22.10.2014 Views

The significance of coherent flow structures for the turbulent mixing ...

The significance of coherent flow structures for the turbulent mixing ...

The significance of coherent flow structures for the turbulent mixing ...

SHOW MORE
SHOW LESS

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

(<br />

ì<br />

(<br />

æ<br />

(<br />

ì<br />

è<br />

ð<br />

(<br />

(<br />

(<br />

(<br />

(<br />

(<br />

ì ¨0/213<br />

(<br />

í<br />

(<br />

4<br />

(<br />

4<br />

(<br />

í<br />

/513 ì<br />

4<br />

<br />

<br />

<br />

4<br />

(<br />

4<br />

(<br />

æ<br />

í<br />

í<br />

4<br />

(<br />

è<br />

(<br />

(<br />

(<br />

<br />

(<br />

(<br />

(<br />

,<br />

(<br />

4.3 Modes <strong>of</strong> Operation I – In-plane <strong>flow</strong>s<br />

<strong>for</strong> multiple-plane recording can be easily generated. Slider 4 to 7 from <strong>the</strong> top specify <strong>the</strong><br />

delay between <strong>the</strong> flash-lamps and <strong>the</strong> Pockels-cells in order to adjust <strong>the</strong> output energy <strong>of</strong><br />

each laser individually and with slider 8 <strong>the</strong> time <strong>for</strong> <strong>the</strong> read-out <strong>of</strong> <strong>the</strong> first camera images<br />

can be adjusted with respect to <strong>the</strong> first laser pulse. In <strong>the</strong> centre menu in <strong>the</strong> lower half<br />

<strong>of</strong> figure 4.4 <strong>the</strong> specifications <strong>of</strong> <strong>the</strong> laser-system (Quantel, BMI) can be chosen as well as<br />

<strong>the</strong> mode <strong>of</strong> operation (high or low energy, flash-lamps only to keep <strong>the</strong> laser material at <strong>the</strong><br />

appropriate temperature, laser <strong>of</strong>f). All o<strong>the</strong>r possibilities like cameras only (<strong>for</strong> field <strong>of</strong> view<br />

adjustments) or cameras toge<strong>the</strong>r with only one oscillator (<strong>for</strong> checking <strong>the</strong> separation by<br />

means <strong>of</strong> <strong>the</strong> polarisation) can be selected in <strong>the</strong> lower left menu by a mouse click on <strong>the</strong> right<br />

bottom. After selecting <strong>the</strong> appropriate set <strong>of</strong> parameters <strong>the</strong> sequence has to be sent to <strong>the</strong><br />

electronic board and can be activated using <strong>the</strong> start bottom at <strong>the</strong> lower right <strong>of</strong> figure 4.4 and<br />

afterwards terminated with <strong>the</strong> neighbouring stop bottom. This user-friendly interface enables<br />

<strong>the</strong> user to per<strong>for</strong>m all alignments and calibrations within reasonable time.<br />

4.3 Modes <strong>of</strong> Operation I – In-plane <strong>flow</strong>s<br />

Once installed <strong>the</strong> multiplane stereo system is well suited to determine different fluid-mechanical<br />

quantities simply by changing <strong>the</strong> time sequence or light-sheet position. For<br />

(*<br />

constant<br />

pulse î) ç è ©) îŠè © separation (<br />

) and overlapping light-sheets, a time<br />

sequence <strong>of</strong> three velocity fields can be measured at any repetition rate by cross-correlating<br />

<strong>the</strong> first acquired grey-level distribution with <strong>the</strong> second, <strong>the</strong> second with <strong>the</strong> third and <strong>the</strong><br />

third with <strong>the</strong> grey-level distribution from <strong>the</strong> last illumination, see figure 4.5. By increasing<br />

(*<br />

<strong>the</strong> time delay between <strong>the</strong> second and third<br />

î+ çäè ©-, ©. î<br />

illumination (<br />

)<br />

<strong>the</strong> first order estimation <strong>of</strong> <strong>the</strong> acceleration field in its Lagrangian and Eulerian <strong>for</strong>m can be<br />

calculated in order to study <strong>the</strong> dynamic behaviour and <strong>the</strong> interaction processes <strong>of</strong> moving<br />

<strong>flow</strong> <strong>structures</strong> [36]. <strong>The</strong> Lagrangian acceleration <strong>of</strong> a moving fluid-element is defined as <strong>the</strong><br />

temporal derivative <strong>of</strong> <strong>the</strong> velocity and can be simply implemented as a difference quotient<br />

(6 6<br />

(6<br />

/513<br />

6 (4.1)<br />

ì (<br />

í7<br />

( 6 6<br />

í<br />

ì ã õ<br />

í<br />

(4.2)<br />

< 4<br />

( 6 6<br />

( 6<br />

ì ã õ<br />

ì¥ã õ<br />

í@<br />

ì¥ã õ<br />

( 6 6<br />

( 6<br />

( < è<br />

( 6 ( 6 6<br />

ã õ í with <strong>the</strong> ì¥ã õ í fluid velocities and measured at and at times and respectively.<br />

( 6 6 ã ì<br />

<strong>The</strong> nonlinear term on <strong>the</strong> right hand side <strong>of</strong> equation 4.2 can be approximated 6 ( to:<br />

4 4<br />

55

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!