research article large scale gas stratification erosion...

Research ArticleLarge Scale Gas Stratification Erosion bya Vertical Helium-Air Jet

R Kapulla G Mignot S Paranjape L Ryan and D Paladino

Paul Scherrer Institut 5232 Villigen Switzerland

Correspondence should be addressed to R Kapulla ralfkapullapsich

Received 5 August 2014 Accepted 25 September 2014 Published 30 November 2014

Academic Editor Arkady Serikov

Copyright copy 2014 R Kapulla et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Containment conditions after certain postulated severe accident scenarios in nuclear power plants might result in the accumulationof hydrogen in the vessel dome Inspired by these accident scenarios an experiment for the OECDNEA benchmark exercise (2014)was carried out in the large scale PANDA facility at the Paul Scherrer Institut in Switzerland The benchmark experiment wasconducted at room temperature and under conditions characterized by an initially positively buoyant jet which becomes negativelybuoyant while interacting with a helium layer The experiment addresses (i) the initial conditions especially at the tube exit and (ii)the details of the entrainment of the helium stratification into the jet and the transport of the mixture towards the lower parts ofthe vessel For the tube exit velocity mean and fluctuating quantities we find a reasonable agreement with pipe flow data but a lackof agreement between past tube exit measurements and our results It is shown that the axial velocity of the jet experiences a strongdeceleration in the vicinity of the helium-rich layer and is finally stopped Fluid accumulates in this zone and part of this fluidis flowing back in a narrow annular region around the upward flowing jet Consequently part of the annular flow is reentrainedinto the rising jet During the layer erosion the flow structure changes from a more downwards oriented annular type to a morehorizontally oriented mushroom type of flow It is found that locations for which we record considerable turbulent kinetic energy119896 extends above the region where the velocity magnitude |V| has decayed to almost zero indicating that the jet deceleration andredirection introduces considerable turbulence in the helium stratification

1 Introduction

Incompressible turbulent round jets with density 120588119895 issuinginto large ideally infinite and quiescent domains with thesame density are often referred to as building block flows andnumerous experimenters have conducted different types ofthese measurements An overview of the different phenom-ena and the physics in turbulent jets can be found for exam-ple in [1ndash3] and a recent review of experimental data is pro-vided in [4 5] However quite often in real life applicationsthe jet flow is influenced by buoyancy [4 6] For example ajet of fluid with density 120588119895 which is directed into a volume offluid of density 120588119886 with 120588119895 = 120588119886 or a jet (120588119895) impinging ontoa stable density stratification (120588119886) is often encountered duringindustrial processes The sewage disposal through a pipe intoa river or the sea is widely used in industry to mix the wastewater with fresh water Jets discharging into a two-layer stablystratified environment have received relatively little attention

despite their fundamental nature and their potential practicalsignificance A ventilated room for example can naturallyform a two-layer stratification and it is of interest to knowhow cold air injected from below mixes in this environment

A jet with the density 120588119895 is called positively buoyantwhen the buoyancy force and the momentum have the samedirection and the buoyancy force adds to the momentumsuch that the velocity decaymdashcommon for nonbuoyant jetsmdashis partly compensated and for strong buoyancy forces the jetmight even accelerate When the buoyancy and the momen-tum forces have opposite directions the jet is called negativelybuoyant that is the negative buoyancy decelerates the jetmuch faster compared with a nonbuoyant jet

These phenomena also have relevance for nuclear safetyanalysis [7ndash12] Three-dimensional computational fluid dy-namics (CFD) codes as well as advanced lumped parameter(LP) codes are increasingly used for safety analysis to simu-late transient containment conditions after various accident

Hindawi Publishing CorporationScience and Technology of Nuclear InstallationsVolume 2014 Article ID 197267 16 pageshttpdxdoiorg1011552014197267

2 Science and Technology of Nuclear Installations

scenarios for present [13] and upcoming generations ofnuclear power plants [14] Consequently the reliability ofsuch codesmust be tested against experimental data collectedunder prototypical thermal hydraulic conditions Large scaletest facilities [15] should be preferentially used to minimizedistortional effects that might arise from geometrical scaling[11]

The experiment presented in the paper describes theinteraction of vertical upward projecting air-helium jetemerging from a tube below a helium-rich air layer Theexperiment is carried out under isothermal and isobaricconditions and focuses onto the flow conditions at the tubeexit in addition to the mechanisms of entrainment of thehelium stratification located just beneath the vessel domeTheexperiment was conducted under conditions characterizedby a jet which is initially buoyant and becomes negativelybuoyant and decelerates when it reaches the helium stratifi-cation Results depicting the mixing transport and transienthelium stratification erosion are presented in terms of 2DPIV measurements which were used to measure the flowvelocities at different locations and in particular at the inter-face between the helium layer and the upward impingingjet Additional gas concentration measurements with a massspectrometer are used to calculate density profiles whichillustrate the erosion process of the density stratification

It should be noted that the present experiment violatesintentionally the Boussinesq approximations of the first andsecond kind The Boussinesq approximation of the first kindis part of a series of simplifications in which the density vari-ation in the continuity equation is neglected The Boussinesqapproximation in the momentum equation thus requires thatthe temperature or density differences in the fluid remainsmall A 10 difference is normally regarded as the upperlimit for this first approximationThe Boussinesq assumptionof the second kind expresses the Reynolds stresses resultingfrom the RANS equations in terms of the mean strain rate

minus11990610158401198941199061015840119895 = ]119905 (

120597119906119894

120597119909119895

+120597119906119895

120597119909119894

) (1)

with ]119905 denoting the scalar isotropic eddy viscosity [16] Itis noted that the introduction of high density gradients inhorizontal stratified flows may lead to the violation of bothkinds of Boussinesq assumptions simultaneously The highdensity gradient violates the small density difference require-ment and the damping of the vertical velocity fluctuationsin the vicinity of the stratification violates the eddy viscosityisotropy assumption Consequently besides the insight intofundamental physical mixing mechanisms in the presenceof steep density gradients and an intended violation of theBoussinesq approximations it is also expected that the con-ducted experiment poses some interesting computationalchallenges

In Section 2 we give an introduction to the experimentalfacility the instrumentation and the initial and boundaryconditions In Section 3we discuss the experimental in-vesselresults of the erosion process in the presence of a helium-richstratification by means of velocity and temperature maps as

well as concentration profiles Some emphasis was put on theerror calculation for the different measurement devices used

2 Experiment

The vessel used for the experiments had an inner diameterof 4m and a height of 8m Figure 1 The air-helium mixtureforming the jet with density 120588119895 and the nominal tube exitvelocity V119895119899 is injected through a tubewhich is positioned off-axis by 648mm with respect to the axis of symmetry of thevessel For the calculation of the nominal velocity we neglectthe formation of boundary layers at the inner tube walls andassume a constant velocity across the horizontal tube exitplane The injection tube has a 180∘ bend 2200mm belowthe tube exit The straight tube past the bend has a length ofasymp30119889119905 with119889119905 depicting the tube inner diameter which is longenough that possible disturbances introduced by the bend areremoved by the turbulence due to the tubersquos high Reynoldsnumber (Re119895 asymp 20000 Table 1) This will be confirmed by thetube exit velocity measurements described in a subsequentsection Consequently the velocity profile at the tube exitshows top hat characteristics with boundary layers typical forturbulent pipe flows In contrast to some past jet experimentswhere a smooth contraction nozzle at the tube exit was usedto pronounce the top hat velocity profile by compressing theboundary layers we used an injection tube with a constantnominal inner diameter of 119889119905 = 753mm Testing for thecircularity of the tube the actual inner diameter measuredat the tube exit in two perpendicular planes amounted 119889119905119886 =

754 and 119889119905119887 = 756mmwhich is in good agreement with thenominal value used henceforth

During the entire experiment the pressure was kept con-stant at about 0994 bar absolute by venting of the air-heliummixture from the vessel via a funnel connected to a flexiblehose-oriented downwards which was located at the bottom ofthe vessel Figure 1The injection tube exit is located 2995mmabove the bottom of the vessel The coordinate system originto describe the experiment is located at the bottom of thevessel and the light sheet for the PIV recordings coincideswith the 119909-119910 plane Figure 1

21 Instrumentation For the 2D velocity measurements aparticle image velocimetry (PIV) system was used The PIVcamera wasmounted in front of the upper vessel window on atranslation stage consisting of two goniometers and a rotationtable By vertically inclining the camera it was possible torecord three different field-of-views (FOVs) to follow theerosion front progression of the helium layerThe three FOVsare depicted as PosA PosB and PosC in Figure 1

An example of a raw PIV image recorded at position Bis shown in Figure 2(a) The image gives an impression of thejet-layer interaction zoneThe seeded jet entering from belowimpinges onto the nonseeded helium-rich layer and pen-etrates the stratification The corresponding instantaneousvelocity field with some selected stream lines is pictured inFigure 2(b)

Olive oil dispersed into small droplets by a spray nozzlewas used as seeding particles for the PIV technique The oil

Science and Technology of Nuclear Installations 3

Lightsheet

Lightsheet

PIVcamera

Funnel

Injectiontube

Initi

al h

eliu

m-

rich

laye

r

x

y

z

xz7984

1813

2995

3000

2200

1333 648

0

1000

2000

3000

4000

5000

6000

7000

8000

0∘

90∘270∘

315∘

135∘225∘

305∘

125∘

180∘Vent

line

empty4000

mm

empty825753

PosAPosB

PosC

(0 0)

g

1205880a

1205880 l

120588jjn

asymp2000

Figure 1 Schematic side and top view of the experimental facility with the initial helium-rich layer located in the vessel dome The maindimensions are given in mm

Table 1 Main measured parameters for the PANDA N04 experiment conducted in the frame of the OECDNEA PANDA benchmark Forthe calculation of physical properties a nominal temperature of 119879 = 22

∘C and the measured pressure of 119901 = 0994 bar were used

NumberJet amb Layer

airgs

hegs

119895dagger

gs120588119895

kgm3V119895119887ms

]119895m2s sdot 10minus5

Re119895119887mdash

120588119900119886

kgm3Δ1205880119895119886

Dagger

1205880119897

kgm3Δ1205880119895119897998771

N04 2153 042 2195 1047 467 181 20000 1173 asymp+11 0772 asympminus36daggerCalculated with 119895 = air + heDaggerCalculated as Δ1205880119895119886 = (120588119900119886 minus 120588119895)120588119900119886 sdot 100998771Calculated as Δ1205880119895119897 = (120588119900119897 minus 120588119895)1205880119897 sdot 100

particles were injected into the air stream that was directedinto the vessel through the injection line

The PIV system setup for the in vesselmeasurements pro-vides 2D velocity fields with an acquisition rate of 5Hz (thePIV setup for the tube exit measurements will be describedin a subsequent section) For the calculation of statisticalquantities 1024 image pairs were averaged which results in anoverall averaging time of 2048 s The PIV system consistedof a Quantel Twins B double pulse laser with a maximumoutput energy of 380mJ and a double frame CCD cameratype Imager Pro Xwhich is identical to the PCO1600 camerawith a resolution of 1600times1200 pixel After calibration of theimages a resolution of 0715 times 0715mm2pixel was achievedwhich corresponds to an effective spatial resolution of115 times 115mm2 for the velocity field The absolute statistical

error with confidence band of plusmn95 for the mean velocitycalculation is 120598 = plusmn0014ms on average

The gas concentration was measured in the facility bymeans of two mass spectrometers (MassSpec) Gas wascontinuously sampled and sent to the MS systems throughcapillaries having a tip inner diameter of 02mm whichrenders possible leak rates during the MassSpec measure-ments negligible Each of these tubes is equipped with athermocouple to record the temperature of the gas at thecapillary inlet associated The MS measurement is sequentialand only one line can be selected at a time via a multiportrotating valve When selected the sampled gas is sent into aquadrupole mass spectrometer which gives the partial pres-sure of the selected gas stream (air and helium) From thesepartial pressures and the temperatures the molar fractions


PosB

asymp700

mm

Helium-richair layer

asymp1000mm

Jet with seedingparticles

Instrumentationwires

(a)

x (mm)y

(mm

)

5600

5800

6000

6200

1

0minus1200 minus1000 minus800 minus600 minus400 minus200

abs

(ms

)

09

08

07

06

05

04

03

02

01

(b)

Figure 2 Example of a PIV raw image recorded for position B showing the seeded jet in the lower part the nonseeded helium-rich airlayer at the top and parts of the instrumentation wires (a) and the corresponding instantaneous velocity field with selected stream lines (b)Dimensions are given in mm

and finally the densities were calculatedTheMS capillaries aswell as the thermocouples are mounted on instrumentationwires throughout the entire vessel One horizontal and onevertical instrumentation wire are visible in the PIV recordingpictured in Figure 2(a) The measurement error of the MSsystem is 1 absolute

For the measurement of gas temperatures for the presentexperiments Type-K thermocouples (TC) with a diameter of1mmwere usedThree of these thermocouples out of the totalbatch of 266 used in the present experiments were calibratedat the ldquoDeutscher Kalibrierdienstrdquo at the ldquoPhysikalisch-Tech-nische Bundesanstalt (PTB)rdquo in Braunschweig (Germany) forthe temperature range 40 to 200∘C Based on the deviation ofthe actual reading from the set value a common calibrationcurve to compensate for this offset was derived from allthree TCs and applied to the entire set (266 TCs) With thecompensation of the offset and from the calibration at thePTB we calculated an error of 120598119905119888 = plusmn07

∘C with a confidenceband of plusmn95 for the temperature reading

22 Initial and Boundary Conditions Prior to the test strati-fied airhelium conditions have been created in the test vesselA helium-rich air layer with density 1205880119897 occupies the region119910 gt 6000mm (Figure 1) while pure air with density 1205880119886 fillsthe region below 119910 = 5000mm Between the air filled lowerpart of the vessel and the helium-rich air layer one finds atransitional region 5000 lt 119910 lt 6000mm where the heliumcontent increases continuously

The measured helium and air molar fractions at time119905 = 0 as a function of elevation are displayed in Figure 3This figure has been compiled fromMassSpec measurementstaken principally along the axis of the vessel However anumber of off-axis measurements have also been included to

00 02 04 06 08 10

HeliumAir

0

2000

4000

6000

8000H

eigh

ty(m

m)

Molar fraction 120594 (mdash)

Figure 3 Initial air and helium molar fraction as a function ofheight in the vessel

demonstrate the flatness of the initial horizontal stratificationA table of the MassSpec measurement points can be foundin [22] in Table A5 Note the near-zero concentration levelof helium for 119910 lt 5000mm (Figure 3) and the nonlinearincrease with height to around 037 helium molar fractionat elevation 119910 = 8030mm The measured and the nominal


parameters of the entire experimental series can be found inTable 1The deviation from the nominal values was below 1For example the nominal mass flow rate was 22 gs while themeasured mean over the entire experiment was calculatedas 2195 gs The air mass flow rate was measured using athermal mass flow meter having an accuracy of 15 of themeasured value according to the manual The mass flow ratewas averaged of 6588 s (3294data points sampledwith 05Hz)with results in a mean flow rate of 2153 gs and a standarddeviation of 023 gs respectively

The mass flow rate of helium was also measured with athermal mass flowmeter and the sampling frequency and thesampling time was the same The helium mass flow meterwas calibrated at themanufacturerrsquos facilitywith air Since theconversion from the air calibration into the heliummass flowrate involved some uncertainties we have decided to usedifferent conversion methods to assess the important heliummass flow rate in the jet (1) We used the manufacturercalibration alongwith themanufacturer supplied software forthe air to helium conversion (2)We used the manufacturerrsquoscalibration together with the ratio of the specific heats for airand helium respectively (3) We compared the flow metermeasurement against the calculated flow rate necessary toincrease the pressure in a large vessel by a certain amount(4) We used the available MassSpec data to calculate thehelium mass flow in an air-helium mixture while the airflow rate was measured with the standard thermal massflow meter Finally we sent out the mass flow meter for aseparate nonmanufacturer calibration lab and used (5) thenew calibration coefficients and (6) the new calibration coeffi-cients together with the specific heat ratios Combining all sixmethods and using statistical calculations the mean heliummass flow rate in the jet amounts to 042 gs and the error wasplusmn0022 gs with a confidence limit of 99

For further calculations the following physical propertiescalculated according to Lemmon et al [23] were used air at119901 = 0994 bar and 119879 = 22

∘C has a density of 120588air = 11735 kgm3and a kinematic viscosity of Vair = 15598 sdot 10

minus5m2s2 andfor helium we obtain 120588he = 016205 kgm3 and ]he = 12162 sdot

10minus5m2s3The jet Reynolds number Re119895119887 at the tube exit

Re119895119887 =V119895119887 sdot 119889119905

]119895(2)

was calculated using the tubersquos nominal inner diameter 119889119905and the bulk velocity V119895119887 Since the flow rate is kept constantduring the entire experiment this Reynolds number charac-terizes themomentum flux of the jet injected To characterizethe initial buoyancy we use the source densimetric Froudenumber

Fr0 =V119895119887

radic(120588119900119886 minus 120588119895) 120588119900119886 sdot 119892 sdot 119889119905

(3)

with the gravity acceleration 119892 and we obtain Fr0 = 156

which indicates a ldquojet-likerdquo flow in the near field of the injec-tion tube To characterize the initial stratification strength

and the buoyant conditions we define two (initial) densitydifferences The density difference between the jet and theambient

Δ1205880119895119886 =120588119900119886 minus 120588119895

120588119900119886 sdot 100(4)

and the density difference between the helium-rich layer andthe jet

Δ1205880119895119897 =120588119900119897 minus 120588119895

1205880119897 sdot 100 (5)

Initially right after the tube exit and for 119905 = 0 s the verticaljet experiences a positively buoyant force the velocity decayis partly compensated or the jet even accelerates as indicatedby Δ1205880119895119886 asymp 11 After a certain distance when the jetapproaches the helium-rich layer the ldquoambientrdquo densitycontinuously decreases such that the initially buoyant jetbecomes increasingly negatively buoyantmdashas indicated byΔ1205880119895119897 asymp minus36mdashwhen penetrating the helium-rich layer andthe axial velocity decays very rapidly the latter calculationneglects the entrainment of ambient gas into the jet on itsway from the tube orifice to the helium-rich layer and the cor-responding density increases Both density differences depictthe nonvalidity of the Boussinesq approximation of the firstkind at the beginning of the experiment as discussed in theintroduction The time dependent buoyancy in the course ofthe experiment will be discussed in a subsequent section

23 Tube Exit Velocities PIV measurements of the instan-taneous values of the Cartesian velocity components (119906 V)of the gas mixture emerging from the injection pipe outletwere madeThe PIV FOVs were taken over the pipersquos internalcross-section in five horizontal planes beginning 6mmabovethe injection pipe outlet From the horizontal measurementplanes velocity profiles were extracted at 119910 = 73mm abovethe outlet a position corresponding the closest approach to119910119889119905 = 01 A schematic of the arrangement is shown inFigure 4 To gain better access these measurements weretaken with the injection line removed from the PANDAvessel though still connected to the same helium and airsupply lines used in the actual test The laser sheet waspositioned at the five (5) lines AndashE at 15mm spacing overthe cross-section of the injection pipe outlet as indicated inFigure 4 The gas mixture in this case was not preheated theambient temperature was estimated at 15∘C

The PIV system setup for the tube exit measurementsprovides 2D velocity fields with an acquisition rate of 75HzFor the calculation of statistical quantities 4096 image pairswere averaged The PIV system consisted of a Litron nano Ldouble pulse laser with a maximum output energy of 200mJand the same camera used for the in-vessel measurementsThe light sheet thickness was approximately 1mm

The optical recording system consisting of the cameraand a Nikon lens (AF Nikkor 119891 = 50mm the aperturewas set to 119891 = 4) was operated in the diffraction limitthat is the particle image size becomes independent of thephysical particle size resulting in particle image sizes larger


Gas injection pipe

Light sheetpositions

Air andhelium

x

x

z

y

5

15

25

1515

1515

A

B

C

D

E

empty825 mm

empty753 mm

asymp6

mm

Figure 4 Relative positions of the FOVs of the PIV velocity measurements at the exit of the injection line note the local coordinate systemused for the measurement planes AndashE which differs from the one given in Figure 1

than 3 pixels on average According to the recommendationsin Raffel et al [24] this is sufficient to minimize so-calledpeak-locking The base analysis was performed with DaVis81 and the extended analysis with in house writtenMATLABroutines After calibration of the images a resolution of0088 times 0088mm2pixel2 was obtained which correspondsto an effective spatial resolution of 053 times 053mm2 forthe velocity field A waterpolyethylene-glycol mixture (10

1) dispersed into small droplets by an atomizer was used forthe seeding particles for the PIVmeasurementsThe particleswere injected into the air stream approximately 5000mm(asymp60119889119905) upstream of the injection pipe exit The primaryparticles have an approximate diameter of11986310 asymp 4 120583mWhilethe helium for the air-helium mixture was dry the air wasdrawn from that available at the pump inlet andwas not driedbefore injection into the pipe Consequently the air reflectsthe humidity of the atmosphere in the PANDA building atthe time of the test This results in an approximate relativehumidity of 60 for the air-helium mixture It is expectedthat a part of the water from the waterpolyethylene-glycoldroplets evaporates already in the pipe and that the dropletshave a final size of11986310 asymp 15 120583mUsing a simplified version ofthe Basset-Boussinesq-Oseen equation (BBO) for the densityratio 120588119901120588119891 ≫ 1 between particle (119901) and fluid (119891) seeRaffel et al [24]

119906119901

119906119891

=1

radic1 + 120596211989112059120

with 120596119891 = 2120587119891119891 1205910 =1205881199011198892119901

18120578119891(6)

with the amplitude ratio 119906119901119906119891 between the particle responseto the amplitude of the fluid motion the expected frequencyof the fluid motion 119891119891 and the particle time constant 1205910 thisallows for the calculation of the amplitude response of suchparticles Figure 5 Equation (6) resembles a secondorder lowpass filter response for the ratio of the velocity amplitudes

1 10

10

08

06

04

02

00100

120591p = 7120583s

dp = 15 120583m

Velo

city

ampl

itude

ratio

upu

f(mdash

)

Fluid oscillation frequency ff (kHz)

Figure 5 Velocity amplitude ratio between particle and fluidmotion as a function of fluid motion frequency

Using an order of magnitude argument it follows that theparticles with time constant 120591119901 = 7 120583s under considerationcan resolve fluid motions up to a frequency of 10 kHz if theminimum allowable amplitude ratio amounts to 119906119901119906119891 asymp 09On the other hand themaximum expected frequencies of thesmallest flow structures close to or in the inertial subrange canbe estimated according to Albrecht et al [25]

119891max119891 =119906119891

2120587119871119906

Re34 (7)


with a characteristic macrolength scale 119871119906 for the velocityfield Using the inner pipe diameter for this length scale119871119906 = 119889119905 = 753mm 119906119891 = V119895119899 = 467ms and Re =

Re119895 = 20000 Table 1 results in 119891max119891 asymp 16 kHz which isin good agreement with the frequency (10 kHz) the particlescan resolve Additionally an integral time scale for the pipeflow can be estimated from 119879119906 = 119871 119906 V119895119899 = 0016 s whichallows estimating the necessary time separation requiredsuch that successive measurements decorrelate that is theybecome statistically independent 2119879119906 = 0032 s This timecorresponds to a maximum allowable sampling frequency ofasymp31Hz which is above the chosen frequency of 75Hz Itcan be concluded that the instantaneous velocity fields arestatistically independent and each velocity field contributesto the convergence of the statistical quantities calculated

The velocity profiles and the calculated statistics shownin Figures 6 and 7 were extracted for 119910119889119905 = 0097 above thetube exit and show the results for the vertical V-component(upwards in the 119910 direction) as well as the lateral 119906-compo-nent (horizontally in the 119909 direction) for the five measure-ment planes (Figure 4) As a consequence of technical restric-tions and time constraints it was not possible to measurethe third velocity component (119908-component horizontally inthe 119911 direction) However the assumption of axis-symmetricoutlet conditions is expected to prevail in this test The radialdistances (119909 direction) were normalized with the nominalpipe diameter 119889119905 = 753mm and the velocity results with thecenter line (119909 = 0) axial mean velocity V119888 = 535ms

From the measured instantaneous velocity components119906119894 (and V119894) mean 119906(V) and time averaged standard deviations1199061015840(V1015840) of the pipe exit velocity data have been calculated The

procedure used was as follows

119906 =1

119873

119873

sum

119894=1

119906119894

1199061015840= radic

1

119873

119873

sum

119894=1

119906119894 minus 1199062

(8)

Additionally we calculate the Reynolds stresses 11990610158401199061015840 (V1015840V1015840 and1199061015840V1015840) and the turbulent kinetic energy 119896 as follows

11990610158401199061015840 =1

119873

119873

sum

119894=1

119906119894 minus 1199062 (9)

1199061015840V1015840 =1

119873

119873

sum

119894=1

119906119894 minus 119906 V119894 minus V (10)

119896 =1

22 sdot 11990610158401199061015840 + V1015840V1015840 (11)

Here 119873 is the number of instantaneous velocity record-ings used in forming the average these were taken from 4096

statistically independent samples obtained at a samplingfrequency of 75Hz which corresponds to an overall averag-ing time of 546 s (91min) Analogous definitions apply foranother velocity component V To calculate 119896 with (11) we

made use of 11990610158401199061015840 = 11990810158401199081015840 (assumption of axis-symmetry)since the third velocity component 119908 was not accessibleFor the normalized axial mean velocity profiles V(119909119889119905)V119888(Figure 6(a)) measured in five planes we find a good agree-ment between planes AndashE and BndashD displaced by 30 and15mm respectively with respect to plane C indicating arotational symmetric velocity profile across the entire tubeexitThis holds also true for the other statistics Figures 6 and7 It should be noted that in the core region of the jet (minus01 lt

119909119889119905 lt 01) a nonzero value for the mean lateral velocitycomponent 119906 has been measured for all the measurementplanes (Figure 6(c)) This is considered as a consequence ofthe slightly rotated camera angle with respect to the jet axisresulting in a ldquovirtual redistributionrdquo of the vertical velocityin the lateral velocity direction which should be zero in thecore of the jet If the central measurement plane C is regardedas representative (119906 = 0013ms V = 535ms) this wouldindicate a camera inclination of 014∘ Removing this bias theldquotruerdquo axial velocity would then be 535001ms To test for thesimilarity of the V profile at the tube exit with turbulent pipeflow we applied two fit functions to the PIV data (Figure 8)a sine fit approach according to Chant [26]

VV119888

= [sin120587

2(1 minus

100381610038161003816100381610038161003816100381610038162119909

119889119905

10038161003816100381610038161003816100381610038161003816

12

)]

12

(12)

as well as the classical 17 power law

VV119888

=

100381610038161003816100381610038161003816100381610038162119909

119889119905

10038161003816100381610038161003816100381610038161003816

17

(13)

Although our experimental data agree reasonably well withthe 17 power law the sine fit (12) gives a much betterapproximation of the data No attempt was made to improvethe performance of (13) by adjusting the exponent 1119899

For the statistical error estimate reference should bemade to Figure 6 Neglecting the boundary layers an averagevalue for the mean axial velocity would typically be of mag-nitude V = 48ms in plane C with a standard deviationacross the profile of around V1015840 asymp 04ms Applying statisticalcalculus for statistically independent samples [27] the two-sided uncertainty with 95 confidence level is estimatedat 120576(V) = plusmn00122ms for the mean vertical velocity V andnondimensionalised 120576(V)V119888 = plusmn00022 Analogous estimatesapply also for the lateral velocities and result in 120576(119906) =

plusmn00092ms (120576(119906)V119888 = plusmn00017) Since the error for thestandard deviations (V1015840 asymp 04ms and 119906

1015840asymp 03ms) is

nonsymmetric [27] the two-sided uncertainty levels can beestimated as follows

V1015840 = 04+00088minus00084ms 119906

1015840= 03+00066minus00063ms

V1015840

V119888= 0074

+00016minus00015

1199061015840

V119888= 0056

+00012minus00011

(14)

A review of previous experiments investigating the scalarfield either close to the tube exit or in fully turbulent pipe flowhas been undertaken to assess the present boundary condi-tions Despite the importance of the inlet conditions onto


10

08

06

04

02

00minus04 minus02 00 02 04

c

xdt

(a)

minus04 minus02 00 02 04

016

012

008

004

998400

c

xdt

(b)


002

001

000

minus001

minus002

minus003

PosAPosBPosCPosD

PosE

u

c

xdt

(c)


008

004

002

006

PosAPosBPosCPosD

PosE

xdt

u998400 c

(d)

Figure 6 Normalized mean axial V and lateral 119906 velocity profiles ((a) and (c)) and the corresponding V1015840 and 1199061015840 ((b) and (d)) for the

measurement planes AndashE (Figure 4) at 119910119889119905 = 0097 above the injection pipe exit

the developing flow field in the near field (0 lt 119910119889119905 ≲ 8)as well as for intermediate distances (8 ≲ 119910119889119905 ≲ 20) [17 28]measurements close to the tube exit are surprisingly scarceTurbulent pipe flow results have been included since the jetoriginates from a pipe and it is expected that the flow field atleast in the core of the jet still shows pipe flow characteristicsfor the short distance past the pipe exit considered hereExcept for the data selected from Eggels et al [21] and

Boguslawski and Popiel [19] size the experiments have beenchosen with bulk Reynolds numbers as close as possible tothe present experiment The results from Boguslawski andPopiel [19] with the higher Reynolds number of 51000 werechosen since they provide results for 119906

1015840 at the tube exitThe data from the literature were digitized and renormalizedaccording to the method introduced for the present papersince different authors usually use different normalization



002

001

000

xdt

k

2 c

(a)


0005

0000

minus0005

minus0010

xdt

u998400

998400 2 c

(b)


004

003

002

001

000

PosAPosBPosCPosD

PosE

xdt

998400998400

2 c

(c)


0008

0006

0004

0002

0000

PosAPosBPosCPosD

PosE

xdt

u998400 u

998400 2 c

(d)

Figure 7 Normalized turbulent kinetic energy 119896 calculated with (11) (a) and Reynolds stresses 1199061015840V1015840 V1015840V1015840 and 11990610158401199061015840 ((b) (c) and (d)) for themeasurement planes AndashE (Figure 4) at 119910119889119905 = 0097 above the injection pipe exit

schemes An overview of the main characteristics for theselected experiments can be found in Table 2 and the resultsof the comparison for V V1015840 1199061015840 are presented in Figures9(a) to 9(c) For the normalized mean axial velocity VV119888 asa function of radial distance 119909119889119905 (Figure 9(a)) we find agood agreement between our results and those quoted in theliterature irrespective of the experimental setupmdashpipe exitor turbulent pipe flowmdashand despite of a weak scatter the data

which becomes larger when approaching either the mixingzone (pipe exit) or the pipe wall (pipe flow) 04 lt 119909119889119905 lt 05

This finding supports to a certain extent the approachof also comparing velocity fluctuations measured inbounded (turbulent pipe flow) with unbounded (tube exit)experiments When examining the normalized axial velocityfluctuations V1015840V119888 see Figure 9(b) our measurements agreebetterwith pipe flow results rather than other jet experiments


Table 2 Flow properties for the jet exit and pipe measurements from selected references used to compare with the present experiments

Reference Fluid Location Meas techn Re119895119887 119910119889119905 V V1015840 1199061015840

Present Air and He Tube exit PIV 20000 0097 radic radic radic

Mi et al [17] Air Tube exit Cold wire 16000 005 radic radic mdashPapadopoulos and Pitts [18] Air Tube exit Hot wire 17500 016 radic radic mdashBoguslawski and Popiel [19] Air Tube exit Hot wire 51000 asymp0 radic radic radic

den Toonder and Nieuwstadt [20] Water In pipe LDA 17800 mdash radic radic radic

Eggels et al [21] Water In pipe PIV 5450 mdash radic radic radic

10

08

06

04minus04 minus02 00 02 04

c

xdt

PIVSine fit

17 power law fit

Figure 8 PIVdatawith a sine fit approach togetherwith the classical17 power law at 119910119889119905 = 0097 above the injection pipe exit

this was a somewhat unexpected resultThis holds true for thecore of the jet 0 lt 119909119889119905 lt 035 where our results are in closeagreement with those reported in Eggels et al [21] despite thelower Reynolds number for the pipe flow In the outer partof the flow 035 lt 119909119889119905 lt 05 the agreement becomes lessprominent but we find a good similarity with the results fromden Toonder and Nieuwstadt [20] This might be a Reynoldsnumber effect that is the data from Eggels et al [21] wererecorded at Re119895119887 = 5400 while those of den Toonder andNieuwstadt [20] were taken at Re119895119887 = 17800 which is muchcloser to our results There seems to be no consensus inthe literature whether [29] or not [30] the magnitude andthe position of the near wall peak of the stream wise (V1015840)turbulence intensity in a fully developed pipe flow is invariantwith Reynolds number Since this discussion is beyond thescope of this paper we followed a pragmatic approach inchoosing the experimental data according to references givenin Table 2 The interested reader might find in both papersexhaustive references to pipe flow measurements and weconclude with a reasonable similarity between the present jet

exit measurements and previous pipe flow results Comparedto the tube exit measurements reported in [17 19 31] themeasurements from our experiments have the same shapehowever the literature values fall consistently below ourresults (Figure 9(b)) Additionally all experimental data missthe expected turbulence intensity increase in themixing zoneregion between the jet-core and ambient 045 lt 119909119889119905 lt 05The latter issue might be caused by an insufficient spatialresolution such that the peak value is missed but might notexplain the lower magnitudes in the core of the jet As arguedabove it is expected that the flow past the tube exit keeps itsmemory to the pipe flow origin at least in the jet-core and wefind also a considerable difference between the jet exit andthe pipe flow data Also the data presented might suffer fromthe digitization process and the subsequent renormalizationbut the procedure used for the jet exit and the pipe flow datawere similar

Finally the radial velocity fluctuations 1199061015840V119888 (Figure 9(c))fit into the picture Again we find a reasonable similaritybetween our and the pipe flow data in the jet core whilethe results differmdashas expectedmdashclose to the mixing zoneThere was only one reference outlining past measurements of1199061015840V119888 which is considerably below our measurement At the

moment this subject must be left open for a refined analysisand future discussions Overall ourmeasurements agree wellwith pipe flow results but show a lack of agreement with pasttube exit measurements

3 In-Vessel Results

For the helium-rich air layer build-up helium was injectedfor a certain amount of time determined in scoping teststhrough a tube 2m below the vessel dome until the heliumconcentration of 037 molar fraction is reached The initialdensity profile for the experiment measured at 119910 = minus648mmoff-axis (Figure 1) are shown in Figure 10 In the lower partof the vessel we have initially an air atmosphere at roomtemperature (119879 asymp 22

∘C 119901 = 0994 bar) while the helium-airmixture with a lower density is trapped in the vessel dome

Themeasurement is initiated by opening a valve to releasethe air-helium jet (1199050 = 0 s) and the entire experiment isfinished when the helium-rich layer is completely erodedsuch that we measure similar densities in the entire vessel(119905 ≃ 5300 s) Mean velocities and velocity fluctuations weremeasured using PIV in three regions (A to C Figure 1) ofthe flow all above and around the axis of the injectionpipe These measurements have been processed to produce


10

08

06

04

02050403020100

xdt

c

Own measurementMi et al 2001

Eggels et al 1994

Papadopoulos and Pitts 1998den Toonder and Nieuwstadt 1997

(a)

050403020100000

005

010

015

020

025

xdt

998400

c


Eggels et al 1994

Papadopoulos and Pitts 1998Boguslawski and Popiel 1979den Toonder and Nieuwstadt 1997

(b)

050403020100000

005

010

xdt

u998400 c

Own measurement

Eggels et al 1994

Boguslawski and Popiel 1979den Toonder and Nieuwstadt 1997

(c)

Figure 9 Comparison of mean and turbulence statistics (V V1015840 1199061015840) of own tube exit measurements with straight pipe tube exit measurementsfrom the literature and turbulent pipe flow results

averaged values over a time period of 2048 s The measureddata refer to the time 119905119888 in the middle of this data averagingperiod that is plusmn1024 s around each specified data itemAn overview of the PIV recordings performed during theexperiment is given in Table 3

Velocity magnitude maps (|V| = radic1199062 + V2) with the cor-responding turbulent kinetic energy maps 119896 (11) measuredin the airhelium jet impinging onto the helium-rich air layerfrom below are presented in Figure 11 for selected instances intime (Table 3)The time steps cover the instance right past thebeginning of the injection (Figure 11(a)) later in time whenthe erosion process has proceeded (Figures 11(b) and 11(c))and finally the time the erosion zone is going to leave theFOV above 119910 = 6900mm (Figure 11(d)) Streamlines havebeen calculated from the underlying velocity field to guidethe eye These streamlines are identical for corresponding|V|-119896 maps The injection tube axis at asymp 650mm was markedwith a dashed line Since the seeding particles for the PIVmeasurements are transported with the jet the helium layer

unaffected by the jet is nonseeded consequently no velocitiesare recorded in those small areas this becomes visible for the119896 maps in the top parts of Figures 11(g) and 11(h) where wefind a region with 119896 = 0

Additionally to assess the quality of the data we havethresholded the statistical quantities being calculated fromminimal 900 valid vectors which results in the abrupt changesof the quantities in areas with a lower number of valid vectorsOne finds also minor horizontally and vertically orienteddistortion zones which were caused by the instrumentationwires used for the temperature and mass spectrometermeasurements (Figure 2) These areas were masked duringthe analysis and the resulting gaps were filled by linearinterpolation from the surrounding quantities to facilitate thecalculation of streamlines

Due to its momentum the jet (primary flow) continu-ously penetrates upwards into the helium-rich layer Causedby the negative buoyancy the axial velocity experiences astrong deceleration in the vicinity of the helium-rich layer


08 10 120

2000

4000

6000

8000

Transitional region

1205880l = 0772kgm3

1205880a = 1173kgm3

Hei

ghty

(mm

)

Density (kgm3)

Figure 10 Initial gas density (1199050 = 0 s) as a function of height in thevessel

Table 3 Labels of the PIV measurements performed (N01 to N07)FOV (A to C) and central sampling time 119905119888

Number Position 119905119888

N01 A 111

N02 B 715

N03 B 978

N04 B 1213

N05 C 1795

N06 C 2030

N07 C 2286

N08 C 2550

(the mixing zone) (Figures 11(b) and 11(c)) and the jet isfinally stopped Fluid accumulates in a continuous process inthis mixing zone and part of the fluid consisting in an air-helium mixture is flowing back in a narrow annular regionaround the upward flowing jet as indicated by the streamlines(Figure 11(a)) Consequently the jet decelerates additionallybecause the downwards annular flow slows down the upwardjet flow and part of the annular flow is reentrained into therising jet The main difference between the early stage ofthe erosion process (N01) and a later time (N02 N05 andN08) is the stronger confinement of the flow around the jet(Figures 11(a) versus 11(b)) this difference can be attributedto three effects firstly the spreading through entrainmentof ambient fluid in the jet with downstream distance sec-ondly the increasing resistance the helium-rich layer thatimposes onto the jet propagation and thirdly the continuousentrainment and downwards transport of the helium-richlayer which decreases the ldquoambientrdquo density Initially (N01)the jet penetrates into the transitional part of the helium-rich

layer 5000 lt 119910 lt 6000mmwhere the density decreases from1166 to 080 kgm3 (Figure 10) Consequently the negativebuoyancy initially imposed by the layer onto the jet is weakercompared with later instances in time when this transitionalregion is eroded (N02 rarr N05 rarr N08) see also [8] Alsoinitially (N01) the jet at the tube exit experiences a positivebuoyancy due to the density difference between jet andambientΔ1205880119895119886 asymp 11which partly compensates the velocitydecay natural for a jet not impinging onto a helium-richlayer This positive buoyancy decreases over time throughthe downwards transport of the helium-rich layer At thestart of the erosion process the secondary flow structureis a downwards oriented annular type During the erosionprocess this structure changes to a horizontally orientedmushroom type of flow (Figure 11N02 toN08) as indicated bythe streamlines This erosion process is shown from anotherperspective for the velocity field recorded at the fixed positionB (Figure 12) at three different instances in time The erosionfront moves upwards (N02 rarr N03 rarr N04) the radius ofcurvature for the streamlines increases and finally themixingzone is above the FOV (N04)

The observations for the velocity magnitude field equallyapply to the turbulent kinetic energy maps (Figures 11(e)versus 11(g)) While we initially find 119896 asymp 01m2s2 in thecore of the jet (N01) the kinetic energy is later distributedto a larger area such that we find 119896 asymp 003m2s2 (N08) In thezero mean velocity region (Figures 11(b) and 11(f)mdashmark A)we record significant turbulent kinetic energy indicating thatthe jet deceleration and redirection introduces turbulence inregions with zero mean velocity

The three temperature contour maps presented inFigure 13 correspond to the PIV measurements in Figure 11for timesN01N02 andN05 and have also been averaged overΔ119905 = 2048 s The temperature contour maps were calculatedby linearly interpolating the temperatures between the ther-mocouple measurement locations depicted by black crossesThe jet was injected on purpose with a slightly elevatedtemperature compared with the ambient and the helium-richlayer to make temperature contour maps possible It shouldbe noted that the density difference between jet and ambientcaused byΔ119879 = 5

∘C is very small when compared with initialdensity difference of 11 (Table 1) For N01 right after thebeginning of the injection of the jet the somewhat colder(119879 asymp 20

∘C) helium-rich layer becomes visible in the vesseldome

The off-axis directed momentum of the jet results in aweak response of the helium layer such that the temperaturemap shows a left-right asymmetry which persists duringthe entire experiments The helium downwards transport isdepicted for time N02 by the almost uniform temperatureregion between the jet injection level and the helium-richlayer Later in time (N05) part of the layer is already eroded

The helium molar fraction 120594he in the jet axis (119909 =

minus648mm) as a function of time for some selected verticallocations is presented in Figure 14 Additionally the molarfraction of helium measured at the tube exit in the jet isprovided with the measurement at location 119910 = 3000mmInitially the helium content of the jet decays from 120594he asymp 013


N01

||

(ms

)

minus1000 minus500minus6505000

5200

5400

5600

0

y(m

m)

x (mm)

08

06

04

02

(a)

N02

5800

6000

6200

A

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

05

(b)

N05

6400

6600

6800

05

04

03

02

01||

(ms

)


y(m

m)

x (mm)

(c)

N08

6400

6600

6800

05

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

(d)

N0101

008

006

004

002

5000

5200

5400

5600

0

k(m

2s2)


y(m

m)

x (mm)

(e)

N02

5800

6000

6200

A006

005

004

003

002

001

0

k(m

2s2)


y(m

m)

x (mm)

(f)

N05

0

k(m

2s2)

003

002

0016400

6600

6800


y(m

m)

x (mm)

(g)

k(m

2s2)

003

002

001

N08

6400

6600

6800


y(m

m)

x (mm)

(h)

Figure 11 Selected velocity magnitude maps |V| ((a) to (d)) and the corresponding turbulent kinetic energy 119896 maps ((e) to (h)) recordedduring the erosion process of the helium-rich layer

at the tube exit (119910 = 3000mm) to 120594he asymp 005 at position 119910 =

4326mm considerably below the helium-rich layer throughthe entrainment of ambient gas from the environmentmdashmostly pure air at this early stage Caused by the continuouserosion of the helium-rich layer at the top and the downwards

transport of helium the helium content of the ambientincreases such that 120594he in the jet at position 119910 = 4326mmincreases accordingly over time At the initial stage of the ero-sion process it is expected that the secondary flow describedpreviously is not passing all theway down to the jet orifice and


N02

5800

6000

6200

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

05

06

(a)

N03

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06

(b)

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06N04

(c)

Figure 12 Development of the velocity magnitude field for position B during time steps 119905 = 715 978 and 1213 s

Injection tube

y(m

m)

x (mm) x (mm) x (mm)

N01 N02 N05

minus2000 2000 minus2000 2000 minus2000 2000

8000

7000

6000

5000

4000

3000

25

245

24

235

23

225

22

215

21

205

20

(∘C)

Figure 13 Temperature contour maps for the entire vessel above the injection level

eventually even further down to the vessel bottom but downto an intermediate level where the density of the annularflow equals the density of the surrounding such that the fluidstarts to spread radially as described in [8 32] Consequentlythe measurement location at the bottom of the vessel (119910 =

1076mm) indicates until 119905 asymp 1500 s no helium transport intothis region The helium content measured at points initially

located in the helium-rich layer (119910 ≳ 6000mm) decays intime such that locations closer to the tube exit decay earlierwhile locations closer to the vessel dome remain initiallyalmost constant and unaffected by the jet but decay later intime The helium content for all positions approaches finallya common level of 120594he asymp 015 a state for which the gas in theentire vessel is homogeneously mixed


00

01

02

03

04

Time (s)0 1000 2000 3000 4000 5000

8030

7478

6926

6700

6496

6092

4326

1076

3000

y (mm)

Heli

um m

olar

frac

tion120594

he(mdash

)

Figure 14 Helium molar fraction measured for selected locationsin the jet axis (119909 = minus650mm) as a function of time with the verticalmeasurement location as parameter The molar fraction at the tubeexit is provided at 119910 = 3000mm

4 Conclusions

Computational fluid dynamics (CFD) codes are increasinglyused for safety analysis to simulate transient containmentconditions after postulated severe accident scenarios innuclear power plants (NPPs) Consequently the reliability ofsuch codes must be benchmarked against experimental dataobtained preferentially in large scale facilities to limit scalingeffects Such an experiment was carried out in the large scalePANDA facility at the Paul Scherrer Institute in Switzerlandfor an OECDNEA benchmark The experiment highlightsthe interaction of a vertical air jet with a helium stratification

For the tube exit measurements we find an excellentagreement between our results for themean axial velocity andthose quoted in the literature irrespective of the experimentalsetupmdashpipe exit or turbulent pipe flow And we have founda reasonable agreement between the shape of the classical17 power law and the experimental data but a muchbetter approximation is provided by the sine law introducedAlthough the general shape of themeasurements of the veloc-ity fluctuations from the literature performed close to the tubeexit is similar to ourmeasurements their magnitudes are sys-tematically below our results Additionally all tube exit mea-surements miss the expected turbulence intensity increase inthe mixing zone region between the jet-core and ambientSomewhat unexpected we found a better agreement betweenour measurements and the pipe flow results for the velocityfluctuations compared with other jet exit measurements

The vertical jet discharges initially into a positively buoy-ant environment and after a certain distance the ambientdensity continuously decreases such that the positively buoy-ant jet becomes increasingly negatively buoyant when pen-etrating the helium-rich layer and the axial velocity decaysvery rapidly Fluid accumulates in thismixing zone and a partof the fluid is flowing back in a small annulus around theupward flow By this transient mechanism the helium-rich

layer is continuously eroded and helium is transported intolower parts of the test section such that the jet initial positivebuoyancy decays over time

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to thank the staff members MaxFehlmann and Simon Suter for their engaged support in con-ducting these experiments

References

[1] W D Baines ldquoEntrainment by a plume or jet at a dens ityinterfacerdquo Journal of Fluid Mechanics vol 68 no 2 pp 309ndash320 1975

[2] C-J Chen and W Rodi ldquoVertical turbulent buoyant jetsa review of experimental datardquo NASA STIRecon TechnicalReport A 80 1980

[3] E J List ldquoTurbulent jets and plumesrdquo Annual Review of FluidMechanics vol 14 pp 189ndash212 1982

[4] G Lipari and P K Stansby ldquoReview of experimental dataon incompressible turbulent round jetsrdquo Flow Turbulence andCombustion vol 87 no 1 pp 79ndash114 2011

[5] C G Ball H Fellouah and A Pollard ldquoThe flow field inturbulent round free jetsrdquo Progress in Aerospace Sciences vol50 pp 1ndash26 2012

[6] J S Turner Buoyancy Effects in Fluids Cambridge UniversityPress 1979

[7] R Kapulla D Paladino G Mignot R Zboray and S GuptaldquoBreak-up of gas stratification in LWR containment induced bynegatively buoyant jets and plumesrdquo in Proceedings of the 17thInternational Conference on Nuclear Engineering (ICONE rsquo09)pp 657ndash666 ASME July 2009

[8] R Kapulla G Mignot and D Paladino ldquoDynamics ofhelium stratifications eroded by vertical air jets with differentmomentardquo in Proceedings of the 15th International TopicalMeeting on Nuclear Reactor Thermalhydraulics vol 2009 pp657ndash666 ASME 2013

[9] G Mignot R Kapulla R Zboray N Erkan and D PaladinoldquoParametric study of containment gas stratification break-upby vertical fluid releaserdquo in Proceedings of the 13th InternationalTopical Meeting on Nuclear Reactor Thermal Hydraulics PaperNURETH13-1087 Kanazawa Japan September 2009

[10] R Zboray and D Paladino ldquoExperiments on basic thermalhy-draulic phenomena relevant for LWR containments gas mixingand transport induced by buoyant jets in a multi-compartmentgeometryrdquo Nuclear Engineering and Design vol 240 no 10 pp3158ndash3169 2010

[11] G Yadigaroglu M Andreani J Dreier and P CoddingtonldquoTrends and needs in experimentation and numerical simula-tion for LWR safetyrdquo Nuclear Engineering and Design vol 221no 1-3 pp 205ndash223 2003

[12] D Paladino R Zboray P Benz and M Andreani ldquoThree-gasmixture plume inducing mixing and stratification in a multi-compartment containmentrdquo Nuclear Engineering and Designvol 240 no 2 pp 210ndash220 2010


[13] MHoukemaN B Siccama J A Lycklama aNijeholt andEMJ Komen ldquoValidation of the CFX4 CFD code for containmentthermal-hydraulicsrdquo Nuclear Engineering and Design vol 238no 3 pp 590ndash599 2008

[14] A Epiney K Mikityuk and R Chawla ldquoHeavy-gas injectionin the generation IV gas-cooled fast reactor for improveddecay heat removal under depressurized conditionsrdquo NuclearEngineering and Design vol 240 no 10 pp 3115ndash3125 2010

[15] M Andreani K Haller M Heitsch et al ldquoA benchmarkexercise on the use of CFD codes for containment issues usingbest practice guidelines a computational challengerdquo NuclearEngineering and Design vol 238 no 3 pp 502ndash513 2008

[16] A Dewan Tackling Turbulent Flows in Engineering Springer2011

[17] J Mi D S Nobes and G J Nathan ldquoInfluence of jet exitconditions on the passive scalar field of an axisymmetric freejetrdquo Journal of Fluid Mechanics vol 432 pp 91ndash125 2001

[18] G Papadopoulos and W M Pitts ldquoScaling the near-fieldcenterline mixing behavior of axisymmetric turbulent jetsrdquoAIAA Journal vol 36 no 9 pp 1635ndash1642 1998

[19] L Boguslawski and C O Popiel ldquoFlow structure of the freeround turbulent jet in the initial regionrdquo Journal of FluidMechanics vol 90 no 3 pp 531ndash539 1979

[20] JM J den Toonder and F TMNieuwstadt ldquoReynolds numbereffects in a turbulent pipe flow for low to moderate Rerdquo Physicsof Fluids vol 9 no 11 pp 3398ndash3409 1997

[21] J G M Eggels F Unger M H Weiss et al ldquoFully developedturbulent pipe flow a comparison between direct numericalsimulation and experimentrdquo Journal of Fluid Mechanics vol268 pp 175ndash209 1994

[22] OECD-NEA OECD-NEA-PSI CFD Benchmark SpecificationNational Environment Agency 2013

[23] E Lemmon M Huber and M McLinden NIST StandardReference Database 23 Reference Fluid Thermodynamic andTransport PropertiesmdashREFPROP Version 90 National Instituteof Standards and Technology Standard Reference Data Pro-gram Gaithersburg Md USA 2010

[24] M Raffel C Willert S Wereley and J Kompenhans ParticleImage Velocimetry A Pratical Guide Springer Berlin Germany2007

[25] H Albrecht M Borys N Damaschke and C Tropea LaserDoppler and Phase Doppler Measurement Techniques SpringerNew York NY USA 2003

[26] L J De Chant ldquoThe venerable 17th power law turbulentvelocity profile a classical nonlinear boundary value problemsolution and its relationship to stochastic processesrdquo AppliedMathematics and Computation vol 161 no 2 pp 463ndash4742005

[27] J Bendat and A Piersol Analysis and Measurement ProceduresJohn Wiley amp Sons New York NY USA 1986

[28] G Xu and R Antonia ldquoEffect of different initial conditions ona turbulent round free jetrdquo Experiments in Fluids vol 33 no 5pp 677ndash683 2002

[29] M Hultmark S C C Bailey and A J Smits ldquoScaling of near-wall turbulence in pipe flowrdquo Journal of Fluid Mechanics vol649 pp 103ndash113 2010

[30] H C H Ng J P Monty N Hutchins M S Chong and IMarusic ldquoComparison of turbulent channel and pipe flowswithvarying Reynolds numberrdquo Experiments in Fluids vol 51 no 5pp 1261ndash1281 2011

[31] G Papadopoulos andWM Pitts ldquoA generic centerline velocitydecay curve for initially turbulent axisymmetric jetsrdquo Journal ofFluids Engineering vol 121 no 1 pp 80ndash85 1999

[32] L J Bloomfield and R C Kerr ldquoTurbulent fountains in astratified fluidrdquo Journal of Fluid Mechanics vol 358 pp 335ndash356 1998

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of


Journal ofPetroleum Engineering


Industrial EngineeringJournal of


Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of


Journal of


Renewable Energy

Submit your manuscripts athttpwwwhindawicom


StructuresJournal of


RotatingMachinery


EnergyJournal of


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


Nuclear InstallationsScience and Technology of


Solar EnergyJournal of


Wind EnergyJournal of


Nuclear EnergyInternational Journal of


High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


scenarios for present [13] and upcoming generations ofnuclear power plants [14] Consequently the reliability ofsuch codesmust be tested against experimental data collectedunder prototypical thermal hydraulic conditions Large scaletest facilities [15] should be preferentially used to minimizedistortional effects that might arise from geometrical scaling[11]

The experiment presented in the paper describes theinteraction of vertical upward projecting air-helium jetemerging from a tube below a helium-rich air layer Theexperiment is carried out under isothermal and isobaricconditions and focuses onto the flow conditions at the tubeexit in addition to the mechanisms of entrainment of thehelium stratification located just beneath the vessel domeTheexperiment was conducted under conditions characterizedby a jet which is initially buoyant and becomes negativelybuoyant and decelerates when it reaches the helium stratifi-cation Results depicting the mixing transport and transienthelium stratification erosion are presented in terms of 2DPIV measurements which were used to measure the flowvelocities at different locations and in particular at the inter-face between the helium layer and the upward impingingjet Additional gas concentration measurements with a massspectrometer are used to calculate density profiles whichillustrate the erosion process of the density stratification

It should be noted that the present experiment violatesintentionally the Boussinesq approximations of the first andsecond kind The Boussinesq approximation of the first kindis part of a series of simplifications in which the density vari-ation in the continuity equation is neglected The Boussinesqapproximation in the momentum equation thus requires thatthe temperature or density differences in the fluid remainsmall A 10 difference is normally regarded as the upperlimit for this first approximationThe Boussinesq assumptionof the second kind expresses the Reynolds stresses resultingfrom the RANS equations in terms of the mean strain rate

minus11990610158401198941199061015840119895 = ]119905 (

120597119906119894

120597119909119895

+120597119906119895

120597119909119894

) (1)

with ]119905 denoting the scalar isotropic eddy viscosity [16] Itis noted that the introduction of high density gradients inhorizontal stratified flows may lead to the violation of bothkinds of Boussinesq assumptions simultaneously The highdensity gradient violates the small density difference require-ment and the damping of the vertical velocity fluctuationsin the vicinity of the stratification violates the eddy viscosityisotropy assumption Consequently besides the insight intofundamental physical mixing mechanisms in the presenceof steep density gradients and an intended violation of theBoussinesq approximations it is also expected that the con-ducted experiment poses some interesting computationalchallenges

In Section 2 we give an introduction to the experimentalfacility the instrumentation and the initial and boundaryconditions In Section 3we discuss the experimental in-vesselresults of the erosion process in the presence of a helium-richstratification by means of velocity and temperature maps as

well as concentration profiles Some emphasis was put on theerror calculation for the different measurement devices used

2 Experiment

The vessel used for the experiments had an inner diameterof 4m and a height of 8m Figure 1 The air-helium mixtureforming the jet with density 120588119895 and the nominal tube exitvelocity V119895119899 is injected through a tubewhich is positioned off-axis by 648mm with respect to the axis of symmetry of thevessel For the calculation of the nominal velocity we neglectthe formation of boundary layers at the inner tube walls andassume a constant velocity across the horizontal tube exitplane The injection tube has a 180∘ bend 2200mm belowthe tube exit The straight tube past the bend has a length ofasymp30119889119905 with119889119905 depicting the tube inner diameter which is longenough that possible disturbances introduced by the bend areremoved by the turbulence due to the tubersquos high Reynoldsnumber (Re119895 asymp 20000 Table 1) This will be confirmed by thetube exit velocity measurements described in a subsequentsection Consequently the velocity profile at the tube exitshows top hat characteristics with boundary layers typical forturbulent pipe flows In contrast to some past jet experimentswhere a smooth contraction nozzle at the tube exit was usedto pronounce the top hat velocity profile by compressing theboundary layers we used an injection tube with a constantnominal inner diameter of 119889119905 = 753mm Testing for thecircularity of the tube the actual inner diameter measuredat the tube exit in two perpendicular planes amounted 119889119905119886 =

754 and 119889119905119887 = 756mmwhich is in good agreement with thenominal value used henceforth

During the entire experiment the pressure was kept con-stant at about 0994 bar absolute by venting of the air-heliummixture from the vessel via a funnel connected to a flexiblehose-oriented downwards which was located at the bottom ofthe vessel Figure 1The injection tube exit is located 2995mmabove the bottom of the vessel The coordinate system originto describe the experiment is located at the bottom of thevessel and the light sheet for the PIV recordings coincideswith the 119909-119910 plane Figure 1

21 Instrumentation For the 2D velocity measurements aparticle image velocimetry (PIV) system was used The PIVcamera wasmounted in front of the upper vessel window on atranslation stage consisting of two goniometers and a rotationtable By vertically inclining the camera it was possible torecord three different field-of-views (FOVs) to follow theerosion front progression of the helium layerThe three FOVsare depicted as PosA PosB and PosC in Figure 1

An example of a raw PIV image recorded at position Bis shown in Figure 2(a) The image gives an impression of thejet-layer interaction zoneThe seeded jet entering from belowimpinges onto the nonseeded helium-rich layer and pen-etrates the stratification The corresponding instantaneousvelocity field with some selected stream lines is pictured inFigure 2(b)

Olive oil dispersed into small droplets by a spray nozzlewas used as seeding particles for the PIV technique The oil


Lightsheet

Lightsheet

PIVcamera

Funnel

Injectiontube

Initi

al h

eliu

m-

rich

laye

r

x

y

z

xz7984

1813

2995

3000

2200

1333 648

0

1000

2000

3000

4000

5000

6000

7000

8000

0∘

90∘270∘

315∘

135∘225∘

305∘

125∘

180∘Vent

line

empty4000

mm

empty825753

PosAPosB

PosC

(0 0)

g

1205880a

1205880 l

120588jjn

asymp2000




NumberJet amb Layer

airgs

hegs

119895dagger

gs120588119895

kgm3V119895119887ms


Re119895119887mdash

120588119900119886

kgm3Δ1205880119895119886

Dagger

1205880119897

kgm3Δ1205880119895119897998771







PosB

asymp700

mm


asymp1000mm



(a)

x (mm)y

(mm

)

5600

5800

6000

6200

1


abs

(ms

)

09

08

07

06

05

04

03

02

01

(b)







00 02 04 06 08 10

HeliumAir

0

2000

4000

6000

8000H

eigh

ty(m

m)











Re119895119887 =V119895119887 sdot 119889119905

]119895(2)


Fr0 =V119895119887


(3)




Δ1205880119895119886 =120588119900119886 minus 120588119895

120588119900119886 sdot 100(4)


Δ1205880119895119897 =120588119900119897 minus 120588119895

1205880119897 sdot 100 (5)






Gas injection pipe


Air andhelium

x

x

z

y

5

15

25

1515

1515

A

B

C

D

E

empty825 mm

empty753 mm

asymp6

mm




119906119901

119906119891

=1

radic1 + 120596211989112059120

with 120596119891 = 2120587119891119891 1205910 =1205881199011198892119901

18120578119891(6)


1 10

10

08

06

04

02

00100

120591p = 7120583s

dp = 15 120583m

Velo

city

ampl

itude

ratio

upu

f(mdash

)




119891max119891 =119906119891

2120587119871119906

Re34 (7)







119906 =1

119873

119873

sum

119894=1

119906119894

1199061015840= radic

1

119873

119873

sum

119894=1

119906119894 minus 1199062

(8)


11990610158401199061015840 =1

119873

119873

sum

119894=1

119906119894 minus 1199062 (9)

1199061015840V1015840 =1

119873

119873

sum

119894=1

119906119894 minus 119906 V119894 minus V (10)

119896 =1

22 sdot 11990610158401199061015840 + V1015840V1015840 (11)





VV119888

= [sin120587

2(1 minus

100381610038161003816100381610038161003816100381610038162119909

119889119905

10038161003816100381610038161003816100381610038161003816

12

)]

12

(12)


VV119888

=

100381610038161003816100381610038161003816100381610038162119909

119889119905

10038161003816100381610038161003816100381610038161003816

17

(13)






V1015840 = 04+00088minus00084ms 119906

1015840= 03+00066minus00063ms

V1015840

V119888= 0074

+00016minus00015

1199061015840

V119888= 0056

+00012minus00011

(14)



10

08

06

04

02

00minus04 minus02 00 02 04

c

xdt

(a)


016

012

008

004

998400

c

xdt

(b)


002

001

000

minus001

minus002

minus003

PosAPosBPosCPosD

PosE

u

c

xdt

(c)


008

004

002

006

PosAPosBPosCPosD

PosE

xdt

u998400 c

(d)








002

001

000

xdt

k

2 c

(a)


0005

0000

minus0005

minus0010

xdt

u998400

998400 2 c

(b)


004

003

002

001

000

PosAPosBPosCPosD

PosE

xdt

998400998400

2 c

(c)


0008

0006

0004

0002

0000

PosAPosBPosCPosD

PosE

xdt

u998400 u

998400 2 c

(d)












10

08

06

04minus04 minus02 00 02 04

c

xdt

PIVSine fit

17 power law fit






3 In-Vessel Results





10

08

06

04

02050403020100

xdt

c


Eggels et al 1994


(a)

050403020100000

005

010

015

020

025

xdt

998400

c


Eggels et al 1994


(b)

050403020100000

005

010

xdt

u998400 c

Own measurement

Eggels et al 1994


(c)








08 10 120

2000

4000

6000

8000

Transitional region

1205880l = 0772kgm3

1205880a = 1173kgm3

Hei

ghty

(mm

)

Density (kgm3)




N01 A 111

N02 B 715

N03 B 978

N04 B 1213

N05 C 1795

N06 C 2030

N07 C 2286

N08 C 2550











N01

||

(ms

)


5200

5400

5600

0

y(m

m)

x (mm)

08

06

04

02

(a)

N02

5800

6000

6200

A

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

05

(b)

N05

6400

6600

6800

05

04

03

02

01||

(ms

)


y(m

m)

x (mm)

(c)

N08

6400

6600

6800

05

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

(d)

N0101

008

006

004

002

5000

5200

5400

5600

0

k(m

2s2)


y(m

m)

x (mm)

(e)

N02

5800

6000

6200

A006

005

004

003

002

001

0

k(m

2s2)


y(m

m)

x (mm)

(f)

N05

0

k(m

2s2)

003

002

0016400

6600

6800


y(m

m)

x (mm)

(g)

k(m

2s2)

003

002

001

N08

6400

6600

6800


y(m

m)

x (mm)

(h)






N02

5800

6000

6200

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

05

06

(a)

N03

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06

(b)

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06N04

(c)


Injection tube

y(m

m)


N01 N02 N05


8000

7000

6000

5000

4000

3000

25

245

24

235

23

225

22

215

21

205

20

(∘C)






00

01

02

03

04

Time (s)0 1000 2000 3000 4000 5000

8030

7478

6926

6700

6496

6092

4326

1076

3000

y (mm)

Heli

um m

olar

frac

tion120594

he(mdash

)


4 Conclusions







Acknowledgments


References






































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















Lightsheet

Lightsheet

PIVcamera

Funnel

Injectiontube

Initi

al h

eliu

m-

rich

laye

r

x

y

z

xz7984

1813

2995

3000

2200

1333 648

0

1000

2000

3000

4000

5000

6000

7000

8000

0∘

90∘270∘

315∘

135∘225∘

305∘

125∘

180∘Vent

line

empty4000

mm

empty825753

PosAPosB

PosC

(0 0)

g

1205880a

1205880 l

120588jjn

asymp2000




NumberJet amb Layer

airgs

hegs

119895dagger

gs120588119895

kgm3V119895119887ms


Re119895119887mdash

120588119900119886

kgm3Δ1205880119895119886

Dagger

1205880119897

kgm3Δ1205880119895119897998771







PosB

asymp700

mm


asymp1000mm



(a)

x (mm)y

(mm

)

5600

5800

6000

6200

1


abs

(ms

)

09

08

07

06

05

04

03

02

01

(b)







00 02 04 06 08 10

HeliumAir

0

2000

4000

6000

8000H

eigh

ty(m

m)











Re119895119887 =V119895119887 sdot 119889119905

]119895(2)


Fr0 =V119895119887


(3)




Δ1205880119895119886 =120588119900119886 minus 120588119895

120588119900119886 sdot 100(4)


Δ1205880119895119897 =120588119900119897 minus 120588119895

1205880119897 sdot 100 (5)






Gas injection pipe


Air andhelium

x

x

z

y

5

15

25

1515

1515

A

B

C

D

E

empty825 mm

empty753 mm

asymp6

mm




119906119901

119906119891

=1

radic1 + 120596211989112059120

with 120596119891 = 2120587119891119891 1205910 =1205881199011198892119901

18120578119891(6)


1 10

10

08

06

04

02

00100

120591p = 7120583s

dp = 15 120583m

Velo

city

ampl

itude

ratio

upu

f(mdash

)




119891max119891 =119906119891

2120587119871119906

Re34 (7)







119906 =1

119873

119873

sum

119894=1

119906119894

1199061015840= radic

1

119873

119873

sum

119894=1

119906119894 minus 1199062

(8)


11990610158401199061015840 =1

119873

119873

sum

119894=1

119906119894 minus 1199062 (9)

1199061015840V1015840 =1

119873

119873

sum

119894=1

119906119894 minus 119906 V119894 minus V (10)

119896 =1

22 sdot 11990610158401199061015840 + V1015840V1015840 (11)





VV119888

= [sin120587

2(1 minus

100381610038161003816100381610038161003816100381610038162119909

119889119905

10038161003816100381610038161003816100381610038161003816

12

)]

12

(12)


VV119888

=

100381610038161003816100381610038161003816100381610038162119909

119889119905

10038161003816100381610038161003816100381610038161003816

17

(13)






V1015840 = 04+00088minus00084ms 119906

1015840= 03+00066minus00063ms

V1015840

V119888= 0074

+00016minus00015

1199061015840

V119888= 0056

+00012minus00011

(14)



10

08

06

04

02

00minus04 minus02 00 02 04

c

xdt

(a)


016

012

008

004

998400

c

xdt

(b)


002

001

000

minus001

minus002

minus003

PosAPosBPosCPosD

PosE

u

c

xdt

(c)


008

004

002

006

PosAPosBPosCPosD

PosE

xdt

u998400 c

(d)








002

001

000

xdt

k

2 c

(a)


0005

0000

minus0005

minus0010

xdt

u998400

998400 2 c

(b)


004

003

002

001

000

PosAPosBPosCPosD

PosE

xdt

998400998400

2 c

(c)


0008

0006

0004

0002

0000

PosAPosBPosCPosD

PosE

xdt

u998400 u

998400 2 c

(d)












10

08

06

04minus04 minus02 00 02 04

c

xdt

PIVSine fit

17 power law fit






3 In-Vessel Results





10

08

06

04

02050403020100

xdt

c


Eggels et al 1994


(a)

050403020100000

005

010

015

020

025

xdt

998400

c


Eggels et al 1994


(b)

050403020100000

005

010

xdt

u998400 c

Own measurement

Eggels et al 1994


(c)








08 10 120

2000

4000

6000

8000

Transitional region

1205880l = 0772kgm3

1205880a = 1173kgm3

Hei

ghty

(mm

)

Density (kgm3)




N01 A 111

N02 B 715

N03 B 978

N04 B 1213

N05 C 1795

N06 C 2030

N07 C 2286

N08 C 2550











N01

||

(ms

)


5200

5400

5600

0

y(m

m)

x (mm)

08

06

04

02

(a)

N02

5800

6000

6200

A

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

05

(b)

N05

6400

6600

6800

05

04

03

02

01||

(ms

)


y(m

m)

x (mm)

(c)

N08

6400

6600

6800

05

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

(d)

N0101

008

006

004

002

5000

5200

5400

5600

0

k(m

2s2)


y(m

m)

x (mm)

(e)

N02

5800

6000

6200

A006

005

004

003

002

001

0

k(m

2s2)


y(m

m)

x (mm)

(f)

N05

0

k(m

2s2)

003

002

0016400

6600

6800


y(m

m)

x (mm)

(g)

k(m

2s2)

003

002

001

N08

6400

6600

6800


y(m

m)

x (mm)

(h)






N02

5800

6000

6200

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

05

06

(a)

N03

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06

(b)

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06N04

(c)


Injection tube

y(m

m)


N01 N02 N05


8000

7000

6000

5000

4000

3000

25

245

24

235

23

225

22

215

21

205

20

(∘C)






00

01

02

03

04

Time (s)0 1000 2000 3000 4000 5000

8030

7478

6926

6700

6496

6092

4326

1076

3000

y (mm)

Heli

um m

olar

frac

tion120594

he(mdash

)


4 Conclusions







Acknowledgments


References






































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















PosB

asymp700

mm


asymp1000mm



(a)

x (mm)y

(mm

)

5600

5800

6000

6200

1


abs

(ms

)

09

08

07

06

05

04

03

02

01

(b)







00 02 04 06 08 10

HeliumAir

0

2000

4000

6000

8000H

eigh

ty(m

m)











Re119895119887 =V119895119887 sdot 119889119905

]119895(2)


Fr0 =V119895119887


(3)




Δ1205880119895119886 =120588119900119886 minus 120588119895

120588119900119886 sdot 100(4)


Δ1205880119895119897 =120588119900119897 minus 120588119895

1205880119897 sdot 100 (5)






Gas injection pipe


Air andhelium

x

x

z

y

5

15

25

1515

1515

A

B

C

D

E

empty825 mm

empty753 mm

asymp6

mm




119906119901

119906119891

=1

radic1 + 120596211989112059120

with 120596119891 = 2120587119891119891 1205910 =1205881199011198892119901

18120578119891(6)


1 10

10

08

06

04

02

00100

120591p = 7120583s

dp = 15 120583m

Velo

city

ampl

itude

ratio

upu

f(mdash

)




119891max119891 =119906119891

2120587119871119906

Re34 (7)







119906 =1

119873

119873

sum

119894=1

119906119894

1199061015840= radic

1

119873

119873

sum

119894=1

119906119894 minus 1199062

(8)


11990610158401199061015840 =1

119873

119873

sum

119894=1

119906119894 minus 1199062 (9)

1199061015840V1015840 =1

119873

119873

sum

119894=1

119906119894 minus 119906 V119894 minus V (10)

119896 =1

22 sdot 11990610158401199061015840 + V1015840V1015840 (11)





VV119888

= [sin120587

2(1 minus

100381610038161003816100381610038161003816100381610038162119909

119889119905

10038161003816100381610038161003816100381610038161003816

12

)]

12

(12)


VV119888

=

100381610038161003816100381610038161003816100381610038162119909

119889119905

10038161003816100381610038161003816100381610038161003816

17

(13)






V1015840 = 04+00088minus00084ms 119906

1015840= 03+00066minus00063ms

V1015840

V119888= 0074

+00016minus00015

1199061015840

V119888= 0056

+00012minus00011

(14)



10

08

06

04

02

00minus04 minus02 00 02 04

c

xdt

(a)


016

012

008

004

998400

c

xdt

(b)


002

001

000

minus001

minus002

minus003

PosAPosBPosCPosD

PosE

u

c

xdt

(c)


008

004

002

006

PosAPosBPosCPosD

PosE

xdt

u998400 c

(d)








002

001

000

xdt

k

2 c

(a)


0005

0000

minus0005

minus0010

xdt

u998400

998400 2 c

(b)


004

003

002

001

000

PosAPosBPosCPosD

PosE

xdt

998400998400

2 c

(c)


0008

0006

0004

0002

0000

PosAPosBPosCPosD

PosE

xdt

u998400 u

998400 2 c

(d)












10

08

06

04minus04 minus02 00 02 04

c

xdt

PIVSine fit

17 power law fit






3 In-Vessel Results





10

08

06

04

02050403020100

xdt

c


Eggels et al 1994


(a)

050403020100000

005

010

015

020

025

xdt

998400

c


Eggels et al 1994


(b)

050403020100000

005

010

xdt

u998400 c

Own measurement

Eggels et al 1994


(c)








08 10 120

2000

4000

6000

8000

Transitional region

1205880l = 0772kgm3

1205880a = 1173kgm3

Hei

ghty

(mm

)

Density (kgm3)




N01 A 111

N02 B 715

N03 B 978

N04 B 1213

N05 C 1795

N06 C 2030

N07 C 2286

N08 C 2550











N01

||

(ms

)


5200

5400

5600

0

y(m

m)

x (mm)

08

06

04

02

(a)

N02

5800

6000

6200

A

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

05

(b)

N05

6400

6600

6800

05

04

03

02

01||

(ms

)


y(m

m)

x (mm)

(c)

N08

6400

6600

6800

05

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

(d)

N0101

008

006

004

002

5000

5200

5400

5600

0

k(m

2s2)


y(m

m)

x (mm)

(e)

N02

5800

6000

6200

A006

005

004

003

002

001

0

k(m

2s2)


y(m

m)

x (mm)

(f)

N05

0

k(m

2s2)

003

002

0016400

6600

6800


y(m

m)

x (mm)

(g)

k(m

2s2)

003

002

001

N08

6400

6600

6800


y(m

m)

x (mm)

(h)






N02

5800

6000

6200

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

05

06

(a)

N03

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06

(b)

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06N04

(c)


Injection tube

y(m

m)


N01 N02 N05


8000

7000

6000

5000

4000

3000

25

245

24

235

23

225

22

215

21

205

20

(∘C)






00

01

02

03

04

Time (s)0 1000 2000 3000 4000 5000

8030

7478

6926

6700

6496

6092

4326

1076

3000

y (mm)

Heli

um m

olar

frac

tion120594

he(mdash

)


4 Conclusions







Acknowledgments


References






































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of
























Re119895119887 =V119895119887 sdot 119889119905

]119895(2)


Fr0 =V119895119887


(3)




Δ1205880119895119886 =120588119900119886 minus 120588119895

120588119900119886 sdot 100(4)


Δ1205880119895119897 =120588119900119897 minus 120588119895

1205880119897 sdot 100 (5)






Gas injection pipe


Air andhelium

x

x

z

y

5

15

25

1515

1515

A

B

C

D

E

empty825 mm

empty753 mm

asymp6

mm




119906119901

119906119891

=1

radic1 + 120596211989112059120

with 120596119891 = 2120587119891119891 1205910 =1205881199011198892119901

18120578119891(6)


1 10

10

08

06

04

02

00100

120591p = 7120583s

dp = 15 120583m

Velo

city

ampl

itude

ratio

upu

f(mdash

)




119891max119891 =119906119891

2120587119871119906

Re34 (7)







119906 =1

119873

119873

sum

119894=1

119906119894

1199061015840= radic

1

119873

119873

sum

119894=1

119906119894 minus 1199062

(8)


11990610158401199061015840 =1

119873

119873

sum

119894=1

119906119894 minus 1199062 (9)

1199061015840V1015840 =1

119873

119873

sum

119894=1

119906119894 minus 119906 V119894 minus V (10)

119896 =1

22 sdot 11990610158401199061015840 + V1015840V1015840 (11)





VV119888

= [sin120587

2(1 minus

100381610038161003816100381610038161003816100381610038162119909

119889119905

10038161003816100381610038161003816100381610038161003816

12

)]

12

(12)


VV119888

=

100381610038161003816100381610038161003816100381610038162119909

119889119905

10038161003816100381610038161003816100381610038161003816

17

(13)






V1015840 = 04+00088minus00084ms 119906

1015840= 03+00066minus00063ms

V1015840

V119888= 0074

+00016minus00015

1199061015840

V119888= 0056

+00012minus00011

(14)



10

08

06

04

02

00minus04 minus02 00 02 04

c

xdt

(a)


016

012

008

004

998400

c

xdt

(b)


002

001

000

minus001

minus002

minus003

PosAPosBPosCPosD

PosE

u

c

xdt

(c)


008

004

002

006

PosAPosBPosCPosD

PosE

xdt

u998400 c

(d)








002

001

000

xdt

k

2 c

(a)


0005

0000

minus0005

minus0010

xdt

u998400

998400 2 c

(b)


004

003

002

001

000

PosAPosBPosCPosD

PosE

xdt

998400998400

2 c

(c)


0008

0006

0004

0002

0000

PosAPosBPosCPosD

PosE

xdt

u998400 u

998400 2 c

(d)












10

08

06

04minus04 minus02 00 02 04

c

xdt

PIVSine fit

17 power law fit






3 In-Vessel Results





10

08

06

04

02050403020100

xdt

c


Eggels et al 1994


(a)

050403020100000

005

010

015

020

025

xdt

998400

c


Eggels et al 1994


(b)

050403020100000

005

010

xdt

u998400 c

Own measurement

Eggels et al 1994


(c)








08 10 120

2000

4000

6000

8000

Transitional region

1205880l = 0772kgm3

1205880a = 1173kgm3

Hei

ghty

(mm

)

Density (kgm3)




N01 A 111

N02 B 715

N03 B 978

N04 B 1213

N05 C 1795

N06 C 2030

N07 C 2286

N08 C 2550











N01

||

(ms

)


5200

5400

5600

0

y(m

m)

x (mm)

08

06

04

02

(a)

N02

5800

6000

6200

A

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

05

(b)

N05

6400

6600

6800

05

04

03

02

01||

(ms

)


y(m

m)

x (mm)

(c)

N08

6400

6600

6800

05

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

(d)

N0101

008

006

004

002

5000

5200

5400

5600

0

k(m

2s2)


y(m

m)

x (mm)

(e)

N02

5800

6000

6200

A006

005

004

003

002

001

0

k(m

2s2)


y(m

m)

x (mm)

(f)

N05

0

k(m

2s2)

003

002

0016400

6600

6800


y(m

m)

x (mm)

(g)

k(m

2s2)

003

002

001

N08

6400

6600

6800


y(m

m)

x (mm)

(h)






N02

5800

6000

6200

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

05

06

(a)

N03

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06

(b)

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06N04

(c)


Injection tube

y(m

m)


N01 N02 N05


8000

7000

6000

5000

4000

3000

25

245

24

235

23

225

22

215

21

205

20

(∘C)






00

01

02

03

04

Time (s)0 1000 2000 3000 4000 5000

8030

7478

6926

6700

6496

6092

4326

1076

3000

y (mm)

Heli

um m

olar

frac

tion120594

he(mdash

)


4 Conclusions







Acknowledgments


References






































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















Gas injection pipe


Air andhelium

x

x

z

y

5

15

25

1515

1515

A

B

C

D

E

empty825 mm

empty753 mm

asymp6

mm




119906119901

119906119891

=1

radic1 + 120596211989112059120

with 120596119891 = 2120587119891119891 1205910 =1205881199011198892119901

18120578119891(6)


1 10

10

08

06

04

02

00100

120591p = 7120583s

dp = 15 120583m

Velo

city

ampl

itude

ratio

upu

f(mdash

)




119891max119891 =119906119891

2120587119871119906

Re34 (7)







119906 =1

119873

119873

sum

119894=1

119906119894

1199061015840= radic

1

119873

119873

sum

119894=1

119906119894 minus 1199062

(8)


11990610158401199061015840 =1

119873

119873

sum

119894=1

119906119894 minus 1199062 (9)

1199061015840V1015840 =1

119873

119873

sum

119894=1

119906119894 minus 119906 V119894 minus V (10)

119896 =1

22 sdot 11990610158401199061015840 + V1015840V1015840 (11)





VV119888

= [sin120587

2(1 minus

100381610038161003816100381610038161003816100381610038162119909

119889119905

10038161003816100381610038161003816100381610038161003816

12

)]

12

(12)


VV119888

=

100381610038161003816100381610038161003816100381610038162119909

119889119905

10038161003816100381610038161003816100381610038161003816

17

(13)






V1015840 = 04+00088minus00084ms 119906

1015840= 03+00066minus00063ms

V1015840

V119888= 0074

+00016minus00015

1199061015840

V119888= 0056

+00012minus00011

(14)



10

08

06

04

02

00minus04 minus02 00 02 04

c

xdt

(a)


016

012

008

004

998400

c

xdt

(b)


002

001

000

minus001

minus002

minus003

PosAPosBPosCPosD

PosE

u

c

xdt

(c)


008

004

002

006

PosAPosBPosCPosD

PosE

xdt

u998400 c

(d)








002

001

000

xdt

k

2 c

(a)


0005

0000

minus0005

minus0010

xdt

u998400

998400 2 c

(b)


004

003

002

001

000

PosAPosBPosCPosD

PosE

xdt

998400998400

2 c

(c)


0008

0006

0004

0002

0000

PosAPosBPosCPosD

PosE

xdt

u998400 u

998400 2 c

(d)












10

08

06

04minus04 minus02 00 02 04

c

xdt

PIVSine fit

17 power law fit






3 In-Vessel Results





10

08

06

04

02050403020100

xdt

c


Eggels et al 1994


(a)

050403020100000

005

010

015

020

025

xdt

998400

c


Eggels et al 1994


(b)

050403020100000

005

010

xdt

u998400 c

Own measurement

Eggels et al 1994


(c)








08 10 120

2000

4000

6000

8000

Transitional region

1205880l = 0772kgm3

1205880a = 1173kgm3

Hei

ghty

(mm

)

Density (kgm3)




N01 A 111

N02 B 715

N03 B 978

N04 B 1213

N05 C 1795

N06 C 2030

N07 C 2286

N08 C 2550











N01

||

(ms

)


5200

5400

5600

0

y(m

m)

x (mm)

08

06

04

02

(a)

N02

5800

6000

6200

A

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

05

(b)

N05

6400

6600

6800

05

04

03

02

01||

(ms

)


y(m

m)

x (mm)

(c)

N08

6400

6600

6800

05

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

(d)

N0101

008

006

004

002

5000

5200

5400

5600

0

k(m

2s2)


y(m

m)

x (mm)

(e)

N02

5800

6000

6200

A006

005

004

003

002

001

0

k(m

2s2)


y(m

m)

x (mm)

(f)

N05

0

k(m

2s2)

003

002

0016400

6600

6800


y(m

m)

x (mm)

(g)

k(m

2s2)

003

002

001

N08

6400

6600

6800


y(m

m)

x (mm)

(h)






N02

5800

6000

6200

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

05

06

(a)

N03

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06

(b)

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06N04

(c)


Injection tube

y(m

m)


N01 N02 N05


8000

7000

6000

5000

4000

3000

25

245

24

235

23

225

22

215

21

205

20

(∘C)






00

01

02

03

04

Time (s)0 1000 2000 3000 4000 5000

8030

7478

6926

6700

6496

6092

4326

1076

3000

y (mm)

Heli

um m

olar

frac

tion120594

he(mdash

)


4 Conclusions







Acknowledgments


References






































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of























119906 =1

119873

119873

sum

119894=1

119906119894

1199061015840= radic

1

119873

119873

sum

119894=1

119906119894 minus 1199062

(8)


11990610158401199061015840 =1

119873

119873

sum

119894=1

119906119894 minus 1199062 (9)

1199061015840V1015840 =1

119873

119873

sum

119894=1

119906119894 minus 119906 V119894 minus V (10)

119896 =1

22 sdot 11990610158401199061015840 + V1015840V1015840 (11)





VV119888

= [sin120587

2(1 minus

100381610038161003816100381610038161003816100381610038162119909

119889119905

10038161003816100381610038161003816100381610038161003816

12

)]

12

(12)


VV119888

=

100381610038161003816100381610038161003816100381610038162119909

119889119905

10038161003816100381610038161003816100381610038161003816

17

(13)






V1015840 = 04+00088minus00084ms 119906

1015840= 03+00066minus00063ms

V1015840

V119888= 0074

+00016minus00015

1199061015840

V119888= 0056

+00012minus00011

(14)



10

08

06

04

02

00minus04 minus02 00 02 04

c

xdt

(a)


016

012

008

004

998400

c

xdt

(b)


002

001

000

minus001

minus002

minus003

PosAPosBPosCPosD

PosE

u

c

xdt

(c)


008

004

002

006

PosAPosBPosCPosD

PosE

xdt

u998400 c

(d)








002

001

000

xdt

k

2 c

(a)


0005

0000

minus0005

minus0010

xdt

u998400

998400 2 c

(b)


004

003

002

001

000

PosAPosBPosCPosD

PosE

xdt

998400998400

2 c

(c)


0008

0006

0004

0002

0000

PosAPosBPosCPosD

PosE

xdt

u998400 u

998400 2 c

(d)












10

08

06

04minus04 minus02 00 02 04

c

xdt

PIVSine fit

17 power law fit






3 In-Vessel Results





10

08

06

04

02050403020100

xdt

c


Eggels et al 1994


(a)

050403020100000

005

010

015

020

025

xdt

998400

c


Eggels et al 1994


(b)

050403020100000

005

010

xdt

u998400 c

Own measurement

Eggels et al 1994


(c)








08 10 120

2000

4000

6000

8000

Transitional region

1205880l = 0772kgm3

1205880a = 1173kgm3

Hei

ghty

(mm

)

Density (kgm3)




N01 A 111

N02 B 715

N03 B 978

N04 B 1213

N05 C 1795

N06 C 2030

N07 C 2286

N08 C 2550











N01

||

(ms

)


5200

5400

5600

0

y(m

m)

x (mm)

08

06

04

02

(a)

N02

5800

6000

6200

A

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

05

(b)

N05

6400

6600

6800

05

04

03

02

01||

(ms

)


y(m

m)

x (mm)

(c)

N08

6400

6600

6800

05

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

(d)

N0101

008

006

004

002

5000

5200

5400

5600

0

k(m

2s2)


y(m

m)

x (mm)

(e)

N02

5800

6000

6200

A006

005

004

003

002

001

0

k(m

2s2)


y(m

m)

x (mm)

(f)

N05

0

k(m

2s2)

003

002

0016400

6600

6800


y(m

m)

x (mm)

(g)

k(m

2s2)

003

002

001

N08

6400

6600

6800


y(m

m)

x (mm)

(h)






N02

5800

6000

6200

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

05

06

(a)

N03

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06

(b)

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06N04

(c)


Injection tube

y(m

m)


N01 N02 N05


8000

7000

6000

5000

4000

3000

25

245

24

235

23

225

22

215

21

205

20

(∘C)






00

01

02

03

04

Time (s)0 1000 2000 3000 4000 5000

8030

7478

6926

6700

6496

6092

4326

1076

3000

y (mm)

Heli

um m

olar

frac

tion120594

he(mdash

)


4 Conclusions







Acknowledgments


References






































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















10

08

06

04

02

00minus04 minus02 00 02 04

c

xdt

(a)


016

012

008

004

998400

c

xdt

(b)


002

001

000

minus001

minus002

minus003

PosAPosBPosCPosD

PosE

u

c

xdt

(c)


008

004

002

006

PosAPosBPosCPosD

PosE

xdt

u998400 c

(d)








002

001

000

xdt

k

2 c

(a)


0005

0000

minus0005

minus0010

xdt

u998400

998400 2 c

(b)


004

003

002

001

000

PosAPosBPosCPosD

PosE

xdt

998400998400

2 c

(c)


0008

0006

0004

0002

0000

PosAPosBPosCPosD

PosE

xdt

u998400 u

998400 2 c

(d)












10

08

06

04minus04 minus02 00 02 04

c

xdt

PIVSine fit

17 power law fit






3 In-Vessel Results





10

08

06

04

02050403020100

xdt

c


Eggels et al 1994


(a)

050403020100000

005

010

015

020

025

xdt

998400

c


Eggels et al 1994


(b)

050403020100000

005

010

xdt

u998400 c

Own measurement

Eggels et al 1994


(c)








08 10 120

2000

4000

6000

8000

Transitional region

1205880l = 0772kgm3

1205880a = 1173kgm3

Hei

ghty

(mm

)

Density (kgm3)




N01 A 111

N02 B 715

N03 B 978

N04 B 1213

N05 C 1795

N06 C 2030

N07 C 2286

N08 C 2550











N01

||

(ms

)


5200

5400

5600

0

y(m

m)

x (mm)

08

06

04

02

(a)

N02

5800

6000

6200

A

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

05

(b)

N05

6400

6600

6800

05

04

03

02

01||

(ms

)


y(m

m)

x (mm)

(c)

N08

6400

6600

6800

05

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

(d)

N0101

008

006

004

002

5000

5200

5400

5600

0

k(m

2s2)


y(m

m)

x (mm)

(e)

N02

5800

6000

6200

A006

005

004

003

002

001

0

k(m

2s2)


y(m

m)

x (mm)

(f)

N05

0

k(m

2s2)

003

002

0016400

6600

6800


y(m

m)

x (mm)

(g)

k(m

2s2)

003

002

001

N08

6400

6600

6800


y(m

m)

x (mm)

(h)






N02

5800

6000

6200

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

05

06

(a)

N03

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06

(b)

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06N04

(c)


Injection tube

y(m

m)


N01 N02 N05


8000

7000

6000

5000

4000

3000

25

245

24

235

23

225

22

215

21

205

20

(∘C)






00

01

02

03

04

Time (s)0 1000 2000 3000 4000 5000

8030

7478

6926

6700

6496

6092

4326

1076

3000

y (mm)

Heli

um m

olar

frac

tion120594

he(mdash

)


4 Conclusions







Acknowledgments


References






































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



















002

001

000

xdt

k

2 c

(a)


0005

0000

minus0005

minus0010

xdt

u998400

998400 2 c

(b)


004

003

002

001

000

PosAPosBPosCPosD

PosE

xdt

998400998400

2 c

(c)


0008

0006

0004

0002

0000

PosAPosBPosCPosD

PosE

xdt

u998400 u

998400 2 c

(d)












10

08

06

04minus04 minus02 00 02 04

c

xdt

PIVSine fit

17 power law fit






3 In-Vessel Results





10

08

06

04

02050403020100

xdt

c


Eggels et al 1994


(a)

050403020100000

005

010

015

020

025

xdt

998400

c


Eggels et al 1994


(b)

050403020100000

005

010

xdt

u998400 c

Own measurement

Eggels et al 1994


(c)








08 10 120

2000

4000

6000

8000

Transitional region

1205880l = 0772kgm3

1205880a = 1173kgm3

Hei

ghty

(mm

)

Density (kgm3)




N01 A 111

N02 B 715

N03 B 978

N04 B 1213

N05 C 1795

N06 C 2030

N07 C 2286

N08 C 2550











N01

||

(ms

)


5200

5400

5600

0

y(m

m)

x (mm)

08

06

04

02

(a)

N02

5800

6000

6200

A

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

05

(b)

N05

6400

6600

6800

05

04

03

02

01||

(ms

)


y(m

m)

x (mm)

(c)

N08

6400

6600

6800

05

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

(d)

N0101

008

006

004

002

5000

5200

5400

5600

0

k(m

2s2)


y(m

m)

x (mm)

(e)

N02

5800

6000

6200

A006

005

004

003

002

001

0

k(m

2s2)


y(m

m)

x (mm)

(f)

N05

0

k(m

2s2)

003

002

0016400

6600

6800


y(m

m)

x (mm)

(g)

k(m

2s2)

003

002

001

N08

6400

6600

6800


y(m

m)

x (mm)

(h)






N02

5800

6000

6200

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

05

06

(a)

N03

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06

(b)

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06N04

(c)


Injection tube

y(m

m)


N01 N02 N05


8000

7000

6000

5000

4000

3000

25

245

24

235

23

225

22

215

21

205

20

(∘C)






00

01

02

03

04

Time (s)0 1000 2000 3000 4000 5000

8030

7478

6926

6700

6496

6092

4326

1076

3000

y (mm)

Heli

um m

olar

frac

tion120594

he(mdash

)


4 Conclusions







Acknowledgments


References






































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of
























10

08

06

04minus04 minus02 00 02 04

c

xdt

PIVSine fit

17 power law fit






3 In-Vessel Results





10

08

06

04

02050403020100

xdt

c


Eggels et al 1994


(a)

050403020100000

005

010

015

020

025

xdt

998400

c


Eggels et al 1994


(b)

050403020100000

005

010

xdt

u998400 c

Own measurement

Eggels et al 1994


(c)








08 10 120

2000

4000

6000

8000

Transitional region

1205880l = 0772kgm3

1205880a = 1173kgm3

Hei

ghty

(mm

)

Density (kgm3)




N01 A 111

N02 B 715

N03 B 978

N04 B 1213

N05 C 1795

N06 C 2030

N07 C 2286

N08 C 2550











N01

||

(ms

)


5200

5400

5600

0

y(m

m)

x (mm)

08

06

04

02

(a)

N02

5800

6000

6200

A

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

05

(b)

N05

6400

6600

6800

05

04

03

02

01||

(ms

)


y(m

m)

x (mm)

(c)

N08

6400

6600

6800

05

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

(d)

N0101

008

006

004

002

5000

5200

5400

5600

0

k(m

2s2)


y(m

m)

x (mm)

(e)

N02

5800

6000

6200

A006

005

004

003

002

001

0

k(m

2s2)


y(m

m)

x (mm)

(f)

N05

0

k(m

2s2)

003

002

0016400

6600

6800


y(m

m)

x (mm)

(g)

k(m

2s2)

003

002

001

N08

6400

6600

6800


y(m

m)

x (mm)

(h)






N02

5800

6000

6200

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

05

06

(a)

N03

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06

(b)

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06N04

(c)


Injection tube

y(m

m)


N01 N02 N05


8000

7000

6000

5000

4000

3000

25

245

24

235

23

225

22

215

21

205

20

(∘C)






00

01

02

03

04

Time (s)0 1000 2000 3000 4000 5000

8030

7478

6926

6700

6496

6092

4326

1076

3000

y (mm)

Heli

um m

olar

frac

tion120594

he(mdash

)


4 Conclusions







Acknowledgments


References






































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















10

08

06

04

02050403020100

xdt

c


Eggels et al 1994


(a)

050403020100000

005

010

015

020

025

xdt

998400

c


Eggels et al 1994


(b)

050403020100000

005

010

xdt

u998400 c

Own measurement

Eggels et al 1994


(c)








08 10 120

2000

4000

6000

8000

Transitional region

1205880l = 0772kgm3

1205880a = 1173kgm3

Hei

ghty

(mm

)

Density (kgm3)




N01 A 111

N02 B 715

N03 B 978

N04 B 1213

N05 C 1795

N06 C 2030

N07 C 2286

N08 C 2550











N01

||

(ms

)


5200

5400

5600

0

y(m

m)

x (mm)

08

06

04

02

(a)

N02

5800

6000

6200

A

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

05

(b)

N05

6400

6600

6800

05

04

03

02

01||

(ms

)


y(m

m)

x (mm)

(c)

N08

6400

6600

6800

05

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

(d)

N0101

008

006

004

002

5000

5200

5400

5600

0

k(m

2s2)


y(m

m)

x (mm)

(e)

N02

5800

6000

6200

A006

005

004

003

002

001

0

k(m

2s2)


y(m

m)

x (mm)

(f)

N05

0

k(m

2s2)

003

002

0016400

6600

6800


y(m

m)

x (mm)

(g)

k(m

2s2)

003

002

001

N08

6400

6600

6800


y(m

m)

x (mm)

(h)






N02

5800

6000

6200

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

05

06

(a)

N03

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06

(b)

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06N04

(c)


Injection tube

y(m

m)


N01 N02 N05


8000

7000

6000

5000

4000

3000

25

245

24

235

23

225

22

215

21

205

20

(∘C)






00

01

02

03

04

Time (s)0 1000 2000 3000 4000 5000

8030

7478

6926

6700

6496

6092

4326

1076

3000

y (mm)

Heli

um m

olar

frac

tion120594

he(mdash

)


4 Conclusions







Acknowledgments


References






































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















08 10 120

2000

4000

6000

8000

Transitional region

1205880l = 0772kgm3

1205880a = 1173kgm3

Hei

ghty

(mm

)

Density (kgm3)




N01 A 111

N02 B 715

N03 B 978

N04 B 1213

N05 C 1795

N06 C 2030

N07 C 2286

N08 C 2550











N01

||

(ms

)


5200

5400

5600

0

y(m

m)

x (mm)

08

06

04

02

(a)

N02

5800

6000

6200

A

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

05

(b)

N05

6400

6600

6800

05

04

03

02

01||

(ms

)


y(m

m)

x (mm)

(c)

N08

6400

6600

6800

05

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

(d)

N0101

008

006

004

002

5000

5200

5400

5600

0

k(m

2s2)


y(m

m)

x (mm)

(e)

N02

5800

6000

6200

A006

005

004

003

002

001

0

k(m

2s2)


y(m

m)

x (mm)

(f)

N05

0

k(m

2s2)

003

002

0016400

6600

6800


y(m

m)

x (mm)

(g)

k(m

2s2)

003

002

001

N08

6400

6600

6800


y(m

m)

x (mm)

(h)






N02

5800

6000

6200

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

05

06

(a)

N03

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06

(b)

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06N04

(c)


Injection tube

y(m

m)


N01 N02 N05


8000

7000

6000

5000

4000

3000

25

245

24

235

23

225

22

215

21

205

20

(∘C)






00

01

02

03

04

Time (s)0 1000 2000 3000 4000 5000

8030

7478

6926

6700

6496

6092

4326

1076

3000

y (mm)

Heli

um m

olar

frac

tion120594

he(mdash

)


4 Conclusions







Acknowledgments


References






































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















N01

||

(ms

)


5200

5400

5600

0

y(m

m)

x (mm)

08

06

04

02

(a)

N02

5800

6000

6200

A

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

05

(b)

N05

6400

6600

6800

05

04

03

02

01||

(ms

)


y(m

m)

x (mm)

(c)

N08

6400

6600

6800

05

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

(d)

N0101

008

006

004

002

5000

5200

5400

5600

0

k(m

2s2)


y(m

m)

x (mm)

(e)

N02

5800

6000

6200

A006

005

004

003

002

001

0

k(m

2s2)


y(m

m)

x (mm)

(f)

N05

0

k(m

2s2)

003

002

0016400

6600

6800


y(m

m)

x (mm)

(g)

k(m

2s2)

003

002

001

N08

6400

6600

6800


y(m

m)

x (mm)

(h)






N02

5800

6000

6200

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

05

06

(a)

N03

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06

(b)

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06N04

(c)


Injection tube

y(m

m)


N01 N02 N05


8000

7000

6000

5000

4000

3000

25

245

24

235

23

225

22

215

21

205

20

(∘C)






00

01

02

03

04

Time (s)0 1000 2000 3000 4000 5000

8030

7478

6926

6700

6496

6092

4326

1076

3000

y (mm)

Heli

um m

olar

frac

tion120594

he(mdash

)


4 Conclusions







Acknowledgments


References






































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















N02

5800

6000

6200

04

03

02

01

||

(ms

)


y(m

m)

x (mm)

05

06

(a)

N03

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06

(b)

5800

6000

6200

y(m

m)


x (mm)

04

03

02

01

||

(ms

)

0

05

06N04

(c)


Injection tube

y(m

m)


N01 N02 N05


8000

7000

6000

5000

4000

3000

25

245

24

235

23

225

22

215

21

205

20

(∘C)






00

01

02

03

04

Time (s)0 1000 2000 3000 4000 5000

8030

7478

6926

6700

6496

6092

4326

1076

3000

y (mm)

Heli

um m

olar

frac

tion120594

he(mdash

)


4 Conclusions







Acknowledgments


References






































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















00

01

02

03

04

Time (s)0 1000 2000 3000 4000 5000

8030

7478

6926

6700

6496

6092

4326

1076

3000

y (mm)

Heli

um m

olar

frac

tion120594

he(mdash

)


4 Conclusions







Acknowledgments


References






































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of










































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of

















research article large scale gas stratification erosion...

Documents