湍流多组分喷流中流速和标量浓度检测方案(激光粒度仪)

智能文字提取功能测试中

1This draft was prepared using the LaTeX style file belonging to the Journal of Fluid Mechanics M. Soleimani nia， B. Marwell， P. Oshkai and N. Djilali2 t Email address for correspondence： majids@uvic.ca Measurements of Flow Velocity and ScalarConcentration in TurbulentMulti-component Jets： Asymmetry andBuoyancy Effects Majid Soleimani nialt， Brian Maxwell2， Peter Oshkail and NedDjilali Department of Mechanical Engineering and Institute for Integrated Energy Systems，University of Victoria， PO Box 1700 STN CSC， Victoria， BC，V8W 2Y2， Canada "Department of Mechanical and Aerospace Engineering， Case Western Reserve University，10900 Euclid Avenue， Glennan 418， Cleveland Ohio， 44106， USA (Received xx； revised xx； accepted xx) Buoyancy effects and nozzle geometry can have a significant impact on turbulent jetdispersion. This work was motivated by applications involving hydrogen. Using heliumas an experimental proxy， buoyant horizontal jets issuing from a round orifice on the sidewall of a circular tube were analysed experimentally using particle image velocimetry(PIV) and planar laser-induced fluorescence (PLIF) techniques simultaneously to provideinstantaneous and time-averaged flow fields of velocity and concentration. Effects ofbuoyancy and asymmetry on the resulting flow structure were studied over a rangeof Reynolds numbers and gas densities. Significant differences were found between thecentreline trajectory， spreading rate， and velocity decay of conventional horizontal roundaxisymmetric jets issuing through flat plates and the pipeline leak-representative jetscAsonsidered in the present study. The realistic pipeline jets were always asymmetric andfound to deflect about the jet axis in the near field. In the far field， it was found that therealistic pipeline leak geometry causes buoyancy effects to dominate much sooner thanexpected compared to horizontal round jets issuing through flat plates. 1. Introduction Hydrogen， a carbon-free energy carrier， is currently viewed as a clean alternative totraditional hydrocarbon-based fuels for transportation and energy storage applications. Itcan burn or react with almost no pollution or green house gas emissions， and is commonlyused in electrochemical fuel cells to power vehicle and electrical devices. It is also usedin an increasing number ofpower-to-gas systems to blend in the natural gas pipelinenetwork. Despite these benefits， previous studies have shown that hydrogen jets resultingfrom an accidental leak are easily ignitable(Veser et al.2011)， owing to a wide range ofpossible ignition limits (between 4%-75% by volume)i Lewis & von Elbe1961). There e，modern safety standards for hydrogen storage infrastructure must be assured beforewidespread public use of hydrogen can become possible. As a result， fundamental insightinto the physics of hydrogen dispersion into ambient air from realistic flow geometries，such as small pipelines， is necessary to properly predict flow structures and flammabilityenvelope associated with hydrogen outflow from accidental leaks. Also， owing to the lowmolecular weight of hydrogen， buoyancy can significantly influence the development of the jet dispersion during a release scenario. In the current investigation， we attempt toquantify the dispersion and release trajectories of horizontal buoyant jets experimentally，as they emerge from a realistic pipeline geometry， using state-of-the-art experimentalimaging techniques. In the last two decades， due to the rapid development of the hydrogen economy and useof hydrogen technologies， several experimental and numerical studieslChernyavsky et al.2011：Houf & Scheferl2008Schefer et al2008aXiao et al.l22011)have investigatedsmall-i-scale unintendedhydrogen rround jet releasein ambient air， while othersEkotolet al.2012；可Houf et al..2013，2010EHajji et al.2015lstudied different accidental hydrogendispersion scenarios in enclosed and open spaces. There has also been extensive workdone to describe the evolution of axisymmetric round turbulent jets in terms of self-similarity correlations， obtained from statistical analysis from both experimentsLipari& Stansby 2011； Ball et al. 2012and simulations(M. Kaushik2015). In addition， someinvestigations(Su et al2010) have quantified the buoyancy effects on vertical round jets，while othersRodil1982Carazzo et al.2006)have provided a quantitative study intothe buoyancy effects on both turbulent buoyant/pure jets and plumes with analyzing ofall available experimental data. Even though jets and plumes both have different statesof partial or local self-similarity(George1989)， their global evolutions in the far fieldtends toward complete self-similarity through a universal route even in the presence ofbuoyancy. Large-scale structures of turbulence drive the evolution of the self-similarityprofile， and buoyancy has an effect in exciting the coherent turbulent structures； thiseffect is more evident in the evolution of plumes into self-similarly much sooner owing tobuoyancy driven turbulence in the near field(Carazzo et al.2006). Horizontal buoyantjets， however， have been much less studied. In general， increasing effects of buoyancy werefound to correlate inversely to the Froude number in axisymmetry horizontal buoyantietsAsh2012) Previous measurements on axisymmetric round hydrogen jetslSchefer et al.20086，a)revealed that， hydrogen jets show the same behavior to jets of helium(Panchapakesan& Lumley1993)， propane and other hydrocarbon fuels(Richards&Pitts1993). Inparticular， the intensity of centreline velocity fluctuations are similar between the jetand plume regions. In contrast， mass fraction fluctuation intensities increased from aconstant asymptotic value of about 0.23 in the jet region to 0.33-0.37 in the plume region(Panchapakesan & Lumley71993；Schefer et al.2008a). It has also been well establishedthat the mass fraction fluctuation intensities along the centerline and radial variations arealso independent of initial density differences between ambient and jet fluids， and collapseonto the same curves， different curves in jet and plume regions， when plotted against theappropriate similarity variablesPanchapakesan & Lumley1993chefer et al.2008aPittsl1991a). It is noteworthy that all aforementioned studies， as well as related previous investi-gations on jets or plumes， have been limited to leaks through flat surfaces， where thedirection of the jet mean flow was aligned with the flow origin. In reality， however， flowpatterns and dispersion of accidental gas leaks would not be limited to flows throughflat surfaces， and leaks through cracks in the side walls of circular pipes should alsoreceive attention. To address this， a recent study was investigated for vertical buoyantjet evolutions through round holes from curved surfaces， numerically and experimentallySoleimani nia et al.2018Soleimani nia et al.2017 Maxwell et al.2017). Through thisrecent work， significant discrepancies were found between the evolution of axisymmetricround sharp-edged Orifice Plate (OP) jets through flat surfaces and those originatingfrom curved surfaces. Most notably，jet deflection from the vertical axis， and asymmetric FIGURE 1. a) Schematic of the experimental layout. b) Illustration of horizontal 3D jet flowmeasurement area (red inset in part a). dispersion patterns are always observed in realistic situations. To our knowledge， however，the horizontal jet dispersion from curved surfaces has not yet been investigated. To investigate the effects of asymmetry and buoyancy on the evolution of horizontaljets issuing from realistic pipeline geometries， jet release experiments were conductedwith air and helium， where flow patterns and dispersion of gas through a curved surfaceoriginating from a source whose original velocity components were nearly perpendicularto the direction of the ensuing jets. From now on， this jet configuration is referred as a3D jet. A round hole as one of possible crack geometries， was considered in this study，although another possibility might include thin cracks around the tube or the faulty tubefittingslverson et al.2015)， which is not considered here. The horizontal 3D jets werereleased through a 2 mm diameter round hole in the side of a round tube (closed at oneend)， with an outer diameter of 6.36 mm and 0.82 mm wall thickness. The outer-scaleflow Reynolds numbers (Res)， based on the orifice diameter， and Mach numbers (Ma)of the jets ranged from 19，000 to 51，500 and 0.4 to 1.2， respectively. However， it is notedthat for hydrogen jets of equivalent momentum flux， the expected Mach number andReynolds number would be 1.5 and 55，915， respectively. At these conditions， hydrogen isexpected to behave very similar to the helium jets considered hereSoleimani nia et al.2018)). These realistic jets were also compared to axisymmetric leaks through flat surfacesaccordingly. Particle imaging velocimetry (PIV) and planar laser-induced fluorescence(PLIF)were used to measure high-resolution instantaneous velocity and concentrationfields， respectively. The purpose of this investigation was to identify and characterizedepartures from standard axisymmetric jet conditions， and to highlight the buoyancyeffect and asymmetric nature of the 3D jets， which ensued from a practical geometryarrangement. It should be noted that， the effect of pipe wall thickness of the crackgeometry has not yet been investigated. 2. Experimental system and techniques 2.1. Flow facility FigureTa， provides a schematic of the experimental setup used for this study. While，Figure 1b， illustrates the jet flow evolution from the tube orifice considered. To capturethe three-dimensionality of the jet， measurements were obtained on two different two-dimensional planes (denoted ac-z and a-y)， as indicated， for both air and helium. Alsoshown in the figure is the jet centreline， which acts as a reference from which measure-ments are later obtained in the s-z plane. Owing to potential deviation of the jet fromthe orifice axis (a-axis)， the jet centreline tangent and normal lines are shown as s andn coordinates in the figure， respectively. Jet Orientation Q (uj) Pj Vj Ma Fr Re ，Type [L/min] m/s] 1 [Kg/m²] [m²/s] [N/m] Air H， 3D 15 147.5 1.17 1.54×10 -5 50.9 0.43 - 19，000 Air V， 3D 15 147.5 1.17 1.54×10 -5 50.9 0.43 19，000 Air V， OP 15 127.6 1.17 1.54x10 -5 38.1 0.37 16，500 He H， 3D 35 399.5 0.165 1.21×10~ -4 51.3 1.2 1.34×10° 51，500 He V，3D 35 399.7 0.165 1.21×10-4 51.4 1.2 1.34×10° 51，500 He V， OP 35 341.9 0.165 1.21 ×10-4 38.3 1 9.8×10° 44，200 TABLE 1. Flow properties The experiments were conducted within a controlled stagnant environment， at roomtemperature and pressure (T~22°，'， po ~ 100 kPa). Flow controllers (Bronkhorst，EL-FLOW series) were used to control mass flow rates of dry air and pure scientificgrade helium to the system， with a high accuracy (standard ±0.5% of reading plus±0.1% full scale) and precision (within 0.2% of the reading). Di-Ethyl-Hexyl-Sebacate(DEHS) tracer particles were used in PIV measurements， while acetone vapour used asfluorescent tracers for the PLIF experiments. After the test gas was mixed and seededwith the PIV and PLIF tracers，the flow entered the test section of the tube. Isothermaland isobaric conditions were ensured in all measurements. Further specific details can befound inSoleimani nia et al.2018). The orifice， through which the gas dispersed，had adiameter of D = 2 mm and was located sufficiently downstream along the tube lengthto ensure fully developed flow within the tube at the orifice location. Within the tube，flow controllers were used to ensure fully developed subsonic and turbulent flow insidethe tube. In order to compare the behaviour of both test gases， for each experimental setup，the averaged momentum flux (M) at the jet exit was estimated and matched for all testcases. This matching was achieved iteratively， by varying the volumetric flow rate (Q) inthe system. Here， M was calculated by first obtaining the time-averaged jet exit velocityfrom two-dimensional PIV measurements. The two-dimensional momentum flux， in unitsof [N/m]， was then calculated from where the subscript ‘j’refers to the conditions at the nozzle， the angle brackets ‘)’ refer to a time-averaged quantity， and also p and r refer to density and radius，respectively. Table1shows the flow properties used in this study， for the horizontal3D jet configurations， as well as vertical 3D and OP jets used for comparison(Soleimaninia et al.ll2018)； H and Vrefer to horizontal and vertical orientations， respectively. In allcases， the jets were characterized by the outer-scale Reynolds number， Re=(uj)8/voo，where， v。 is the ambient fluid kinematic viscosity and 8 is the width of the mean axialvelocity profile， evaluated from limits of 5% of the centreline velocity at x ~0. 2.2. Measurement techniques Particle imaging velocimetry (PIV) was used to capture the two-dimensional velocityflow field information. A dual-head Nd： YAG pulsed laser (New Wave’s SOLO III 15HZ) was used to illuminate a two-dimensional cross-section of the flow， which was seededwith Di-Ethyl-Hexyl-Sebacate (DEHS)， with a typical diameter of less than 1 um， to act FIGURE 2. Instantaneous a) velocity and b) molar concentration fields obtained from Helium3D jet in c-z plane from two individual imaging windows stitched together. as a tracer particle. The light sheet had an approximate height of 5 cm and thicknessof 1 mm. The field of view of the camera (PIV CCD) was a 40x30 mm’ window withan approximate pixel size of 6.5 um in physical space. Following the procedure of Sul& Clemens(2003， we estimate this resolution to be comparable to the finest scales ofthe flow， with respect to the Nyquist criterion. Each pair of images were then processedusing LaVision DaVis 8.4 software to calculate the global instantaneous flow velocity field.Following the PIV uncertainty propagation methodSciacchitano & Wieneke2016)，.weestimated conservative uncertainty values of 3% and 6% in the time-averaged velocityand Reynolds shear stress profiles， respectively. To measure the gas concentration， we applied planar laser-induced fluorescence (PLIF).To simultaneously apply PLIF， the flow was also seeded with acetone vapour at consistentrate of ~ 10% by volume. A Pulsed Nd： YAG laser (Spectra-Physics INDI-40-10-HG)was used in order to excite the acetone molecules in a light sheet with an approximateheight of 5 cm and a thickness of 350 um， which was then recorded with a PLIF CCDcamera. The camera field of view for all cases corresponded to a 38×28 mm windowwith an approximate pixel size of 6.5 um. The images were taken at a frequency of 5 Hzand then processed using LaVision DaVis 8.4 software. Following correcting for errorsassociated with background noise， fluctuations in cross-sectional laser beam intensity，and laser energy per pulse deviations， one can assume the remaining non-uniformityof the scalar field is due to signal to noise ratio (S/N). The error in the S/N can beestimated from the standard deviation ofthis ratio in an uniform low signal region of theflow field. Based on this data， and uncertainty propagation method， we estimated theuncertainty in the time-averaged and variances of concentration field to be conservativevalues of 4% and 7%， respectively. For each experimental case， a total of 500 images wereacquired to determine the time-averaged molar concentration，(X)， and variances， Xfields. Further details of the experimental procedure can be found in(Soleimani nia et al.2018). Finally， to retain the spatial resolution of the flow field， the full measurement regionis covered by two individual imaging windows with at least a 20% overlap between eachwindow. Figure 2 shows examples of the instantaneous velocity and concentration fields，for the helium 3D jet in the s-z plane. It should be noted that the flow fields wereconstructed from two different experiments， where individual imaging windows have beenstitched together. Distances reported here have been normalized such that where D， the diameter of the orifice， is taken as the reference length scale. FIGURE 3. Time-averaged velocity and molar concentration contours from round jet on sideof tube (3D jet) for air and helium， obtained from a) velocity contours in sc-z plane， b) molarconcentration contours in a-z plane， c) velocity contours in c-y plane and d) molar concentrationcontours in x-y plane. 3. Results 3.1.T1ime-averaged flow fields The time-averaged velocity and molar concentration contours， obtained in both thexc-z and a-y planes for all of the 3D jet experiments conducted here， are shown inFig.3For both experiments， significantly larger jet spreading was observed in the s-zplanes compared to the a-y plane. Clearly， the flow structure was asymmetric in bothexperiments. The jets were also found to deviate significantly from the horizontal c-axis，for both gases in the x-z plane. In this plane， near the potential-core region， there wasalso more jet spreading on the lower side of the jet compared to the top side. In the-y planes of both gases， there were two high-velocity peaks (saddle-back behaviour)， aty±0.5D， on each side of the s-axis， with a much shorter potential-core length (≈2D)compared to the s-z plane. This saddle-back behaviour was previously found to originatefrom a velocity deficit region which forms inside the orifice due to flow separation as thegas inside the tube encountered the edge of the orifice (Soleimani nia et al.2018). Also， 14 FIGURE 44. Jet centre-lines taken along the location of maximum velocity magnitudes(/u)|max(z)) in s-z plane from measurements. Also shown for comparison are vertical 3D& OP jets(Soleimani nia et al.2018and horizontal round OP jets experimentsAsh2012. there was a shorter potential-core length observed for helium (≈3D)， compared to air(≈5D)， as observed in the velocity contours of the x-z planes. In general， the concentration profiles were qualitatively similar to the velocity profilespresented in Fig.[3. with two exceptions. First， the concentration core lengths in bothplanes were found to be shorter than the velocity potential cores. The concentrationcore lengths were approximately ≈ 4D in the c-z plane for both gases， and ≈2D and≈1D，for air and helium， respectively in the s-y plane. Also， much higher concentrationlevels， with higher spreading rates， were observed for helium in the far field compared toair. This observation can be attributed to a low Schmidt number (Sc <1)， where massdiffusion rates are higher than momentum diffusion rates. 3.2. The jet centreline trajectory In Fig.4the jet centreline trajectories， determined in the xc-z plane， are presented forall cases. Here， the trajectories were determined by the maximum velocity magnitude，u)max(c)， locations. Also shown for comparison are the jet centreline trajectoriesobtained from previous vertical 3D jet experiments(Soleimani nia et al.2018)，andfrom horizontal sharp-edged orifice flat-plate (OP) helium jet measurementsAshl2012).In order to determine the effect of buoyancy on the horizontal jets， lines of best fit，using linear regression to power law expressions， were obtained for the far field (beyondx ≥10D)， and are also shown in Fig. In general， the jet trajectory for the verticaland horizontal air jets were found to be described by a nearly linear relation (i.e. powerlaw exponent ~ 1). The horizontal helium jet， however， was found to have a powerlaw exponent ~ 1.3. Upon extrapolating these relations to the far field， beyond theexperimental data collected， it became clear that buoyancy of the helium jet causedsignificant deflection from the horizontal axis， despite the high Froude number (Fr=1.34 ×10). It should be noted that for horizontal flat-plate OP helium jets， with acomparable Froude number (Fr =1×106)， such buoyancy effects were not observedAsh2012. FIGURE 5. a) Inverse time-averaged velocity decay and b) jet velocity widths (2Lu(1/2)) obtainedalong the (u)max(r) centrelines， in xc-zplane from measurements.Note， n-coordinate refersto lines which are normal to the centreline， and coplanar with the x-z plane (see the coordinatesystem in Fig.1 b). Also shown， for comparison are axisymmetric round jet correlationslWitze1974)， and vertical 3D & OpJjets， horizontal round OP'jets and round pipe jet experiments(Soleimani nia et al.2018：Ash2012：EHussein et al.1994：Amielh et al.1996 3.3. Velocity decay and jet spreading rates Fig.5a shows the inverse time-averaged velocity decay ((uj)/(uc)) along the jetcentrelines (s-coordinate illustrated in Fig.1b) for all experiments. Here， the subscript‘C'refers to the conditions at the jet centreline， while the subscript‘’refers to thejet exit condition. Also shown， for comparison， are velocity decay correlationsWitzel1974)for compressible subsonic and supersonic axisymmetric round jets， alongwithvelocity decay rates obtained from vertical 3D and OP jet experimentsSoleimani nialet al.2018)， and horizontal OP helium jet measurements(Ash2012).Upon comparisonto the Witze correlations(Witze1974)， the air and helium OP jet experiments werefound to reproduce well the expected velocity decay rate， with helium jet decaying fasterthan the air jet. On the other hand， the decay rates observed in the experimental 3Djets were much faster compared to the axisymmetric jets. In general， upon comparisonbetween horizontal and vertical 3D jets， buoyancy was not found to significantly affectthe velocity decay rates. In the x-z plane， Figure5b presents the jet velocity widths (2Lu(1/2))， that havebeen obtained by determining the locations where (u)|=0.5(u)max(c) along lineswhich were orthogonal to the jet-centrelines. These orthogonal lines have been indicatedpreviously as coordinate ‘n’in Fig. b. For the 3D jets， in all cases， a slight contraction inthe jet widths has been observed from 1D 5D， FIGURE 8. Axial development of turbulence intensities along jet centrelines， a) tangentialturbulence intensity component(us(rms)/(uc))and b) orthogonalturbulence intensitycomponent (un(rms)/(uc)) for experiments. Also shown， for comparison are vertical13D& OPjets， horizontal OP jet， and round pipe jet experiments(Soleimani nia et al.]2018Ash2012Amielh et al.1996) in the far field， the experimental 3D air and helium jets developed into the self-similarGaussian distribution obtained from the OP jets for the full range of n. Fig. 8shows the normalized axial evolution of the r.m.s. velocity fluctuation com-ponents in the s and n directions， tangential and orthogonal to jet centreline， whereu(rms) =(u2)1/2. It should be noted that the prime (') represents the instantaneousfluctuating quantity(u'=u-(u)). For the 3D vertical and horizontal helium jets，the tangential turbulence intensity reached an asymptotic value of ~26% at x = 3D，whereas such a value was not observed untilx = 20D andx= 15D for the 3D horizontaland vertical air jets， respectively. This trend was also observed in pipe jet measurementsAmielh et al.1996)and also the current vertical OP jets， where helium reached theasymptotic value closer to orifice， at x =15D， compared to air at c =32D. However， itappears that this asymptotic value of ~26% would be reached in the far field (x>33D)for all jets， except the horizontal helium OP jet measurements Ash2012.. It shouldbe noted that lower turbulent intensities of the horizontal helium OP jet， observed inboth tangential and orthogonal components， are likely due to higher initial turbulentintensities reported for the horizontal helium OP jet (not shown)(Mi etal.2007)1.. Also.lower spatial resolution of the PIV measurement compared to the current experiments(almost 3 times less)， may have been a factor. The same remark is valid for the orthogonalturbulence intensity， as the 3D helium jets reached the asymptotic value of~19-22%more closer to orifice at s = 5D， compared to air at x = 15D. Also， the OP verticalhelium jet reached this peak turbulence intensity at x =15D， whereas such turbulenceintensity was not recovered untilx =30D for air. In general， the intensity of tangentialvelocity fluctuations was higher than the orthogonal components， as observed in previousstudies Panchapakesan & Lumley993； Amielh et al. 1996 FIGURE 9. Normalized axial evolution of mass fraction fluctuation intensities along jetcentrelines， Ye(rms)/(Ye)， for experiments. Also shown， for comparison are vertical 3D& OPjets，and round piipe jet experimentsSoleimani nia et al.20181Becker et al.l1967Pitts1991a：IRichards& Pitts1993). the asymptotic value of ~ 33% for the rest of the measurement domain. For the horizontal3D air jet， the unmixedness reached a value of ~20 - 24% at 5D< x<15D， which isin good agreement with the values reported in literature for the far field (~21-24%)(FPanchapakesan & Lumley1993；Chen & Rodi|1980Richards & Pitts1993). Then，the unmixedness recovered the asymptotic value of ~ 33% at x = 19D for the rest ofobservation domain. For the vertical OP air jet， the observed profile followed closely thevalues of those reported for smooth contraction (SC) air jets(Becker et al.1967)in thenear field (5D < x <15D)， and then increased to the asymptotic value of~23% for therest of the domain. On the other hand， for the vertical OP helium jet， the unmixednessreached a peak value of 0.43 at x =7D， then slowly decreased to the value of ~ 33% inthe far field， from sx > 20D. it should be noted that， even though the unmixedness valueswere not consistent between the helium and air OP jets in the measurement domain，extrapolation of the data (not shown) revealed that the far field unmixedness wouldconverged to the same value at about a >50D. Higher order statistics were also acquiredfor the experiments conducted here. The time-averaged Reynolds stress profiles obtainedfrom measurements， (uun)， are presented in Fig. 10a). In this case， the Reynolds stressquantities have been normalized by local centreline velocity， (u)(s). In the s-z plane，the air and helium experiments captured well the far field self-similar profile， with thehelium have slightly higher magnitude of the Reynolds stresscompared to the air， asseen before in the axisymmetry jets t re n tr e ( 1993Soleimani niain the -n dire et al.ctir2018)). However， to the left of the jet centre(in the -n direction)， the horizontal 3D jetexperiments were found to have a higher magnitude of the Reynolds stress comparedto the axisymmetry jets， in the near field a ≤10D. Also， within for ≤5D， a higherReynolds stress was observed beyond n/L1/2|<1. Finally， the normalized concentration variance profiles ((Y")/(Y?))， obtained fromexxperiments， are presented in Fig. 10 b). In the a-z plane， the initial development of the3D air jets had a higher variance of concentration to the left of the jet centre (in the -ndirection) within the ranges of a ≤ 10D. While， helium jet initial profile exhibited semi air： FIGURE10. a) Normalized time-averaged Reynolds shear stress((usun)/(uc))) and b)concentration variance ((Y)/(Ye)) profiles along jet centrelines for air and helium experiments.Here， the profiles are taken at various heights for air and helium measurements in sc-z planes. symmetry saddle-back profile up to x ≤2D，after this point variances profile recoveredthe semi Gaussian profile with a maximum magnitude at x ~ 3D. Beyond a ≥10D jetheights， in the far field， the concentration variance profiles revealed self-similar profilefor both air and helium 3D jet experiments. Also in the core region， much like theaxisymmetry jet evolutions， the 3D jet experiments were found to contain a minimumvariance near the jet centre， except for helium jet at ~ 3D. In general， the magnitudesof mass fraction variance of the helium were higher compared to air， more specifically inthe near field. 4. Discussion 4.1. Self-similarity analysis In the previous section， for both near and far fields， different velocity and scalarstatistical properties were reported for 3D and OP jets of helium and air. It has been wellestablished that these variations are influenced by differences in density， initial conditionsand turbulence structures of the jets (Richards & Pitts 1993Xu &Antonia 2002Miet al.2001a). Self-similarity (or self-preservation) state in turbulent flows is described as when the flow statistical quantities can be assumed by simple scale factors which dependon only one of the variables. As a consequence， both velocity and scalar pseudo-similaritysolutions， in constant or variable density jets， evolve in similar ways when appropriatesimilarity variables have been usedl (Panchapakesan & Lumley1993：Pitts1991a；Chen &Rodil1980). These pseudo-similarity solutions have been used to develop the analyticalmodels， and approximate the velocity & scalar decays and growth rates in jet flows.However， It should be noted that the turbulent structure throughout the entire flowfield is particularly influenced by the initial jet outflow conditions. As a result， differentsimilarity states in the far field are possibleGeorge Mi et al.20016)). In this section，self-similarity analyses conducted on the current measurement data are presented. The pseudo-similarity solution， in the turbulent jet， is approximate in the pure jetregion， where inertia forces dominate the flow. To estimate the extent of the pure jetregion， the following non-dimensional buoyancy length scale (along the x-axis， shown inFig.1b) was usedChen & Rodi1980)： where the Froudu；pie number is Fr (=(Poo-Pj)g)，D and g is the acceleration due to gravity.For the flow conditions reported in Tablele1Cb varies from 0 to 0.042 for 0< x < 30D，the range of current measurements. Therefore， the hypothetical range of the pure jetregionChen & Rodi1980)cb < 0.5， is satisfied for all flow conditions considered in thisstudy. The centreline velocity and mass fraction decays for nonreacting jets， for both constantand variable density flows， can be correlated as and where the subscripts ‘j’and‘C’refer to the conditions at the jet exit and centreline，respectively； Xo，u and Xo，y are the dimensional jet virtual origins obtained from in-verse centreline velocity and mass fraction decay profiles， respectively， and Cu & Cyare empirical constants obtained with least-mean-square fitting the measured data toEqs.4.2-|4.3. The concept of effective diameter， is defined to account for variations in both the jet fluid density and mean jet exit velocityprofile in the turbulent jet flowsThring & Newby1953， Becker et al.1967 Dowling&DimotakisK1990；Pitts1991a，Richards & Pitts1993)； where mj and Mi are the exit masSflux and momentum flux for the jet， respectively. Physically， Def， corresponds to theorifice diameter of a jet having the same momentum and mass flux， but with a densityof the ambient fluid instead of the jet fluid. Since asymmetry structures were alwaysobserved at the jet exitSoleimani nia et al.2018)， three dimensional measurementsof velocity and concentration are required to accurately calculate Def in the 3D jets.However， if the density and velocity profiles are uniform at the jet exit， then Def takesthe form as originally introduced byThring & Newby(1953)， Def=D("). It should FIGURE111. Inverse axial velocity and massfraction decay along jet centrelinesSversusdownstream distance non-dimensionalized by Def and Def， a) velocity ((uj)/(uc)) and b) massfraction ((Y)/(Yc)) for experiments. Also shown， for comparison are vertical 3D & OP jets， andround pipe He & H2 jet experimentsSoleimani nia et al.2018：1Richards & Pitts1993：Scheferet al.20086) be noted that in the case of constant density jet (air jet) the effective diameter is equalto the orifice diameter. Here， different effective diameter (Def) versions available in the literature， are exam-ined by collapsing the helium data on to the comparable air data， for both hyperbolicdecay velocity and scalar laws (Eqs.42--4.3). For the mass fraction decay law， theoriginal effective diameter Def=D(Bi) Thring & Newby1953， used to collapse thescalar data. For the measured velocitydata， a modified version of effective diameter，given as D**=D()2Talbot et al.12009)， provides a better correlation in the nearfield ofthe flow. Here the subscript oo'rrefers to the outer ambient fluid， air. However， themodified version of effective diameter (De=D(一e)p)e reequires knowledge of the localcentreline concentration； this version cannot be applied in the absence of concentrationdata. Upon further analysis， it was found that if the second root， in the original effectivediameter (Def=D("))， is replaced by ~ thrid root， then the velocity data shows goodcorrelation with the collapsed curves of the aggregate 3D jet data in both the near andfar fields. Therefore， this new modified version of effective diameter， Def=D()p0o.3was used to correlate the centreline velocity decay (Eq.4.2)). It should be noted that thelatter modified version of effective diameter， Def， may only valid for the current 3D jetexperiments， due to the effects of specific conditions at the jet such as geometry， effectivesurface area， flow structures， density profiles， and velocity profiles. In Fig. 11，the centreline revolution of the inverse velocity (Fig. 5 a) and mass fraction(Fig.6a) profiles have been reconstructed for the 3D jets as a function of distancefrom the virtual origins， normalized with effective diameter， i.e.[(X-Xo)/Def]. Self-similarity decay lines， obtained by curve fitting the results， are also shown for OP，Smooth Contraction (SC)， pipe round free， and pipe round confined jets(Quinn12006：Panchapakesan & Lumley l1993Richards & Pitts1993PittsI1986；Schefer et al.20086The experimental data for all helium jets were collapsed onto the comparable air jets，verifying that the correct version of effective diameter along with virtual origin distancesare the appropriate scaling parameters to correlate both velocity and scalar pseudo-similarity solutions in the constant or variable density jets. The velocity decay rates ofall 3D jets are very similar to OP jets based on a comparison of velocity decay plots Jet R， Xo，u/D C Xo，y/D Cy Air， 3D Horizontal -3.07 0.174 -1.07 0.326 Air， 3D Vertical -2.78 0.170 -3.39 0.319 Air， OP Vertical 3.08 0.169 -0.68 0.224 Air， OP Vertical ( Quinn 2006) 2.15 0.167 He， 3D Horizontal 0.14 -1.29 0.175 -0.95 0.313 He， 3D Vertical 0.14 -1.45 0.170 -6.42 0.316 He， OP Vertical 0.14 3.54 0.170 2.32 0.221 He， SC Vertical (Panchapakesan & Lumley 1993 0.14 0.152 0.271 He， Pipe Vertical (Richards & Pitts 1993川 0.14 3.0 0.212 He， Pipe Vertical (Pitts|1986) 0.14 4.45 0.256 H2， Pipe Vertical (Schefer et al. ]2 2008bM 0.069 4.0 0.208 TABLE 2. Centerline velocity and scalar pseudo-similarity decay properties a). However，the mass fraction decay profiles of 3D jets show a steeper decay rate than isobserved for OP jets(1 b). This observation further supports the fact that the velocityfield spreads slower than the concentration field. This conclusion is supported by thepreferential transport of scalar quantities over momentum flux that is evident in previousstudiesTalbot et al.2009Lubbers et al.2001). It is also clear that a pipe confined jetof hydrogenSchefer et al.20086)ffollows the same decay rate of those pipe confined jetsof helium(Richards & Pitts1993).). This observation is consistent with the fact that thescalar decay rate is independent of initial density ratio but influenced notably by the jetinitial conditions and other potential factors such as measurement conditions. Furthercomparisons of the centreline pseudo-similarity decay properties are shown in Table 2.Here， R， is a ratio of the jet fluid density to the ambient flfuuiidd， ，R pR =， =. For bothvelocity and mass fraction quantities， these self-similarity properties are obtained fromdata fitted by a least-mean-square algorithm to Eqs. (4.2)-(4.3). Table 2also providesa comparison of self-similarity properties of OP， SC， pipe round free， and ipipe roundonfined jets (Quinn2006：Panchapakesan & Lumley1993；Richards & Pitts1993：Pittsl986Schefer et a . It should be noted that dimensional virtual origin distances， Xo，u and Xo，y， are normalized by the orifice diameter(D). Upon comparison of the velocity decay slopes， for the air OP jets， the value of Cu =0.169 is ingood agreement with the value of 0.167 reported previously for the air OPietQuinnI2006)). The small difference is associated with higher Reynolds number ofRe=1.84×10 compared to present study (Re=1.65×104)， which results in a decreaseof the velocity decay rate. The helium OP jet shows slightly higher decay rate to that ofthe air OP jet， as shown previously in Fig. 5 a， but with a minor increase of the virtualorigin， cou. It is well known that the virtual origin of a jet is highly influenced by the jetinitial conditions and does not vary in any systematic manner. The vertical helium andair 3D jets have almost the same decay slopes， whereas the horizontal helium 3D jet has aslightly higher slope than the comparable horizontal air jet， as previously noticed in Fig.a. In general， a higher velocity decay rate is observed for 3D jets compared to OP， SCand pipe jets based on a comparison of the velocity decay slopes. This is associated withenhanced turbulent mixing in the 3D jets， as a result of their asymmetry flow pattern，specifically in the near field. In contrast， by comparing the helium mass fraction decay slopes in table 2， it is foundthat reported Cy values in the literature for SC and pipe jets are larger than those OPvalues obtained in the current study. This is in contrast with the well established factthat the OP jets exhibit the highest mixing rate， followed by the SC jets and finally the FIGURE12. Centreline evolution of normalizedmassfraction fluctuation intensities，Ye(rms)/(Ye)， versus downstream distance non-dimensionalized by Def for experiments. Alsoshown， for comparison are vertical 3D & OPjets， and round pipe jet experiments Soleimanillnia et al.2018：Becker et al.1967；Pitts1991a：Richards & Pitts1993l) pipe jetsMi et al.2001a). It should be noted that the value of Cy = 0.271 reportedfor SC helium jetPanchapakesan & Lumley1993)，is obtained without considering thescalar virtual origin， Xo，yr， in Eq.(4.3). In addition， Cy = 0.256 reported for the pipeiet(Pitts1986))，， is correlated based on a different exponent in the effective diameterquaation. The pipe jet data has been correlated using the factor of()0.6 instead() in the original version of Def which would explain the higher Cy value reportedfor the pipe jet in their measurements. The mass fraction decay slope observed for helium3D jets is smaller than for air 3D jets. However， upon comparison of mass fraction decayslopes between the 3D and other jets， it is found that the 3D jets have the highest decayslopes. This result further supports the fact that significantly higher turbulent mixing andentertainment rates occur in the 3D jets compared to the axisymmetry jets， as recentlyconcluded in the experimental and numerical study on vertical 3D jet Soleimani niaet al.2018). 4.2. Buoyancy effect For the 3D jets， it was found that the perpendicular stream-wise axis of the hole，relative to the flow direction within the tube， resulted into a deflection of the jet awayfrom it's horizontal x-axis. Initially， from Fig.4 all 3D jets emerged with a similardeflection angle. But only after a>2D， both horizontal and vertical air jets were foundto deflect more than helium jets. Buoyancy forces， aside from less significant contributors，are a probable cause of the increased deflection observed for vertical air jets in comparisonto helium jets. But from the comparison of helium jets centreline trajectories (Fig.buoyancy effect is clearly the main contributor in the significant deflection of horizontalcase from the horizontal s-axis compared to vertical jet. Whereas such deflection werenot observed in horizontal air jet compared to vertical case. Figure 122 reconstructed the unmixedness profile (Fig.9) for the 3D jets as a functionof distances from the virtual origin (Xo，r) and normalized by effective diameter (Def). Along with same remarks observed as those presented in Fig.9，it is clear that effectivediameter would not be a necessary length scale for unmixedness profile， since helium andair data are already collapsed on the same curves by scaling with the jet orifice diameter(D). All 3D jets recovered the asymptotic value of~26%， reported for variable densityfree round jet(Pitts1986l， which is closer to the orifice compared to axisymmetry OPjets. Further downstream，the horizontal 3D jets reached a higher asymptotic plateau(~33%) in the far field. This difference might be solely associated with buoyancy，which becomes dominant closer to the orifice， in the horizontal cases compared to thevertical 3D jet. Other parameters such as co-flow， initial conditions， Reynolds number，and measurement uncertainty could also play a significant rolePittsl1991a). However，their effects are negligible since the similar experimental system andparameters havebeen used in current measurements. Despite these differences， it is clear that centrelineunmixedness is independent of R， and achieves asymptotic value based on the initialconditions at some downstream distance， influenced by Reynolds number. However， theinitial increase in the mass fraction fluctuation intensity in the near field occurs morerapidly in lower density gas，helium compared to air. 4.3. Asymmetry effect For 3D jets， flow separation of the emerging gas originating from inside the tube，similar to flow over a backward step， is always observed at the entrance of orifice. Thisphenomenon was also previously reported in vertical 3D jetsSoleimani nia et al.2018)，This flow separation contributes to the velocity and scalar deficit near the edge of theorifice located on the lower side of the jet (in the +n direction)， and results in a slightcontraction in the width of the jet has been observed in both velocity and concentrationfield (Figs.5b &6b) in the range of 1D 关闭