The structure of the velocity and scalar fields in a multiple-opposed jets reactor

Isaac Newton Institute, September 30, 2008

CNRS – UNIVERSITE et INSA de Rouen

The structure of the velocity and scalar fields in a

multiple-opposed jets reactor

L. Danaila

J.F. Krawczynski, B. RenouA. Mura, F.X. Demoulin, I. Befeno, G.

BoutinCORIA, Saint-Etienne-du-Rouvray, FRANCELCD, Futuroscope, Poitiers, FRANCE

Financial support: ANR ‘Micromélange’

Prof. P.E. Dimotakis of Caltech was responsible for the conceptual and detailed design of the PaSR and contributed to the initial experiments.



OUTLINE

II. Experimental set-up: Partially Stirred Reactor (PaSR)

Experimental methods: PIV, LDV (1 and 2 points), PLIF

III. Description of the flow

IV. Characterization of the mixing

I. Motivation of the great work: theoretical vs. applied research

Instantaneous aspect: instabilities in the central region

Mean velocity field

Fluctuating field and isotropy

Spectral analysis

Fine-scale properties of the flow

V. Conclusions



I. MOTIVATION: Improved understanding of Turbulent Mixing

• Why?– Combustion, propulsion, chemical and other industrial problems

• How?– Create SHI – Stationary, (nearly) Homogeneous, and (nearly) Isotropic flow

and mixing: closed vessels and/or propellers, HEV…

The ‘porcupine’: R. Betchov, 1957

‘

Synthetic jets’ in cubic chamber - W. Hwang and J.K. Eaton (E. Fluids, 2003)

Propellers - Birouk, Sahr and Gokalp (F. Turb. & Comb, 2003)

Synthetic jets - J.P. Marié

French Washing Machine

Ignition, stability, extinction ? Pollutants emissions ? Better efficiency ?




•Issues?

– Optimal configuration: basic PaSR (Partially Stirred Reactor) model

Z1

Z1

Z0

Z0

Exit

Assumptions:

Mean: Homogeneity at large scales, Stationary case

Fluctuations of the smaller scales

Characteristic times:

R (Residence time); T (Turbulence time);

M (Mixing time); C (Chemical time)

S.M. Correa and M.E. Braaten (1993)

Main advantages:

Ideal tool to test micro-mixing

models

(IEM, Curl, Curl modified, …)




Question

Why a SHI flow must be created since few such flows exist in reality ?

Turbulent flows are very complex by nature interest to examine simpler flows

Create a reference and an academic experimental configuration

Ideal to develop and valid statistical theories of turbulence

Analytical approaches

Limitation of DNS for high Re

High Re can be reached in forced turbulence

Ultra Low-NOx Combustion Dynamics



II. EXPERIMENTAL SET-UP

Design of the PaSR versus objectives:

- Large range of Reynolds number Re: 60 – 1000

- Pressure variations 1- 3 bars

- Different flow configurations

Pairs of Impinging jets

Sheared flow

- Modularity of the system

- Large range of flow rates and internal volumes

- Characteristic times R and T compatible with chemical time

- Reactive configuration for future work

P. Paranthoen, R. Borghi and M. Mouquallid (1991)



II. EXPERIMENTAL SET-UP*

Volume PaSR: V = 11116 cm3

Injection velocity: UJ = 4.5 - 47 m/s Return flow= porous top/bottom plates Residence time: tR = 8 -46 ms

Reynolds number 60 Rl 1000 (center)

*Prof. P.E. Dimotakis of Caltech was responsible for the conceptual and detailed design of the PaSR and contributed to the initial experiments.



Velocity field: 1) Particle velocimetry– Resolution and noise limitations– PIV resolution linked to size of interrogation/correlation window, e.g., 16, 32,

and 64 pix2, and processing algorithm choices• Does not resolve small scales: the smallest 100% =1.7 mm• Problem to estimate energy dissipation directly

– Towards adaptive/optimal vector processing/filtering

2) LDV in (1 point and) 2 points – Simultaneous measurements of One velocity component in two points of the

space: spatial resolution 200 * 50 microns; sampling frequency= 20 kHZ

Scalar field: PLIF on acetone Small-scale limitations set by spatial resolution (pixel/laser-sheet size)

The smallest resolved scale 100% =0.7 mm

Signal-to-noise ratio per pixel– Adaptive/optimal image processing/filtering

II. EXPERIMENTAL SET-UP and measurements



Re 104D (mm), 2H (mm), H/D

10, 60, 3

10, 60, 3

6, 60, 510, 60,

310, 60, 3 6, 60, 5 6, 60, 5 6, 60, 5

Qv (m3/h) 60 86 60 129 155.2 100 129 155.2

Vinj (m/s) 6.63 9.50 18.42 14.26 17.15 30.70 39.60 47.65

TR (ms) 43.56 30.39 43.56 20.26 17.15 26.14 20.26 17.15

P (bar) 1.40

(m²/s) x10-5 1.089

6089 8728 10149 13092 15751 16915 21821 26252

26252

6089

8 injection

conditions

DVinj Re

II. EXPERIMENTAL SET-UP and measurements

2 Geometries:

H/D=3

H/D=5



A forced box turbulence

x

y z

-locally, in each part of the PaSR, we recognize a ‘classical’ zone,

e.g. Injection zone = impinging jets

« Mixing » zone = stagnation zone

Return flow (top/bottom porous)

Presence of giant vorticity rings

III. DESCRIPTION of the FLOW: Mean flow properties

=16 French

Washing

machines



GIANT COHERENT RINGS

Strong circomferential

mixing layers

III. DESCRIPTION of the FLOW: Mean flow properties



x

y z

1

222 2 vuq

l

2

3

injVV

Strong energy injection

III. DESCRIPTION of the FLOW: fluctuating field



III. DESCRIPTION of the FLOW: fluctuating field

I

II

Energy Isotropy?

Structures: azimuthal enstrophy



k-3

Horizontal and vertical cut in 2D spectrum

1) Energy injection

2) Restricted scaling range E(k) k-5/3

3) Scaling range E(k) k-3 1D

spectra in

k-2.33

Properties similar to turbulence in rotation presence of coherent

structures

fk1pixelsk

Energy

injection

What about the small scales? Unresolved by PIV

Large-scale information from PIV

LDV measurements in 1 and 2 points.

CUT-OFF

III. DESCRIPTION of the FLOW: fluctuating field; spectral approach from PIV



Vinj

=7m/s

I

II

I

II

I : Impinging point

II: Return zone

(Gaussian)

From LES, vortices (Q criterium)

III. DESCRIPTION of the FLOW: fluctuating field; local approach

Vinj

=17m/s

Local approach



• 3-rd order SF• 2-nd order SF with the Kolmogorov constant

Ck=2 .. • Normalized dissipation which L?

Attention to initial conditions versus universality .. However, a reliable test

• The most reliable test is the 1—point energy budget equation, when the pressure-related terms could be neglected (point II).

III. DESCRIPTION of the FLOW: fluctuating field; local approach;

PIV for determining small-scale properties

3'u

LC

‘Traditional’ Spectral method Inertial range

Corrected spectra (see Lavoie et al. 2007);

Drawback: the theoretical 3D spectrum E(k)

should be known ..

Drawback: spectra are to be calculated over locally homogeneous regions of the flow, and require 2^N points

Here:



III. DESCRIPTION of the FLOW: fluctuating field; PIV for determining small scale properties 3-rd order SF

3

PIV

( u) 4

r ε 5

Iterative Methodology

• Measure , consider the Kolmogorov constant as 4/5 and infer Epsilon

• Determine the turbulent Reynolds number, infer the Kolmogorov constant (forced turbulence) and start again

Grid turbulence data: Mydlarski & Warhaft 1996, Danaila et al. 1999

3u



JETS

Antonia & Burattini, JFM 2006

III. DESCRIPTION of the FLOW: fluctuating field; PIV for determining small scale properties 3-rd order SF



The other tests• 2-rd order SF with the Kolmogorov constant

• Normalized dissipation which L? Attention to initial conditions versus universality .. However, a reliable test

for • The most reliable test is the 1—point energy budget

equation, when the pressure-related terms might be neglected (point II).

III. DESCRIPTION of the FLOW: fluctuating field; PIV for determining small scale properties

3/23/22 rCu K

3'u

LC

5.0C

NDISSIPATIO

PRODUCTIONDIFFUSIONVISCOUS

DIFFUSIONPRESSUREDIFFUSIONTURBULENTDECAY

R

Uw

y

Vv

R

Uu

y

U

R

Vuv

y

q

R

q

RR

q

pvy

puRRR

vqy

uqRRRy

qV

R

qU

²²²1

111²

2

1²

2

11²²

22

2

22

150R

/r

3/2r



III. DESCRIPTION of the FLOW: fluctuating field; back to PIV for determining small scale properties

011 2

y

Pv

yuvR

RRy

VV

NDISSIPATIO

PRODUCTIONDIFFUSIONVISCOUS

DIFFUSIONPRESSUREDIFFUSIONTURBULENTDECAY

R

Uw

y

Vv

R

Uu

y

U

R

Vuv

y

q

R

q

RR

q

pvy

puRRR

vqy

uqRRRy

qV

R

qU

²²²1

111²

2

1²

2

11²²

22

2

22

For the stagnation point I,

The pressure-velocity correlation

Term cannot be neglected, since

The mean pressure is important

At high Reynolds and low ratios H/D




RESULTS: Point I

PIV finite differences

PIV 3 other methods




RESULTS: Point I

Conclusion (point I) R_lambda maximum=750

2/1ReRe

2/1Re




RESULTS: Point II

PIV finite differences

PIV 4 other methods



III. DESCRIPTION of the FLOW: fluctuating field; back to PIV for determining small scale properties RESULTS: Point II

Conclusion (point II) R_lambda maximum=350

2/1ReRe 2/1Re



Residence time

Cascade time

Kolmogorov time

Red circles: point I

Blue diamonds: point II



a) LDV in 1 point mean velocity, RMS, small-scales quantities (definitions, correlations, SF2, SF3, 1-point energy budget equation… ). Good to determine the RMS and to compare with the PIV results (15% difference).

Drawback: Taylor’s hypothesis is needed, in a flow where the turbulence intensity varies from 100% to infinity (stagnation points ..).

b) LDV in two points simultaneous measurements of one velocity component in 2 spatial points (separation parallel to the measured velocity direction)… many points.

Different methods: SF2, SF3, definition of

1-point energy budget equation (pressure … good for point II).

III. DESCRIPTION of the FLOW: fluctuating field; LDV for determining small scale properties

2

2

lim15r

uOr

These measurements only reinforce the

Conclusions pointed out by large-scale PIV



Jets instabilities

Interface probability, along the jets axis

l

Gaussian shape of the Pdf

= 1 = 0

(Denshchikov et al. 1978)

IV. DESCRIPTION of the scalar mixing: fluctuating field



Large pannel of structures

Large-scale instabilities (jets flutter)

Mechanisms controlling the mixing?

H/D=3 H/D=5

Instantaneous fields of the mixing fraction

IV. Description of the scalar mixing: fluctuating field



H/D=3 H/D=5

Invariance / injection conditions

Similarity V

IV. Description of the scalar mixing: mean field






Conclusions

• Pairs of impinging jets

• Return flow by top/bottom porous locally axisymmetric flow

strong sheared layers

• Flow only (very) locally homogeneous difficulties to apply the classical spectral approach (spectral corrections because of finite size of the probe, and so on ..)

• Techniques to infer the (local) dissipation and turbulent Reynolds number

Structure functions (SF2, SF3) are better adapted

Inertial-range properties are quite useful to infer small-scale properties of the flow (dissipation)

1-point energy budget equation- where the pressure velocity correlations are negligible



Conclusions

•The turbulent Reynolds number goes up to

750 in the points among opposed jets

350 in the return flow (Gaussian statistics)

•Mixing is done more rapidly than the velocity field: one injection

point, and at one very small scale

• The velocity field is injected at several scales and in several points

• Analogy kinetic energy- scalar does not hold



Influence des grandes structures de concentration uniforme

Evolution du pic vers des niveaux de concentration inférieure présence de structures à petites échelles

Plus grande stabilité gradients plus importants mélange aux petites échelles plus efficace




3

PIV

( u) 4

r ε 5

JETS

MID-SPAN

III. Description of the flow: fluctuating field; PIV for determining small scale properties 3-rd order SF

The sign changes at

Large scales (inhomogeneity)



Results Champ instantané de la vitesse azimutale dans le plan des jets

expérience

simulation


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The structure of the velocity and scalar fields in a multiple-opposed jets reactor

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