I. OXIO, 2
Figure 2.12: Behaviour of Ergodic Sequence0.
Experimental Validation of Diffusion Coefficient Calculation
In order to investigatethe accuracyof the calculationof the diffusion coefficients
of above,it is necessary comparethe performanceof the models
the particles,presented to
against available experimentaldata. However, relatively little reliable experimentaldata
existswhich can be usedfor comparison.Ideally an experimentwould provide data on the
dispersionof a rangeof particlesin a stationary,homogeneous isotropic flow of infinite
extent;this beingconsistent usedin the model. The use of this type
with the approximations
of flow would thereforeenablethe test of the model under optimal conditions. While such
flows are not found in nature, as homogeneous flow are generally non-stationary and
stationary flows are generally non-homogeneous, decaying grid generatedturbulence
providesa good approximation. The decaycharacteristics this type of turbulenceare well
known andthroughthe applicationof suitabletemporaland spatial scaling it can be treated
asquasi-stationary.Also correctionscan be madeto accountfor the inhomogeneity found
in the meanflow directionandit can be consideredisotropic, in planesperpendicularto the
meanflow, thus allowing the applicationof a one-dimensional
havebeenchosen comparison,all of which use
a form of decaying turbulence.Firstly the well known experimentof Snyder
and Lun-fley (1971) ( S&L) which is consideredas the definitive experimentin this area;
secondly the experimentof Wells and Stock (1983) (W&S) in which the extra effect of
crossingtrajectorieswasconsidered finally the numericalexperimentof Elghobashiand
Truesdell (1992) (EM), which has beenmentionedin the precedingchapter.
These experimentswill be discussedbelow and comparisonsmade between the
various types of model derived in chapter2 and the given experimentaldata.
3.2 Data of Snyder and Lumley
This experiment considered be the definitivework on the dispersionof particles
in simple flow situations, and thus is used extensivelyin the literature as a test of models.
This experiment together with the numerical simulation of the sameflow performed by
E&T, which is discussedlater in this chapter, constitute the two main test-cases the
validation of the model derived above.
The experime-ntalapparatus used by S&L consisted of a vertically orientated
turbulent channelflow in a test section 16 ft (4.88 m) in length and 16 in (40 cm) square.
Ile turbulence was generatedfrom a 20 Alsec (6.55 m/s) flow through a grid with a mesh
lengthof 1 in (2.54 cm), which gavea grid Reynoldsnumberof approximately 10,000.Tie
flow conditions where chosenin order to allow direct comparisonwith the early work of
Ilie flow is nbn-homogenoussinceits intensity changesby a factor of 5/2 during
the initial period of decay,Batchelor (1953). As this decayis rather slow it is possibleto
consider the flow as self-similar with just a changein scaleswith downstreamdistance.As
a result scaling can be applied to obtain a homogenousand stationary flow. Thus the
turbulence flow with propertiesequivalent to the those
could be treatedasa homogeneous
measuredat an arbiamy scalingpoint. This point was taken to be 73 mesh(X/M) lengths
downstream.7le corrections were madeby (i) compensating velocity fluctuations by
normalising by the r. m.s fluctuation observed at the point in question at the time of
observation and (ii) compensatingfor the increasinglength scaleby dividing separations
usedin the experimentby their central location
The particlesusedin the experinient
werechosento spana large rangeof relaxation
times and particle diameters,ranging from a particle which would be expectedto closely
follow the flow field, a hollow glassbead,to one which would exhibit large inertial effects,
a solid copper particle. Ille relevant particle characteristicscan be found in table 3.1.
Ile particles were injected at the grid and their mdial positions were measured at
10 downstreamlocations, spacedlogarithmically starting at 43 meshlengthsdownstream
and ending at 171 mesh lengths. Particle radial displacementswere measuredfrom