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Numerical studies of turbulent and separated flows
by
Astrid Herbst
June 2006
Technical Reports from
KTH Mechanics
SE-100 44 Stockholm, Sweden
Typsatt i -LATEX.
AMS
Akademisk avhandling som med tillst˚and av Kungliga Tekniska H¨ogskolan i
Stockholm framl¨agges till offentlig granskning f¨or avl¨aggande av teknologie
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Tekniska Ho¨gskolan, Lindstedsv¨agen 26, Stockholm.
cAstrid Herbst 2006
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Universitetsservice US-AB, Stockholm 2006
Fu¨r Oma

Numerical studies of turbulent and separated flows
Astrid Herbst 2006
KTH Mechanics
SE-100 44 Stockholm, Sweden.
Abstract
Thenumericalsimulationoftime-dependent,inherentlythree-dimensionalflow
problemshasbeenemployedasausefulandaccuratemeansforpredictionand
understanding of flow configurations. In particular, direct numerical simu-
lations (DNS) and large-eddy simulations (LES) of highly intermittent flows
exhibiting separationandofaturbulentwalljetareperformed. Fortechnolog-
icalapplicationsturbulentflowsencounteringpressure-drivenseparationareof
great interest. One example of the occurrence of adverse pressure gradients is
the flow in the diffuser-like air intake of a modern aircraft, where flow control
may be beneficial to improve the flow quality.
As a first step, the effect of periodic excitation on the turbulent bound-
ary layer flow over a flat plate separating due to an adverse pressure gradi-
ent is studied as a model problem and investigated through direct numerical
simulations. The flow can be forced to remain attached by applying time-
periodic perturbation for a certain frequency range at sufficiently high ampli-
tudes. The results show that control with a spanwise periodic input is more
effective than with a spanwise homogeneous control input. As a further ex-
tension the pressure-induced separation of a turbulent boundary layer on a
semi-infinite swept flat plate is studied without periodic forcing.
Going towards a more complex flow geometry exhibiting pressure-driven
separation, we consider the planar asymmetric diffuser using LES. A resolu-
tion check has been performed highlighting the broad range of the relevant
temporal and spatial scales and thus the sensitivity of the simulation results
to the computational grid. Regarding the flow physics, the effect of different
Reynoldsnumbersoftheinflowing,fullyturbulentchannelflowonvariousflow
quantities has been studied. The results consistently show that by increasing
theReynoldsnumberacleartrendtowardsalargerseparatedregionisevident;
at least for the studied, comparably low Reynolds-number regime.
Further, the first direct numerical simulation of a turbulent wall jet is
performed following the flow through the transition region to its downstream
turbulent part. A weak subharmonic behaviour in the transition region is re-
vealed by animations of the flow. Despite the low Reynolds number and a
comparablyshortcomputationaldomain, the turbulent flow exhibits a reason-
able self-similar behaviour, which is most pronounced in the near-wall region
using inner scaling.
Descriptors: Boundary layer, turbulent separation, direct numerical simula-
tion, large-eddy simulation, plane asymmetric diffuser, wall jet.
Preface
This thesis considers numerical simulations in turbulent and separated flows.
Thethesisisdividedintwoparts,thefirstpartconsistsofashortintroduction
to the field and a summary of the following papers. The papers are re-set in
the present thesis format and included in the second part of the thesis.
Paper 1. Herbst, A. H.& Henningson, D. S. 2006 The influence of peri-
odic excitation on a turbulent separation bubble. Flow, Turbulence and Com-
bustion 76, 1-21.
Paper 2. Herbst, A. H., Deubelbeiss, S., Spehr, S., Hanifi, A. &
Henningson, D. S. 2005 Instability characteristics of harmonic disturbances
in a turbulent separation bubble. Proceedings of XVII Congresso AIMETA di
Mechanica Teorica e Applicata.
Paper 3. Herbst, A. H., Brandt, L. & Henningson, D. S. 2006 The
effect of the sweep angle on the turbulent separation bubble on a flat plate.
Internal report.
Paper 4. Herbst, A. H. , Schlatter, P., & Henningson, D. S. 2005
Simulations of turbulent flow in a plane asymmetric diffuser. Submitted to
Flow, Turbulence and Combustion.
Paper 5. Levin, O., Herbst, A. H. & Henningson, D. S. 2005 Early
turbulent evolutionofthe Blasiuswalljet. Submitted to Journal of Turbulence
in a revised version.
vi
PREFACE vii
Division of work between authors
The first paper is on the influence of periodic excitation on a turbulent
separation bubble separating from a flat plate due to an adverse pressure gra-
dient. The directnumericalsimulationswereperformedwith a numericalcode
which has already been used in various research projects. The code is based
on a pseudospectral technique and originally developed at the Department of
Mechanics (DM) by Anders Lundbladh, Arne Johanssonand Dan Henningson
(DH). The numerical implementations needed for this work was performed by
Astrid Herbst (AH). The writing was done by AH with help from DH.
Thesecondpaperhighlightstheinstabilitycharacteristicsofharmonicdist-
urbances in a turbulent separation bubble. The paper is based on the mas-
ter thesis by S. Spehr with AH and DH as advisors and S. Deubelbeiss with
Ardeshir Hanifi (ArH) as advisor. Additional numerical simulations were per-
formed by AH and parts of the analysis were repeated and enhanced. The
writing was done by ArH and AH.
Thethirdpaperfocusesontheeffectofthesweepangleonaturbulentsep-
arationbubbleonaflatplate. Thedirectnumericalsimulationswereperformed
by AH using the same simulation code as in the first paper. The analysis of
the data was done by AH and Luca Brandt (LB). The figures were prepared
by AH and the writing was done by LB and AH with help from DH.
The fourth paper is a numerical study of the flow in the plane asymmet-
ric diffuser using Large Eddy Simulation. The simulations were performed
by AH using a code developed at Center of Turbulence Research which was
received from Hans-Jakob Kaltenbach. The code is based on a hybrid finite-
difference/spectral method. The simulation code was parallelised by AH. The
analysis of the data was done by AH and Philipp Schlatter (PS). The figures
were preparedby AH and the writing was done by AH and PS with help from
DH.
The fifth paper is devoted to the early turbulent evolution of the Blasius
walljet. Thenumericalcodeforthespatialsimulation,carriedoutbyOriLevin
(OL), originates from the same source as the one used in the first paper. All
the figures and animations were preparedby OL. The analysis of the statistics
wereperformedby OLandAH. The writingwasdoneby OLandAHwiththe
help of DH.

Contents
Preface vi
Part 1. Summary 1
Chapter 1. Introduction 3
Chapter 2. Governing equations and simulation techniques 5
2.1. Navier-Stokes equations 5
2.2. Simulation techniques 5
Chapter 3. Application to turbulent separated flows 8
3.1. Aspects of turbulent separated flows 8
3.2. Control of separated flows 9
3.3. Periodicexcitationofaturbulentseparationbubble onaflatplate 11
3.4. The effect of the sweep angle on a turbulent separation bubble on
a flat plate 16
3.5. Flow in a plane asymmetric diffuser 17
Chapter 4. Application to the turbulent wall jet 24
Chapter 5. Conclusions 30
Acknowledgments 32
Bibliography 33
Part 2. Papers 37
Paper 1. The influence of periodic excitation on a turbulent
separation bubble 41
Paper 2. Instability characteristics of harmonic disturbances
in a turbulent separation bubble 67
ix
x CONTENTS
Paper 3. The effect of the sweep angle on the turbulent
separation bubble on a flate plate 81
Paper 4. Simulations of turbulent flow in a plane
asymmetric diffuser 105
Paper 5. Early turbulent evolution of the Blasius wall jet 145