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Numerical Investigations on a Hot Jet in Cross Flow. Directeurs de thèse: P. Millan, ONERA S. Deck, ONERA. Encadrants: F. R. Menter, ANSYS H. Bézard, ONERA M.-J. Esteve, AIRBUS. Benjamin Duda 3e année DMAE/DAAP Bourse CIFRE. Outline. Introduction Motivation & Objectives Methodology

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numerical investigations on a hot jet in cross flow

Numerical Investigations on a Hot Jet in Cross Flow

Directeurs de thèse:

P. Millan, ONERA

S. Deck, ONERA


F. R. Menter, ANSYS

H. Bézard, ONERA

M.-J. Esteve, AIRBUS

Benjamin Duda

3e année


JDD 2012Outline
  • Introduction
    • Motivation & Objectives
  • Methodology
    • Test Case Definition
    • Scale-Resolving Simulations
    • Validation
    • Physical Analysis
    • Industrial Application
  • Conclusion & Outlook
motivation objectives
JDD 2012Motivation & Objectives
  • Jet in cross flow appears at air system exhausts
  • Turbulent, transient and fully three dimensional flow including heat transfer at high Reynolds number
  • Complex interaction of large and small scale structures depending on blowing ratio rjWj /(r∞U∞)
  • Prediction of flow and temperature field for aircraft safety and weight reduction
  • Flow analysis




Thermal shield






boundary conditions jicf similarity parameters
JDD 2012Boundary Conditions & JICF Similarity Parameters
  • Wind tunnel inlet
    • velocity: 47.18 m/s (Ma = 0.14)
    • total temperature: 291 K
    • turbulence intensity = 0.5 %, mt/m = 10
  • Hot air supply
    • mass flow: 0.03542 kg/s
    • total temperature: 353 K
    • turbulence intensity = 0.5 %, mt/m = 10
  • Wind tunnel outlet
    • static pressure
  • Mock-up walls
    • no-slip boundary condition, adiabatic
  • Wind tunnel walls
    • free-slip boundary condition
scale resolving simulations
Scale-Resolving Simulations

JDD 2012

  • Jet in cross flow simulations require the resolution of at least a part of the turbulence spectrum
  • Pure Large Eddy Simulations for high Reynolds number and wall-bounded flows are too expensive
  • Focus on hybrid turbulence models and zonal formulations:
    • Resolve large, energy containing and geometry dependent vortices
    • Model smaller and more universal turbulent structures
    • Stable flow regimes with RANS

Idealized spectrum ofturbulence kinetic energy

log E

energy transfer




log k

RANS ← Hybrid → LES ↔ DNS

Page 6

categorization of turbulence modeling approaches
JDD 2012Categorization of Turbulence Modeling Approaches





turbulence modeling approaches
JDD 2012Turbulence Modeling Approaches
  • Integrated approach
    • Single transient calculationof entire domain withlocalresolution of turbulencescales
  • Sequential approach
    • Two consecutivecalculations
    • Steady RANS in entire domain
    • Extraction of subdomain and boundary conditions
    • Scale-resolving simulation only in subdomain
categorization of turbulence modeling approaches1
JDD 2012Categorization of Turbulence Modeling Approaches










integrated hybrid approach i
JDD 2012Integrated Hybrid Approach I

Scale-Adaptive Simulation (SAS)

  • Introduction of additional source term QSASto w-equation in SST model
  • Active in areas with inherent flow instabilities and sufficient grid refinement
  • Sensor for instability is von Kármán length scale LvK
  • Production of w leads to decrease of eddy viscosity mt
  • No explicit dependence on grid spacing D
  • k-wSST capability in stable flow regimes, e.g. attached boundary layers
integrated hybrid approach ii
JDD 2012Integrated Hybrid Approach II

Delayed Detached Eddy Simulation (DDES)

  • DES: Blending of RANS (k-w SST) and LES (dynamic k subgrid scale) formulation
  • LES in regions with CDESD < Lt, RANS elsewhere
  • Explicit dependence on grid spacing D
  • Delayed formulation: Attached boundary layers are forced to RANS regime with help of shielding functions
integrated zonal approach
JDD 2012Integrated Zonal Approach

Embedded Large Eddy Simulation (ELES)

  • Definition of a spatially fixed fluid zone where scale resolution using LES is desired
  • Rest of domain is calculated using (U)RANS formulation
  • Conversion of turbulent kinetic energy content from RANS models to resolved turbulent fluctuations in LES zone
    • Vortex generation method at RANS-LES interface

RANS zone

LES zone


Model interface

(conformal or non-conformal mesh interface)

resolution requirements meshing strategies
Resolution Requirements & Meshing Strategies

JDD 2012

  • Boundary layer: accuracy and heat transfer require y+<1
  • Jet and cross flow interaction region:
    • Grid spacing D and time step Dt small enough for scale resolution
    • Ideally isotropic mesh due to unknown vortex orientation
  • Strategies:

12.9x106 cells

13.1x106 cells

21.0x106 cells

  • Hexahedral mesh based on multi-block approach
  • Hybrid Cartesian mesh with prismatic & hexahedral inflation layers
  • Hybrid tetrahedral mesh with prismatic inflation layers

Page 13

scale resolvability of turbulence models
Scale Resolvability of Turbulence Models

JDD 2012

Judge scale resolution qualitatively withQ-criterion:Q=0.5(|Wij|2-|Sij|2)





Page 14

time averaged temperature distribution i
Time Averaged Temperature Distribution I

JDD 2012

Turbulence models (on hex)

  • Good agreement in far field
  • Slope of SAS and DDES agree well with small offset in near field
  • Incapability of URANS to resolve scales explains poor mixing and strong temperature gradient

Meshing strategies (with SAS)

  • Generally very good agreement
  • Small underestimation for hex and cart mesh
  • Tet mesh is closest to exp data due to smaller cells


Page 15

time averaged temperature distribution ii
Time Averaged Temperature Distribution II

JDD 2012

Turbulence models (on hex)

  • Lateral spreading of temperature in good agreement with all three SRS
  • Poor URANS prediction due to unphysical damping of lateral jet wake movement

Meshing strategies (with SAS)

  • Generally very good agreement
  • Small underestimation for hex mesh at center


Page 16

2 nd order time statistics
2nd Order Time Statistics

JDD 2012






Hexahedral mesh

Page 17

spectral analysis
Spectral Analysis

JDD 2012

Hexahedral mesh with identical time step

Dominant frequency at StD = 0.14 is predicted correctly for SAS, DDES and ELES

Very broad peak for URANS

No high frequency contribution in URANS simulation due to incapability of resolving turbulent fluctuations

Page 18

time step study sas on hex mesh
Time Step Study (SAS on hex mesh)

JDD 2012

  • Improving agreement with decreasing time step
  • Small differences for 1st order time statistics
  • Good prediction of dominant frequency for all time steps
    • But different contribution to energy content of fluctuation since magnitude of spectral peak differs by a factor of 2

Page 19

stationary flow topology i
Stationary Flow Topology I

JDD 2012

Recirculation zone consists of two connected upright vortices

RANS resemblance

Instability causes stagnation point (SP) to oscillate and induces dynamics


Page 20

pod for jet in cross flow configuration
JDD 2012POD for Jet in Cross Flow Configuration
  • Memory requirement: 22GB
  • Time consumption:
    • 35min for data import
    • 35min for POD (u, v, wand T)
    • 30min for LRA (r=2)

POD box with 440,000 sampling points

(Resampled from 300 SAS time steps on hex mesh)

pod modes
JDD 2012POD Modes
  • First mode contains ‘mean’ flow
  • Higher order modes contain representation of flow dynamics
    • 2nd mode shows wake meandering
    • Temporal evolution, shape and spatial spreading

time coefficient ak=2(Dt)

! StD = 0.14 !

orthonormal function fk=2(x,y,z)

for y-velocity component

low rank approximation with first two modes
JDD 2012Low-Rank Approximation With First Two Modes

Interaction of turbulent scales leads to ‘chaotic’ temperature field

Originaltransient SASdata

Reconstructeddata clearlyshows wakemeandering

hairpin vortices
Hairpin Vortices

JDD 2012

Q Criterion






  • Most pronounced for DDES
  • High dynamics of wake lead to strong deformation of structures
  • Vortices entrain cold cross flow fluid and are important for mixing

Page 24

preliminary study for real aircraft application
Preliminary Study for Real Aircraft Application

JDD 2012

5 drop shaped ejectors in a row on generic configuration

Hexahedral mesh with 25.5·106 cells

SAS model

Page 25

process for industrial application i
Process for Industrial Application I

JDD 2012

  • RANS calculation of aircraft with clean nacelles
  • Extraction of results on boundaries of subdomain
  • Mesh generation in subdomain with real exhaust geometry
  • SAS calculation only in subdomain with fixed RANS boundary conditions

Validation of scale-resolving turbulence models

Analysis of transport and mixingphenomena

Application to industrial configuration

Finalising simulations and compilation of dissertation

Conferences & Publications:

7th International Symposium on Turbulence and Shear Flow Phenomena (TSFP-7), 28 - 31 July 2011, Ottawa, Canada

European Turbulence Conference (ETC 13), 12 -15 September 2011, WarsawPoland

Invited speaker at ANSYS Turbulence Seminare, 6 December 2011, Munich, Germany

AIAA Journal publication in perparation

JDD 2012