ONERA’s SA-DDES computations.

- The NLR computation with the zonal model has imposed simple synthetic turbulence at the interface. The

zonal model does not employ an SGS model in order to suppress the dissipation, which gives actually the

“best” attainable result in terms of early shear layer development. The NLR computation with X-LES

includes the improvements for the grey area (high-pass filter and stochastic SGS model). With these

improvements, X-LES gives results approaching the results of the zonal computation [37]. Only the

results for the zonal model are shown here in the cross-plotting. Moreover, the time step corresponds to

CFL=1/8 based on the resolution in the test region and the velocity u1.

- The computational domain used by ONERA [39] is characterized by a larger size of the computational

domain which was found necessary to meet exactly the velocity profiles at the trailing edge. Besides,

DDES as well as ZDES mode 1 (RANS incoming boundary layer) and ZDES mode 3 (fluctuating inlet

conditions) have been assessed.

It is important to note that the grid resolutions used by the partners are different. The computational domain in

the FOI computations simulates the size of the flat plate (both the length and thickness) in WT testing. In other

computations using the NLR common grid, the plate thickness is assumed to be zero, and the locations of the

inflow sections for the upstream upper and lower boundary layers have been adjusted to match the measured

velocity profiles near the plate trailing edge.


24

As presented below, the difference in the computational settings in order to match the measured velocity

profiles of the two incoming boundary layers near the plate leading edge has played an essential role in the

prediction of the mixing layer development.

a) FOI; simulation 1; Q=105 s

2 b) INTA; Q=500 s

2

c) NLR; Q=8.4 105 s

2 d) ONERA-ZDES (mode 3); Q=8.4 10

5 s

2

d) ONERA-DDES; Q=8.4 105 s

2 e) ONERA-ZDES (mode 1); Q=8.4 10

5 s

2

Figure 3.1: Instantaneous Q-contours for the different simulations


25

The development of the shear layer can be judged best from the Q-criterion of a snapshot instantaneous flow

field. For the different simulations the results are shown in Figure 3.1. Note that the level of the Q-criterion is not

the same for all figures. Clear from these figures is that the standard DDES simulation show very little turbulent

content. Given the different grids for the remaining three simulations, the results compare qualitatively well: level

and detail are comparable

Based on these figures one is inclined to say that the HYB0 (FOI) and zonal methods (NLR and ONERA) are

capable of representing qualitatively the turbulent shear layer development, whereas the DDES model is not. This

conclusion will be elaborated further below by assessing other flow quantities.

It should be noted that the FOI computations, conducted at an early stage of the project and using a different

setup, were intended to provide reference solutions for modelling improvement to be tested on the same grid.

Unlike the proposed computational domain illustrated in Figure 1.2, a freestream condition at the inflow section

was imposed by including the whole splitting plate in the computational domain, while the converging section of

the WT (see Figure 1.1) was not considered due to the lack of information. Consequently, in the absence of flow

acceleration, the velocity profiles in the boundary layers differ significantly from the experimental measurements,

as shown in Figure 3.2, when approaching the trailing edge of the plate. This suggests that an appropriate

representation of the two incoming boundary layers prior to their mixing is essential for accurate predictions of

the resulting shear-layer properties. Moreover, the beveled trailing edge was not considered, but using a flat plate

with the same thickness in the FOI mesh, As shown below for the momentum thickness, the predicted wake after

the plate was exaggerated in the FOI computation.

Figure 3.2: Time-averaged streamwise velocity profiles and resolved fluctuations at x = 0.5mm after the

plate trailing edge by FOI. The example, computed without accounting for the WT convergence for the lack

of information, demonstrates the significant effect of incoming boundary layers on the prediction of the

developing shear layer.

The spreading rate of the shear layer is shown in Figure 3.3. Here and in all subsequent figures the color scheme is

fixed as follows: FOI results in green, INTA results in red, NLR results in orange, and ONERA results in blue.

The spreading rate can be visualized either by the momentum thickness, which is an integrated value over the

cross section perpendicular to the streamwise direction, or the vorticity thickness, which is based on the maximum

velocity gradient along the cross section. The momentum thickness critically depends on the height of the cross

section and whether the flow attains the free stream values. As the ONERA mesh has a larger height, no

momentum thickness results of ONERA are shown (it has been observed in the ONERA computations that the

computation of the momentum thickness is much more sensitive than the computation of the vorticity thickness).

For the FOI results there is a problem with the computation of the flow gradient due to the specifics of the mesh

near the centerline, so no vorticity thickness is shown for the FOI results.

The momentum thickness results in Figure 3.3a) show that the NLR results agree very well with the

experiment. The FOI results show the correct slope, but start at negative values of the momentum thickness. This

indicates that the wake behind the splitter plate is too strong: local velocities are less than the free stream velocity

u2 below the plate for a significant part of the cross-section. As discussed above, this has been caused by the

incoming boundary layer. The INTA results show a delayed spreading and a subsequently higher spreading rate

further downstream, with a slope higher than that of the experiment.


26

a) Momentum thickness b) Vorticity thickness

Figure 3.3: Spreading rate of shear layer measured in momentum and vorticity thickness

a) x=150mm b) x=250mm

c) x=650mm d) x=800mm

Figure 3.4: Velocity profiles

This pattern in the INTA results is repeated in the vorticity thickness, shown in Figure 3.3b). The DDES results of ONERA show the same behavior as those of INTA, although the spreading rate further downstream

seems to have the same slope as the experiment. The zonal ZDES result of ONERA agrees well with the


27

experiment, apart from the initial formation right behind the splitter plate. As demonstrated by other simulations

of ONERA [38] (not shown here), the initial development of the shear layer can be improved by adding synthetic

turbulence at the RANS-LES interface. This is consistent with the NLR results, although it should be mentioned

that NLR’s synthetic turbulence model is not as sophisticated as that of ONERA.

Velocity profiles are shown in Figure 3.4 at five different stream-wise stations. It is clear that the agreement

between the different simulations improves further downstream the comparison is done. At the last station all

results show a fully developed flow. At upstream stations, the differences are larger. The wake in the FOI results

at x =150 mm up to 250 mm shows an overdeveloped wake. This may be a result of the velocity profiles of

incoming boundary layers are inconsistent to the experimental measurement. The ONERA results show

decelerating flow at the early stations, a wake effect which is not fully understood. None of the simulations have

the same profile as the experiment at the first station.

Self-similarity velocity profiles are shown in Figure 3.5. All but the ONERA results show a ‘thinner’ profile

than the experiment at the early stations. As this effect is there for both DDES and ZDES simulation of ONERA,

this is either caused by the upstream RANS solution, the larger flow domain, or the fact that the splitter plate in

the experiment has finite thickness. At the last stations, the self-similarity plots are hardly distinguishable. Even

the evidently under-developed DDES results show the same profile as the experiment. This clearly shows that one

should distrust self-similarity plots.

a) x=150 mm b) x=250 mm

c) x=650 mm d) x=800 mm

Figure 3.5: Self-similarity velocity profiles


28

In the following figures (Figure 3.6 to Figure 3.8) the Reynolds stresses are shown. The DDES results strongly

deviate from the experiment at practically all stations, even far downstream. The other results (zonal, HYB0,

ZDES) show differences from the experiment in the initial shear layer, but they all tend towards the experiment in

downstream direction, resulting in a fair comparison of the stress levels at the last station.

a) x=150 mm b) x=250 mm

c) x=650 mm d) x=800 mm

Figure 3.6: Resolved normal stresses, <u'u'>

The HYB0 results show some improvement when the span-wise resolution is increased. There is little

difference between the HYB0 and LES simulations, as one might expect as the complete wake is in LES mode in

the hybrid simulations, in which the same SGS model (Smagorinsky model) has been used in the HYB0

formulation.

The growth rate of the shear layer can be related to the level of the Reynolds shear stresses. Higher stresses

imply higher mixing and entrainment and therefore a higher growth rate. The DDES results under-predict the

stresses and therefore also the growth rate in the initial shear layer, but over-predict both at the downstream

stations. The NLR and FOI results initially over-predict the stresses, which then decay towards the experiment

further downstream. Thus, the growth rate is initially too high in these results, but it is consistent with the

experiment downstream. The ZDES results show a similar behavior, although it is preceded by an under-

prediction of the stresses and growth rate.

The over-prediction of the stresses is typically caused by the turbulence being too two-dimensional, showing

strong spanwise vortices. This happens in all computations as a transition process towards full 3D turbulence. For

the DDES computations it happens far downstream, whereas for the other computations it happens close the


29

trailing edge. In the experiment, however, this process is not present, as the turbulence in the shear layer is fed by

the turbulence from the boundary layers.

a) x=150 mm b) x=250 mm

c) x=650 mm d) x=800 mm

Figure 3.7: Resolved normal stresses, <v'v'>.

Finally, Figure 3.9 shows the spectra at x = 200 mm and x = 800 mm. It is evident from the results at x=200 mm

that the DDES model does not produce the correct spectrum. The frequency content at x=800mm of FOI, ONERA

and NLR is consistent with the different grid resolutions used.

Based on the computations for this test case, the following conclusions have been reached.

The standard DDES model is unable to predict the turbulent development of the shear layer.

HYB0, zonal methods (with and without synthetic turbulence) and improved X-LES are able to predict

the correct spreading rate in terms of momentum and vorticity thickness.

Detailed comparison of the performance of the different models based on the velocity profiles and

Reynolds stresses reveals quite some differences between the methods, especially at the start of the shear

layer. In this regions, the turbulence in the computations “transitions” to full 3D turbulence. This process

apparently depends strongly on the model employed and the resolved/modelled upstream incoming

boundary layers.


30

a) x=150mm b) x=250mm

c) x=650 mm d) x=800 mm

Figure 3.8: Resolved turbulent shear stresses <u'v'>.

a) x=200 mm b) x=800 mm

Figure 3.9: Power spectral density (PSD) of streamwise velocity.


31

3.2 Backward-facing Step Flow

A large amount of flow simulations have been carried out by three AG49 partners. Table 3.2 shows an overview

of the computations that are considered as the final results. Seven Hybrid models have been assessed and DDES

was used by two partners. It is also worth noting that each partner used a second-order accurate (both in time and

space) numerical solver with an implicit time integration.

Table 3.2: Overview of computations carried out for backward-facing-step test case

Partner model Struc/

Unstr.

Convective

fluxes

Time

integration

Time step

t

No. of sub-

iterations

CIRA DDES-SA

DES-SST

UZEN

Struct 2

nd-order central

2nd

-order implicit

(dual) 10

-6s 18

FOI HYB0, HYB1,

LES (Smag.)

CALC

Struct 2

nd-order central

2nd

-order Cranck-

Nicholson

7×10-7

s

(1.e-3h/U∞)

2 to 3

ONERA RANS, DDES,

ZDES(mode 2)

FLU3M

Struct AUSM

2nd

-order

implicit (Gear) 10

-6s 4

In the following paragraphs the results are discussed. First, some flow visualizations are examined. Next, the

Reynolds averaged data, namely mean and fluctuating streamwise velocity field, are analyzed. Finally, some

spectral analysis of the velocity field is discussed.

Figure 3.10: Instantaneous eddy viscosity fields for the backward facing step (TC 1.2).Upper-left: DDES

(CIRA), Upper-right: DDES (ONERA); Lower-left: SST-DES(CIRA), Lower-right: ZDES (ONERA).


32

Figure 3.10 displays the instantaneous eddy viscosity field for the backward facing step for both DDES

calculations, SST-DES and ZDES. The eddy viscosity levels are close to zero for the SST-DES calculation,

indicating clearly a Modelled Stressed Depletion (MSD) case. Though different t/ values are observed in the

two DDES calculations (presumably due to the different numerical methods employed, see Table 3.2, the behavior

of the model is nearly the same. The attached boundary layers on the upper wall as well as upstream from the

separation are treated in RANS mode. The behavior of ZDES (in its mode II) in the attached boundary layers is

similar to DDES owing to its design. The main differences between DDES and ZDES come from the treatment of

the separated area where very low levels are observed within ZDES while high eddy viscosity levels are advected

from the RANS regions in the DDES calculations. This can be attributed to the much stiffer source terms

characterizing the ZDES formulation.

Figure 3.11 Instantaneous Schlieren for the backward facing step (TC 1.2).TOP: Left: DDES(CIRA) Right:

DDES (ONERA), BOTTOM: Left: SST-DES(CIRA) Right: ZDES (ONERA)

These different behaviors of the models have dramatic consequences concerning the flow development

downstream the step as educed from Figure 3.11 showing the instantaneous Schlieren as well as an iso-surface of

the Q criterion. Indeed, the slow Large Eddy Simulation development in the mixing layer is clearly evidenced in

the DDES calculations since the mixing layer becomes unstable only at x/h 3. Conversely, ZDES switches

immediately in LES mode downstream of the separation point as highlighted by the eddy viscosity fields (see

Figure 3.10). The flow topology featured by the DES-SST calculation is completely different showing one again

the sensitivity of this BFS flow to the modelling approach.


33

Figure 3.12: Mean streamwise velocity at several locations


34

Figure 3.13: Streamwise velocity fluctuation profiles at several locations

To get a more quantitative insight between the different approaches used within this project, Figure 3.12

presents the mean velocity profiles obtained from the different partner computations compared with experiment

and a reference RANS-SA calculation. Upstream from the step (i.e. x/h <0), the flow remains attached but several


35

discrepancies between the different calculations can still be noticed. While an excellent agreement with

experiment is obtained with the HYB1 model from FOI, the DES-SST calculation features a quasi-laminar

behavior (see also Figure 3.10). Note also that RANS, DDES and ZDES are quite similar owing to their design.

Downstream the step (e.g. at x/h = 1.1), most calculations yield to an overestimation of the backflow intensity

which is only well predicted by the HYB1 and ZDES models. These findings also apply at further downstream

locations. It is also worth noting that significant differences are obtained between both DDES calculations (CIRA

& ONERA) though the same grid and models are used. In addition, the DES-SST calculation displays several

recirculations on the top and lower walls which are neither observed in the experiment nor by the other

calculations.

The velocity fluctuation profiles at several streamwise locations are displayed in Figure 3.13. Analogous to

the mean velocity profiles, poor predictions are obtained with the DES-SST calculation. The level of fluctuations

is also dramatically overestimated by the Smagorinsky model. Conversely, the early stages of the mixing layer are

well predicted by the HYB1 and ZDES models.

The spectra of the fluctuating vertical velocity component are displayed in Figure 3.14 for three locations.

The first station is located in the early stage of the mixing layer close to the step and spectra display several peaks

at frequencies characterizing the roll-up of the shear layer. As an example for the ZDES calculation, the frequency

fh/U0=1.6 corresponds (when scaled with the vorticity thickness) to f/U0= 0.165 which is the fundamental

frequency of the Kelvin Helmholtz fKH in the present case. The subharmonic (i.e. fKH/2) is also clearly identified

here at fh/U0= 0.8. In accordance with Figure 3.12, ZDES improves results in the early stages of the mixing layer

while the fluctuations levels are dramatically underestimated with DDES. It is worth noting that the HYB0, HYB1

and LES (with Smagorinsky model) results are close to each other.

Figure 3.14: Power Spectral Density of the vertical velocity component fluctuations

At station 2, only the sub-harmonic is growing due to the vortex pairing inside the mixing layer. Its signature is

shifted towards lower frequencies at fh/U0 ≈ 0.4) since the mixing layer has thickened. At this location, the DDES

spectrum is again characterized by lower fluctuation levels and lacks high frequency content. Figure 3.10


36

evidences that within DDES the mixing layer becomes unstable only at x/h ≈ 3, leading to very large unphysical

structures whose spectral signature is evidenced by a low frequency peak in Figure 3.14.

The last point is still located in the mixing layer but is already affected by the reattachment region so that the

level of velocity increases in a broadband manner. Spectra display a low frequency contribution near fh/U0= 0.16

which is close to the range of the expected shedding frequency. Driver et al. [41] identified the shedding at

normalized frequencies lying in the range 0.114−0.13.


37

4 Complex Aerodynamic Flows

4.1 LEISA High-Lift Configuration

An overview of the simulations performed by the partners is given in Table 4.1, where Lz denotes the spanwise

extension of the computational domain, C is the retracted chord length and Nz denotes the number of cells in

spanwise direction. Moreover we give the number of convective time units (CTUs) used for statistical averaging

and the number of physical time steps per CTU, Nt per CTU. All simulations used a laminar slat and a

transitional wing and flap, except ONERA and DLR-3, who assumed full turbulent boundary layer around flap.

Regarding the NLR-simulations, (1) : delayed mode, (2): stochastic SGS-model and (3): high-pass filtering for

SGS. Recall that the spatial discretization of NLR is 4th

-order (4) and that the temporal discretization is also

improved (5). ONERA-2 used a synthetic eddy method with dynamic forcing [39, 74].

Table 4.1: An overview of the simulations performed by the partners

Partner Hybrid

model

# Nodes per

2D plane Lz/c Nz

CTUs

(average) Nt per

CTU

DLR-1 SA-DDES 200000 0.09 40 5 582.8

DLR-2

SA-DDES

with RANS

box

200000 0.09 64 10 582.8

DLR-3 SA-IDDES 200000 0.09 64 10 582.8

FOI-1 HYB0 200000 0.08 40 15 291.4

FOI-2 SA-DDES 200000 0.08 40 25 291.4

FOI-C1 HYB0 200000 0.08 40 11 582.8

FOI-C2 HYB0 200000 0.16 80 10 582.8

FOI-C3 HYB0 200000 0.16 160 10 582.8

FOI-C4 HYB0 200000 0.16 160 6 1165.6

NLR-1 TNT kω

XLES (2), (3) 81000 (4) 0.18 64 18.2 1421.3 (5)

NLR-2 TNT kω

XLES (1), (3) 81000 (4) 0.18 64 16.1 1421.3 (5)

NLR-3 EARSM

XLES (2), (3) 81000 (4) 0.18 64 16.1 1421.3 (5)

ONERA-1 SA-ZDES

(mode I+II) 380000 0.16 128 5.1 58275

ONERA-2

SA-ZDES

(modes

I+II+III) (6)

380000 0.16 128 5.1 58275

The computations are compared by cross-plotting of the results by different partners. First we compared the

results for the SA-DDES model by DLR and FOI using the same transition treatment, the same mesh and

computational domain, and a similar physical time step size. Moreover we note the underlying numerical scheme

of TAU and EDGE is very close. As shown in Figure 4.1, very good agreement is observed between the partners

for both Cp and Cf. Both simulations reveal that there is no separation on the flap with the SA-DDES model.


38

Figure 4.1: Cp-distribution on the flap (left) and Cf-distribution on the flap (right). Comparison of SA-DDES

results by DLR and by FOI on the same mesh and using a very similar numerical method.

A valuable study regarding the influence of the spatial and temporal resolution was performed by FOI in

collaboration with Chalmers [75-78]. In the first step they investigated the influence of the spanwise extent of the

computational domain and of the spanwise mesh spacing. This is shown in Figure 4.2. A spanwise extent of the

domain of 16% (retracted) chord gives a significant change compared to a small extent of 8% (retracted) chord. A

refinement of the mesh in spanwise direction from 80 cells (for spanwise extent 16%) to 160 cells also gives

noticeable changes in the results yielding a further improvement. This spanwise extent and resolution was used by

ONERA and NLR, but could not be afforded by DLR. Moreover, FOI made a study for different physical time

step sizes varying from t=4e-5 second, t=2e-5 second and t=5e-6 second. Regarding the mean flow separation

behavior on the flap, t=2e-5 second seems to be sufficient. However, regarding the turbulence resolution in the

slat cove (for acoustic analysis), a smaller time step would be needed, as also pointed out by NLR and ONERA.

Figure 4.2: Cp-distribution in the region of the suction peak on the main wing and on the flap. Based on FOI-

Chalmers studies on the effect of the spanwise extent of the computational domain, the spanwise grid resolution

and the physical time step.

In the FOI computations, a comparison was further conducted using different hybrid RANS-LES models with the

same CFD solver, as well as the same grid resolution, spanwise extent and physical time step. It is shown that on

the mesh with small spanwise extent, there are noticeable differences between the SA-DDES results and the

HYB0 results, as shown in Figure 4.3. This is to a larger extent related to the inherent modelling mechanism. The

DDES model restricts the RANS mode accounting for the whole boundary layer, while the HYB0 model tends to

resolve turbulence in a part of the boundary layer and is more sensitive to the spanwise domain size in relation to

the spanwsie correlations of resolved turbulent structures in the boundary layer. However, when increasing the


39

spanwise extent of the computational domain and the spanwise mesh spacing, although not shown here, it is noted

that the the results by SA-DDES and HYB0 become much closer to each other.

Figure 4.3: Cp-distribution on the main wing element (left) and on the flap (right) obtained by FOI for the HYB0

model and the SA-DDES model. By increasing the spanwise extent of the computational domain and the

resolution in spanwise direction, the HYB0 models results come much closer to the SA-DDES results and also to

the experimental data. This is a consequence of the HYB0 model feature to resolve turbulence in a part of the

boundary layer.

NLR performed a study on the effect of hybridized RANS and/or LES mode using the same numerical solver and

other numerical settings. In the first step, they used the same hybrid concept (i.e., X-LES, a stochastic SGS-model

and high-pass filtering) but changed the background RANS model from TNT-k-(NLR 1) to TNT-EARSM

(NLR 3). As shown in Figure 4.4 (left), only a moderate change is observed in the separation on the flap. In the

second step, they compared X-LES and high-pass filtering with a stochastic SGS model in one case and a delayed

shielding function (NLR 2) in the other case. There is a noticeable influence on the separation behavior of the

flap, see Figure 4.4 (middle and right). By applying a delayed function, they arrive to obtain almost the same

separation behavior on the flap for the delayed X-LES as for the TNT-EARSM RANS simulations (denoted NLR,

TNT-EARSM in the legend of Figure 4.4). In the simulation NLR-1 the delayed function was not used. The flap

separation bubble becomes more extended and the separation point slightly shifts upstream compared to the TNT-

EARSM RANS results.

Figure 4.4: Cfx-distribution and Cp-distribution on the flap for different X-LES results obtained by NLR. Left:

effect of RANS background model from TNT k-ω (NLR 1) to TNT EARSM (NLR 3); Middle and Right: TNT k-

ω based X-LES with (NLR 2) and without (NLR 1) a delayed shielding function.


40

ONERA performed a detailed investigation on the role of dedicated changes in the ZDES method. We

compare the ZDES results with the SA-DDES results by DLR and FOI, see Figure 4.5. From the hybrid modelling

point of view, the first main difference between ZDES and DDES is the length-scale switch from RANS to LES,

in particular near the trailing edges of the elements. Regarding the mean aerodynamic flow properties, i.e., Cp and

Cf, however, this causes only very small changes in the flow solution. The results by ZDES are close to the SA-

DDES results. On the positive side, ZDES gives a small separation bubble whereas DDES predicts a fully

attached flow on the flap. Additionally, the ZDES in the so-called mode I+II+III was used, in which synthetic

turbulence was added. However, then the small separation on the flap disappeared.

Figure 4.5: Cp-distribution on the main wing element (left) and on the flap (right) obtained by ONERA using

different versions of ZDES compared with the SA-DDES results by DLR and FOI.

What can be summarized for the application of hybrid RANS-LES for three-element airfoils compared to

RANS? First we consider the mean aerodynamic predictions. We would like to underline that the flow around

three-element airfoils with its boundary layers, in particular on the flap at adverse pressure gradient, and the

interaction of the free shear layers of the wakes with the attached boundary layers are beyond the range of test-

cases for which DES and DDES have been invented. From the view of the mean aerodynamic data Cp and Cf, for

hybrid models which treat the attached boundary layers in RANS mode, we can expect only that the result with

hybrid RANS-LES models reaches the quality of RANS result. Of high interest is the interaction of the boundary

layer on the flap with the wake flow of the main wing element both under the effect of an adverse pressure

gradient, which influences the flow separation on the flap.

On the other hand, regarding more physical insight into the flow field, in particular the regions of separated

flow which are a high interest in the generation of noise, the use of hybrid RANS-LES methods gives a significant

improvement in the predictive accuracy compared to RANS. An important aspect is the turbulent kinetic energy in

the slat cove, which can be resolved much more accurate using hybrid methods than using RANS, as was shown

in detail by ONERA [74].

We wish to emphasize the very fruitful cooperation among the partners involved in this application challenge

test-case. As the partners were aware of already during the kick-off meeting of AG49, the application of hybrid

RANS-LES methods to a three-element airfoil flow gives rise to a multitude of questions regarding the hybrid

modelling details and regarding the numerical resolution requirements, which are clearly too much to be answered

by a single research group. Keeping this in mind, each partner performed some deep investigation into some

dedicated important aspects of hybrid simulations for three-element airfoils. These investigations required the

development and the coding of a variety of hybrid model versions and a huge amount of computing resources for

performing simulations for all of them, including the highly valuable studies on the numerical resolution

requirements accomplished by FOI in cooperation with Chalmers. The simulations performed by the partners are

complementary and give rise to a world-wide unique experience in the application of hybrid RANS-LES methods

to three-element airfoils in high-lift configuration.

With the LEISA highlift flow, we started with an intensive interest to explore whether a delayed DES

(DDES) approach is suitable for a three-element airfoil flow characterized by confluent boundary layers and


41

wakes, and further, whether an IDDES-approach with inherent WMLES mode would provide improved

predictions. Moreover, it is also interesting to investigate the role of the underlying RANS model for such a flow

with mild flow separation induced by an adverse pressure gradient on a smooth surface.

Figure 4.6: Illustration of the flow field in the slat cove region and on the upper side of the wing obtained by

ONERA using ZDES in mode I+II+III (see below).

In order to address these questions, three simulations were performed in DLR on TC 2.1 using two different SA-

based DDES and an SA-based IDDES, see Figure 4.7 and Figure 4.8. DLR investigated different approaches for

resolving the confluent boundary layers of (i) main-wing element boundary layer and slat wake and (ii) of flap

boundary layer and the wake of the main-wing element. On the one hand, DLR performed two SA-DDES, one as

a standard SA-DDES and a second simulation in which the boundary layers were extra-shielded in RANS mode

by placing a RANS block over the main wing element. On the other hand, the aim was to resolve the unsteady

turbulent content at least in the outer part of the boundary layers using the IDDES approach. Therein, the

assumption was that sufficient turbulent content was generated by the upstream elements.

Figure 4.7: Cp-distribution on the main wing element (left) and on the flap (right) obtained by DLR using SA-

IDDES compared with the SA-DDES results.

Regarding the SA-DDES the comparison of the results with the results by FOI helped to find best practice

guidelines regarding mesh design, spanwise extent of the computational domain, mesh spacing in spanwise

direction, choice of the time step size and time required to obtained statistically converged solutions. Hence the

cooperative work within GARTEUR enabled us to learn how to use DDES for a three-element airfoil in terms of

numerical resolution requirements. Regarding the behavior of the SA-DDES model concerning the aerodynamics


42

prediction of the Cp-distribution and the separation behavior on the flap, we found that for the present flow of a

moderate angle of attack, SA-DDES can expected to be only as good as the underlying SA-RANS model. Since

the SST-RANS results where in much better agreement with the experiment than the SA-RANS model, we

conclude that it is worth studying SST-based DES models for such a flow with pressure induced separation on a

smooth surface.

Figure 4.8: Cf-distribution on the main wing element (left) and on the flap (right) obtained by DLR using SA-

IDDES compared with the SA-DDES results.

Regarding the use of IDDES as a WMLES, DLR was the only partner in AG49 who tested this approach. It

is noted that, under the effect of an adverse pressure gradient, the interaction of the boundary layer on the flap

with the wake flow of the main wing element influences significantly the flow separation on the flap. This has

thus motivated to resolve this interaction using LES. We found in DLR computations that the resolution of the

IDDES was not fully satisfactory for the predicted Cf-distribution on the main-wing element in comparison to the

RANS results, see Fig 4.8. Using SA-IDDES; the predicted Cf on the upper side of the main wing element is

significantly lower than expected from the RANS results. This is probably due to a too low resolution of resolved

turbulent shear stress due a not fine enough mesh (and possibly a not fine enough physical time step size) and due

to a delayed formation (in streamwise direction) of turbulent content in the simulation. It is necessary to get more

insight into these issues. Additional simulations are required for investigating the required streamwise and

spanwise mesh resolution, as well as the temporal resolution. Moreover, in relation to the modelling, it seems that

the IDDES needs a certain streamwise distance before enough turbulent content for a correct level of Cf is

generated. Hence we might consider to add synthetic turbulence on the elements to ensure a reasonable turbulent

content inside the boundary layers. On the positive side, regarding the separation behavior on the flap and the

interaction of the main-wing-wake and the flap boundary layer, we see a large potential for IDDES used as

WMLES for an improved prediction of the flap separation. However, we also learned from this test case and the

corresponding study of the test cases for three-element airfoils available in the literature (e.g., EUROPIV,

EUROLIFT), that there are significant uncertainties also in the present test case. The most important uncertainties

are the positions of laminar-turbulent transition and the correction of the incidence angle. Although we performed

an elaborating precursor RANS study on these issues, a significant uncertainty regarding the test-case setting still

remains.

Summarizing the lessons learned, DLR concludes that it is worth investigating SST-based IDDES with a

method to use synthetic turbulence for triggering turbulent content in the LES-regions for this test case in future

collaborative work.

4.2 VFE-2 Delta Wing

The VFE-2 geometric configuration is a Delta wing with 65° leading-edge sweep angle designed by Chu and

Luckring [71]. The original wing model is equipped with a sharp and three rounded leading edges with different

leading edges radii denoted as small, medium and large L.E. radius. The VFE-2 wing is equipped with the sharp


43

and medium radius leading edge. The wing is mounted in the wind tunnel using aft mounted sting. The geometry

used in AG49 is the medium radius leading edge (MRLE) wing. The flow around this geometry is more difficult

to predict than on sharp leading edge due to strong dependency of the vortex position on Reynolds number. A

visualization of the characteristic primary vortices is shown in Figure 4.9.

Fig 4.9: Visualization of primary vortices. Isosurface of averaged streamwise vorticity colored by averaged

streamwise velocity. Computation by TUM.

The chosen test case is a flow at angle of attack 23 degrees and Reynolds number 1million based on MAC,

Cr. This case is a challenging case of high angle of attack flow with vortex breakdown. The two tested values of

the Mach number were M = 0.07 and M = 0.14, after initial testing the value of Mach number was set to M = 0.14

due to better convergence with compressible solvers.

Table 4.2: Computational information in FOI, CIRA and TUM simulations

Partners FOI CIRA TUM

Method HYB0 (see Section

2.1.4)

X-LES with immersed

boundaries and wall model

Implicit LES with immersed

boundaries and wall model

Spatial

discretization

Finite volume, 2nd

-

order central scheme

Finite volume, 2nd

-order

central scheme

Finite volume, ALDM for

convective terms

Temporal

discretization

2nd

-order implicit

scheme

2nd

-order implicit scheme 3rd

-order explicit Runge-Kutta

scheme

Mesh Unstructured mesh

33 M cells

Cartesian type with local

grid refinement, 6.5 M cells

Cartesian type with AMR

(adaptive mesh refinement), 74

M cells

Time step 5.0×10-5

second 6.94 ×10-4

second 3.26x10-8

second

Time for averaging

(t*U∞/Cr)

~ 25.5 25 ~20


44

Computations for this test case, TC 2.2 (VFE-2 delta wing), were carried out by CIRA, FOI and TUM. NLR,

who had originally considered to conduct simulations for this TC, decided to compute TC 2.1 instead. Previously,

NLR had already computed the flow around the VFE-2 delta wing with sharp leading edge [37]. Table 4.2

provides the information of numerical settings used by CIRA, FOI and TUM, respectively.

The computational mesh used in FOI computation was made at Cassidian and provided for use to the group.

However, CIRA and TUM have used solvers based on IBM (Immersed Boundary Method), and different meshes

have thus been employed. The mesh used by FOI is an unstructured mesh consisting of 33 million mesh nodes for

the full span model. The mesh is clustered around the leading and trailing edge of the wing and around the wing

apex, as shown in Figure 4.10.

Fig 4.10: Illustration of surface mesh on the VFE-2 Wing

Fig 4.11: Distribution of surface pressure coefficient on wing sections at (top raw) 0.2Cr, 0.4Cr, 0.6 Cr; and (lower

raw) at 0.8Cr and 0.95Cr. HYB0 computation in comparions with RANS results.

All calculations were considered fully turbulent, the sting geometry was included in the numerical model and the

wing is calculated in the free space rather than in the wind tunnel. In the FOI computation, the choice of the time

step was motivated by capturing the boundary layer instability modes. After 3000 time steps for the initial

development of the computed flow, about 7000 time steps were used for statistical analysis.


45

Figure 4.11 shows a comparison of the surface pressure coefficient obtained by FOI using the RANS

EARSM model and the hybrid RANS-LES HYB0 model. The largest difference occurs at 20% of the chord length

where the RANS model does not predict correct development of the vortex around the wing apex. Unlike the

wind-tunnel data and the HYB0 computation which predict a string primary vortex, the RANS model has claimed

two vortices with less intensive strengths, and the primary vortex being located more inboard compared to the WT

data. In the downstream positions at, e.g., 80% Cr and 95%, the RANS solution does not predict the vortex

breakdown that is shown in the WT data. The HYB0 model is in very good agreement with the WT data,

predicting correctly the vortex motion as well as the position of the vortex above the wing. Both solutions show

symmetric flow around the wing.

Figure 4.12 presents the comparison of the mean pressure coefficient from the CIRA, FOI and TUM

computations compared to the TUM wind tunnel data [79, 80] at five different positions of the chord. The

positions are x/Cr = 0.2, 0.4, 0.6, 0.8, 0.95. The CIRA computations were not able to predict the development of

the primary vortex at 20% of the chord length. The position of the primary vortex has been predicted fairly well

between 40% to 80% of chord, although the intensity of the suction is a bit larger than the measured data in the

wind tunnel suggesting the vortex is closer to the wall. A further local grid refinement (LGR) should improve the

primary vortex predictions. The TUM computation has predicted an incorrect pressure coefficient distribution at

20% of the chord length. Both position and magnitude of the suction peak differ from the experimental data. A

finer grid close to the wing apex might remedy these discrepancies. Figure 4.13 shows an example of LGR based

on the flow field solution. However, as shown in Figure 4.12, the TUM predictions at 40%, 60% and 80% of the

chord length are in good agreement with the experimental data and are very close to the predictions by FOI. At

95%, the suction has been predicted too high in the TUM computation, whereas the FOI computation has

reproduced the WT data trend with a clear indication of the vortex breakdown. The FOI predictions are in a good

agreement with the experimental data in all positions, but the suction in the primary vortex is predicted a bit larger

in 40% and 60% of chord.

Figure 4.12: Mean pressure coefficient distribution at x/cr = 0.2, 0.4, 0.6 (top raw), 0.8 and 0.95 (lower raw). –

Experiment was made by TUM [79, 80]; HYB0 computation by FOI, X-LES by CIRA and ILES by TUM.


46

Fig 4.13: Local view of the CIRA mesh on the VFE-2 Wing. Note the local grid refinement (LGR) based on the

flow field solution data.

In addition, FOI has provided the RMS of surface pressure fluctuations. It is noted that, because the computational

data were slightly asymmetric, the RMS data on both sides of the wing were further averaged before being

compared to the WT data. Figure 4.14 shows their comparison to the wind tunnel measured data at 60%, 80% and

95% positions, respectively. The comparison to WT data shows fairly good agreement at 60%, at downstream

positions, however, the level of the RMS data predicted by CFD are almost twice as high compared to the wind

tunnel data, although the shape predicted by CFD is similar to the wind tunnel data. This is somewhat surprising

considering the good agreement of the predicted pressure coefficient with the wind tunnel data. This has probably

been caused in part by possible local laminar boundary layer around the leading edge in the experiment, while the

computation has been conducted by assuming fully developed turbulent flow due to the lack of information about

the location of laminar-turbulent transition.

Figure 4.14: RMS pressure coefficient distribution at x/Cr = 0.6, 0.8, and 0.95 (from left to right). Experiment by

TUM [79, 80], Computation by FOI.


47

5 Summary and Conclusions

5.1 Best-Practice Guidelines

The major target of AG49 has been to explore and evaluate hybrid RANS-LES modelling approaches by means of

computations of different test cases. In the project work, partners have used different solvers (and thus different

numerical algorithms/schemes), and in some cases also different grid resolutions. In view of the flow

configurations of the test cases analyzed, the following four main factors, among others, are recognized to be

associated severely to a relatively poor performance in the computations.

a) Inherent modelling mechanism. This is referred to modelling formulation that is recognized as an inherent

weakness in modelling/resolving some typical flow features, for example, the so-called “grey area”,

nestling in many hybrid RANS-LES computations.

b) Grid resolution. It is often related to insufficient grid resolution in some critical flow regions, and/or due

to inappropriate grid arrangement that may cause possible mal-functioning of RANS-LES interaction.

c) Numerical schemes. This concerns inappropriate settings of the numerical scheme adopted, typically, a

high level of numerical dissipation, insufficient convergence of solution at each physical time step. The

former may usually lead to damping of resolved physical flow fluctuations, while the latter may trigger

spurious numerical oscillations and being misinterpreted as physical flow fluctuations.

d) Incoming flow conditions. It is indicated by inaccurate or even wrong representation of mean flow and

turbulent conditions at the inflow section, or in the incoming boundary layer that is approaching the

focusing flow region of interest.

In connection to these factors, partners have analyzed the predictions with a particular emphasis on an exploration

of the reason behind the discrepancies from experimental measurements. In Table 5.1, the hybrid RANS-LES

models used in the computations of the test cases are summarized. It should be noted that, besides the standard

formulation, some modelling variants (modes) have also been employed. These include the variants to the X-LES

model, the ZDES model and to the SA-IDDES model.

Table 5.1: Summary of models used in TCs and their performance

Model TC 1.1 TC 1.2 TC 2.1 TC 2.2

Reasonable

performance

Relatively poor

performance

Reasons for poor

performance

SA-DDES x x x TC 1.2 TC 1.1 a) & c)

SA-IDDES x x TC 2.1 TC 1.1 a) & c)

SST-DES x TC 1.2 a) & d)

X-LES x x x TC 1.1/2.1 TC 2.2 a)

b)

Zonal (no SGS) x TC 1.1 -- --

ZDES x x x TC 1.1/1.2/2.1 -- --

HYB0 x x x TC 1.2/2.1/2.2 TC 1.1 b) & d)

HYB1 x TC 1.2 -- --

ILES x TC 2.2 b)

LES(Smag. ref) x x N/A N/A --

RANS (SA, ref) x N/A N/A --

a) This was shown in CIRA’s computation, in which a fairly coarse grid was used around the wing and in which the X-

LES improvements of NLR were not included.

For TC 1.1 (spatial developing mixing layer), the main focus has been to scrutinize the modelling performance in resolving the initial shear-layer instability accounted for by the LES mode, yet closely associated to the incoming

RANS-modelled boundary layers immediately after the plate trailing edge. This is a typical “grey area”. While the


48

DDES-type model has been formulated as a remedy to the so-called “modelled stress depletion (MSD)” problem

of DES formulation, the results have shown that the DDES computation has suffered from a severe delay of the

shear-layer instability in the prediction due to the fact that the incoming boundary layers are accommodated by the

RANS mode.

The other models, including the zonal model and X-LES by NLR, ZDES by ONERA and HYB0 by FOI,

have claimed a relatively fast three-dimensional development of the mixing layer in line with the experimental

observation. In view of the modelling formulation, it is noted that the early destabilizing of the shear layer has

been caused mainly due to (i) reduction of the turbulent viscosity (either through the SGS length scale adopted in

the LES mode, high-pass filtering, or brutally setting it to zero) and/or (ii) the interfacing location (in terms of

wall distance) of RANS and LES modes in the boundary layer. The penetration of the LES mode in the boundary

layer, which is attempted to be avoided in the DDES model, has actually played a positive role in triggering early

shear-layer instabilities. The partly LES-resolved incoming boundary layers may have alleviated to some extent

the “grey area” problem. Moreover, the computations have also demonstrated the significance of incoming flow

conditions. The predicted upstream boundary-layer velocity profiles may significantly affect the prediction of the

developing shear layer. On the other hand, an addition of synthetic turbulence or stochastic forcing may improve

the prediction of shear-layer instability.

In the computation by INTA (DDES and IDDES) using two different time steps, it was tested that activation

of ft2 in the DES formulation may give rise of a low level of RANS eddy viscosity in the boundary layer, which

has enabled a relatively quick development of strong instabilities in the mixing layer.

The free shear layer in the backward-facing step flow emanating from the step edge is similar to the mixing

layer, but to be further reattached on the bottom wall. Four different DES and other hybrid models have been

used, including SST-DES, SA-DDES ZDES and HYB1. The DES model has caused an unphysical boundary layer

separation on the top wall due to the well-recognized “MSD” problem. For the two DDES computations, one of

them may have been contaminated by inappropriate numerical settings. In general, the ZDES and HYB1 models

have enabled better predictions as compared to the DDES computation. The “grey area” problem in the initial

stage of the shear-layer development has been shown much severe in the DDES computation.

Based on the computations of the two fundamental flow cases, of all the models used, it is observed that

DDES may become awkward in resolving the initial development of turbulent free shear layer emanating

from upstream boundary layer. The model has given rise of the most severe “grey-area” problem. The

IDDES computation may preserve the same problem for this case for adopting the DDES mode.

Zonal and other hybrid RANS-LES models (including ILES), which allow LES mode to enter into near-

wall layer, have presented desired performance of triggering early shear-layer instabilities for flow

separation induced by geometry. Special caution should however be paid to the grid-induced flow

separation, when the boundary layer separation, from which the frees shear layer is stemmed, has been

caused due to adverse pressure gradient.

Specification/prediction of the incoming upstream boundary layer may significantly affect the resolved

turbulent flow properties in the initial development of the shear layer.

For the LEISA high-lift flow, the best-practice lessons learned concern the resolution requirements for spatial and

temporal resolution and the spanwise extent of the computational domain. Moreover, we resume the lessons

learned for the details of the hybrid RANS-LES models, namely (i) role of the RANS background model, (ii) role

of the length scale switch from RANS to LES, i.e., delayed function, ZDES-type length scale switch etc, (iii) role

of using methods to trigger the generation of turbulence, i.e., stochastic forcing or synthetic-eddy methods.

First we consider the issue of the resolution requirements. Based on the detailed investigation by FOI, we

conclude that for three-element airfoil configurations a spanwise extent of the computational domain of 16% of

the retracted chord length and 160 points in spanwise direction (corresponding to Δz/c=0.001) is needed.

Regarding the physical time step side for properly resolving the mean flow field and the separation behavior on

the flap, t = 2e-5 second seems to be sufficient.

Secondly we summarize the findings for the variation of details of the hybrid models. The role of the RANS

background model became clear. We recommend to use a hybrid model with an underlying RANS model with a

high level of predictive accuracy for three-element airfoil flows. However, the mean aerodynamics predictions are

still influenced to a significant amount by details in the hybrid model. An important aspect is the mechanism to

switch between RANS and LES region and the position relative to the wall where the switching actually occurs.


49

Here the results do not allow for a clear conclusion, since they depend on the partner and the RANS-background

model used. First we consider the case that the same SA model as background model is used. For the SA

background model, the DDES results by DLR and FOI are quite close to the ZDES results by ONERA. This is a

little surprising, since the ZDES length switch demonstrated a large improvement in the prediction of shear-layer

instability for the mixing layer TC 1.1. It is not clear yet, why regarding the separation behaviour on the flap

almost no changes can be seen in the mean aero results when changing between ZDES and DDES. On reason

could be that the DDES suffers from a lack of accuracy due to the small spanwise extent of the computational

domain using 9%c compared to the ZDES with 16% c. On the other hand, for the results by NLR a significant

influence and improvement of the flap separation can be made by using a delayed function compared to the

simulation without delayed function.

The role of triggering turbulence is also not clear. Two partners studied this feature but they used different

methods. NLR used a stochastic SGS model with high-pass filtering. For the NLR results, flow separation on the

flap was observed more upstream then in the case of using a delayed function. On the other hand, ONERA used a

synthetic-eddy method and observed that the separation on the flap was reduced, i.e., separation occurred further

downstream.

For the flow around the VFE-2 Delta-wing with a round leading edge, apart from the grid resolution that

should be fine enough to resolve the vortex formation and interaction, local laminar boundary layer around the

leading edge seems to be an important issue, which was however not taken into account in the two contributed

computations due to the lack of related information. Nonetheless, it is shown that a simple algebraic hybrid

RANS-LES model is able to produce good prediction for the surface pressure, although the pressure fluctuations

are sensibly over-predicted due possibly to fact that the boundary layer transition around the leading edge was

ignored in the full-turbulence computation.

5.2 Concluding Remarks

The work in AG49 has been a collaborative exploration of several hybrid RANS-LES modelling approaches in

computations of four different test cases by means of cross comparisons. In the framework of the project a number

of existing hybrid RANS-LES models have been investigated. Moreover, several improved variants have been

initially explored in the procedure of the project work, including these to the X-LES model using a stochastic

supplement to the SGS formulation, a high-pass filter and a more sophisticated based model, to the HYB0 model

with an energy-backscatter function added to the SGS model, as well as to the ZDES with a vortex-based SGS

length scale. These improvements have in general shown desirable performance in the modelling, particularly, in

resolving the initial development of shear-layer instabilities as compared to the original model.

For the fundamental flows, mixing layer (TC 1.1) and backward-facing step flow (TC 1.2), none-DDES type

modelling approaches have shown better performance to resolve the developing free shear layer in the “grey

area”. Of interest, a good consistency between the different DDES computations performed by the different

partners has been observed. DDES-type models produce much delayed mixing-layer instabilities, as compared to

other hybrid RANS-LES models explored in the project work by partners. Nevertheless two methods, namely, the

X-LES and ZDES models, have been assessed successfully and have shown to improve significantly the issue of

slow LES development in free shear layers. The prediction or description of the incoming boundary layer, both

the mean flow and the turbulent fluctuation, prior to entering the mixing layer plays an essential role in the

prediction of the follow-up mixing layer when making detailed comparisons with the experiment. For the three-

element airfoil flow (TC 2.1), the findings on the resolution requirements for this test case are highlighted. They

are a very important result for future investigations of such test cases. Regarding conclusions for the hybrid model

details, only some more loose statements can be given. The reason for this is in particular the lack of experimental

data. We emphasize that the richness of results gained from the different simulations by all the partners shed a lot

of light to the application of hybrid RANS-LES to multi-element airfoil flows, which would not have been

possible by a single partner. The variety of simulations and investigations by the partners provide a worldwide-

unique valuable experience for the improvement of hybrid RANS-LES methods ultimately for full aircraft

simulations in take-off and landing configuration. For the Delta-wing flow (TC 2.2), a reasonable prescription of

laminar boundary layer around the leading edge is an important issue that should be taken into account. Overall,

the hybrid RANS-LES modelling has shown an improved predictive capability for this flow characterized

typically by vortex formation, interaction and breakdown, as compared to RANS models.


50

For flow separation stemming from attached boundary layer and induced by geometry (e.g., in TC 1.1 and TC

1.2), the base model (in RANS mode), taking the zero-, one- to two-equation forms as being formulated in the

hybrid methods used, is not a significant issue, provided that the capability of the RANS mode has been well

calibrated in computation of attached boundary layer flows. When boundary layer separation occurs in the

presence of adverse pressure gradient, e.g., for TC 2.1, the importance of using a high-quality base model was

observed in the formulation of (D)DES-type modelling. The based model in general should be able to reasonably

predict the flow separation in the form of RANS. For the other model aspects like the method for length scale

switch from RANS to LES and the use of methods to trigger the generation of turbulent content, the results within

AG49 clearly demonstrated the large potential of the new modelling improvements but a detailed future work is

still needed. As a large advantage of hybrid RANS-LES compared to RANS, we see the clear improvement in

predictive accuracy for the turbulence in the regions of separated flow, i.e. in the slat cove for the multi-element

high-lift flow, which is viewed as a potent noise-generating region. As a main conclusion for future work, the

detailed investigation of hybrid RANS-LES methods in the sense of a wall-modelled LES for the flow separation

on the flap under the effect of an adverse pressure gradient and by a proper resolution of the interaction of wake

flow and boundary layer flow using LES seems very promising, which is highlighted in the computations with the

HYB0 and ZDES model on sufficiently refined grids. For further development of hybrid RANS-LES and

embedded LES approached, the work done in AG49 on the fundamental test cases and on the complex

aerodynamic test cases forms a valuable experience and knowledge data base.

Acknowledgement: The AG49 has been monitored by Torsten Berglind (FOI) on behalf of GARTEUR GoR.

Torsten Berglind and Björn Palmberg in FOI have kindly read the manuscript and provided useful comments. The

support from all involved organizations is gratefully acknowledged. In addition, in the FOI contribution on the

LEISA highlift flow, the FOI-Chalmers joint computations were made by Mr. Bastian Nebenfuhr at Chalmers

using the FOI Edge solver. Dieter Schwamborn and Silvia Reuss have contributed to the DLR work on the LEISA

highlift flow.


51

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