A Computational Fluid Dynamics (CFD) Investigation of the Wake Closure Phenomenon

Materials Science and Engineering A 379 (2004) 264–276

A computational fluid dynamics (CFD) investigationof the wake closure phenomenon

Jason Ting a,∗, Iver E. Andersonba Alcoa Inc., Specialty Metals Division, Alcoa Technical Center, Alcoa Center, PA 15069-0001, USA

b Ames Laboratory (US DOE), Iowa State University, 222 Metals Development Building, Ames, IA 50011, USA

Received 5 September 2003; received in revised form 10 February 2004

Abstract

Using a computational fluid dynamics (CFD) software, the gas dynamics of the open-wake and closed-wake conditions of an annular-slithigh-pressure gas atomization (AS-HPGA) nozzle were investigated to validate the predictions of a pulsatile atomization model that was re-cently proposed. The location of the recirculation zones, the oblique shocks and the Mach disks were analyzed for this type of closed-coupledgas atomization nozzle. The stagnation pressures located downstream of the Mach disk, in closed-wake condition, were found to be approxi-mately twice as high as the stagnation pressure in an open-wake condition at a slightly lower atomization gas pressure. The turbulence modelutilized within the CFD calculation scheme appeared to be inadequate for calculating aspiration pressure just below wake-closure pressurewhen the recirculation zone is extremely long and narrow. However, overall, the CFD calculation correlated well with the experimental re-sults, showing that the aspiration pressure progressively lowers as operation pressure increases in open-wake condition, and rises as operationpressure increases in closed-wake condition.© 2004 Elsevier B.V. All rights reserved.

Keywords: Gas atomization; CFD; Wake-closure; HPGA nozzle; Recirculation zone

1. Introduction

One of the many methods of producing spherical metallicpowder is by a gas atomization process—a process that is notyet thoroughly understood. The practice of gas atomizationin the metal powder manufacturing industry is widespread.Spherical metal alloy powders produced by the gas atomiza-tion process have very attractive material properties becauseof the high solidification rate the powders experience. Thishigh solidification rate promotes microstructure refinementin the resulting powders that is unattainable by conventionalingot casting metallurgy. This is particularly beneficial forreducing elemental segregation in highly alloyed materials,where microstructure refinement and alloy homogeneityare desirable. Furthermore, the spherical morphology of thepowder is ideal for the growing metal injection moldingand thermal spray coating industries.In general, two gas atomization processes exist in the

powder manufacturing industry: close-coupled and free-fall

∗ Corrresponding author.E-mail address: [email protected] (J. Ting).

atomization. In close-coupled atomizers, the molten metalstream is delivered into the atomizing gas via a ceramic meltdelivery tube immediately adjacent to the high pressure at-omizing gas. In free-fall atomizers, the molten metal streamis allowed to free-fall a distance before the atomizing gasimpinges upon the stream. The close-coupled atomizationprocess is preferred over the free-fall process in the produc-tion of fine powder because the close proximity of the at-omizing gas to the melt delivery tube, enhancing the moltenmetal breakup and making the formation of finer powderparticles more efficient. However, close-coupled atomiza-tion can be difficult to practice and it is considered by manyto be more an art than a science. The difficulty mainly liesin the general lack of understanding of the gas recirculationeffect within the atomization zone and how it relates to ini-tial disruption and distribution of the melt flow, prior to themelt disintegration.The inherent gas recirculation effect is created by the

global flow and pressure patterns of the atomizing gas, atthe base of the ceramic nozzle. This attached recirculationzone is an extension of the ceramic melt delivery tube, cre-ating a local environment at the melt orifice that affects the

0921-5093/$ – see front matter © 2004 Elsevier B.V. All rights reserved.doi:10.1016/j.msea.2004.02.065

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J. Ting, I.E. Anderson /Materials Science and Engineering A 379 (2004) 264–276 265

ambient gas pressure. The gas pressure at the melt orifice,also commonly known as the aspiration pressure, is knownto influence the melt flow rate. It was previously hypothe-sized [1] that the recirculation zone can be viewed as a con-trol volume, and that the gas enters the recirculation zonethrough the wake front (also known as stagnation front) ofthe recirculation zone, and exits along the circumferentialedge of the melt tip base. The aspiration pressure is a mea-sure of the force of the total recirculating gas flow actingagainst the melt orifice area. The control volume hypothe-sis [2] states that the aspiration pressure is a consequenceof the mass balance between the gas entering and leavingthe recirculation zone. Since pressure is proportional to thedensity of the gas, the stagnation pressure in the primary re-circulation zone has a direct contribution to the mass of gasentering the recirculation zone and the resulting aspirationpressure measured at the melt orifice. Under high-pressureatomization conditions, the melt feeding stability at the meltorifice can be better controlled if the melt orifice experi-ences a subambient pressure. Operating in this preferred as-piration condition, a subambient pressure at the melt orificeshould provide for an intrinsically more stable melt feed bydrawing the melt towards the atomization zone, resulting ina consistent powder yield.The relationship between the melt flow rate and the fine

metal powder yield, however, is mostly empirical. A liter-ature review of gas-atomized metal powders indicates thatthe best-known and most commonly quoted correlation forgas atomized metal droplet diameter (or mass median diam-eter) comes from analysis of a free-fall atomization processby Lubanska [2]. In Lubanska’s proposed correlation, theimportant process parameters and material properties are re-lated to the mass median diameter of droplets (MMD) bythe following equation,

MMDd0

= kD

[(1+ mL

mG

)vL

vGWe

]12, (1)

with

We = ρLU2Gd0

σ(Weber equation), (2)

where d0 is the melt delivery tube orifice diameter, havingvalues between 6.35 and 4.725mm; kD is a constant whosevalue was found to be between 40 and 50 for various metalsand inorganics, mG and mL are the mass flow rates of atom-ization gas and liquid metal, respectively; vG and vL are thekinematic viscosities of the gas and the liquid, respectively;and We is the dimensionless Weber number. In the Weberequation, ρL and σ represent the density and surface tensionof the liquid, respectively, and UG is the gas velocity at im-pact with the liquid. It is obvious from the above empiricalanalysis that material properties such as viscosity, density,and surface tension are invariant for a predetermined melttemperature, and that the dimension d0 of the atomizer isconstant for a given atomizer geometry. Thus, the mass me-dian diameter is a strong function of the gas velocity and the

gas and liquid flow rates, mG and mL. This flow rate ratio(mG/mL) in Lubanska’s equation is commonly referred toas the “gas-to-metal ratio” (GMR) in melt atomization.Intuitively, one would assume that, at a fixed d0, the GMR

is related to the operating pressure of the atomizer gas sup-ply, such that the high and low GMRs are directly associatedwith the high and low atomization gas pressures, respec-tively. This, however, is not always true in a close-coupledatomization process. It was recently shown that the GMRcan change dramatically (by 37.2%) at two atomization pres-sures that differ by less than 1.5% (or 130 kPa) [3,4]; thesetwo pressures were on either side of the wake-closure pres-sure (WCP). The wake-closure phenomenon, which occursat the WCP, is a gas dynamic condition where the recir-culation zone is truncated by the sudden appearance of aMach disk [5]. Simultaneously, the subambient aspirationpressure, measured at the melt orifice, suddenly becomesdeeper (i.e., lower below atmospheric pressure). The abruptdrop in aspiration pressure with the appearance of the Machdisk is due to the restrictive flow the Mach disk imposes onthe truncated recirculation zone [3,4]. As mentioned before,with less mass of gas flowing into the recirculation zone,the aspiration pressure measured at the melt orifice deepens,i.e., there is a greater suction that acts on the exit of the pourtube. The gas flow conditions before and after the aspira-tion drop are known, respectively, as “open” and “closed”wakes [5]. The previous atomization studies [3,4], indicatethat the deep aspiration observed in the closed-wake condi-tion causes the melt flow to slow, which is contrary to whatone would assume intuitively from increased suction.In the same studies [3,4,6], a pulsatile atomization model

was proposed to relate the abrupt melt flow rate decrease tothe gas dynamics of the atomization process. The model re-vealed that the gas dynamics around the melt delivery tubeorifice, which influence the aspiration pressure, also con-trolled the melt flow rate and the GMR during atomization.The proposed pulsatile atomization model [3,4] was ableto explain how the atomization of a nickel-based alloy im-mediately above the wake-closure pressure could produce amedian powder size that is 42% smaller than that atomizedimmediately below the WCP; given that the increase in theatomization gas pressure was less than 1.5%. In addition, themelt flow rate was observed to slow when operating abovethe wake closure pressure, where the aspiration pressure isdeeply subambient.The premise of the proposed pulsatile atomization model

requires the existence of a high-pressure stagnation pointlocated immediately downstream of the Mach disk, in theclosed-wake operating condition [3,4,6]. In the model, whena dense melt flows into the recirculation zone, it disrupts thegas dynamics of the Mach disk (the Mach disk disappears),turning the recirculation zone into an open-wake condition.The stagnation pressure that was located behind the Machdisk (now absent) promptly enters the recirculation zone,pushes upwards against the melt orifice, and disrupts tem-porarily the melt flow. The disrupted melt flow allows for

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266 J. Ting, I.E. Anderson /Materials Science and Engineering A 379 (2004) 264–276

the atomizing gas to re-establish the gas dynamics of theclosed-wake condition, with a deep subambient aspiration,and to resume the melt flow. This oscillation effect betweenthe two states, closed- and open-wakes, can also be used toexplain the pulsatile effect actually observed in liquid sprayatomization [7–9]. In the open-wake condition, a weakerstagnation pressure exists and the Mach disk is absent, i.e.,the pulsatile effect is expected to be absent in the open-wakecondition [3,4].It seems reasonable that the dynamic balance between

the strong aerodynamic forces of the supersonic atomizationgas and the high momentum and heat content of the meltflow could produce an oscillation between closed-wake andopen-wake atomization behavior. However, the magnitudeof the stagnation pressures at open and closed-wake con-ditions, and the relative location of the stagnation pressurefronts have not been thoroughly investigated in the previouseffort at modeling the gas-only flow in close-coupled gas at-omizers using CFD [10–12]. The prior CFD results that wereobtained provided a good correlation to actual aspirationmeasurements and matched (reasonably well) the Schlierenimages of the atomization nozzles, which showed Mach diskand stagnation fronts features. Unfortunately, none of themodels focused on the stagnation pressure magnitudes ineither the open-wake or closed-wake conditions, making itdifficult to support or refute the proposed model. Therefore,a CFD method was used in this study to qualitatively locateand quantitatively measure the stagnation pressure fronts inopen-wake and closed-wake conditions. The velocity andpressure profiles along the central axis from the CFD modelwere also examined to gain understanding of the gradientsin these properties that occur in both conditions.

2. Experimental procedure

An annular-slit HPGA (AS-HPGA) nozzle, based upon adiscrete-jet HPGA (DJ-HPGA [1]) geometry [13], was con-structed. The AS-HPGA nozzle has parallel surfaces for theinner and outer walls of the annular-jet, and a gas flow apexangle of 45◦, or 22.5◦ from the central axis. The DJ-HPGAnozzle is an ensemble of 20 discrete jets, 0.737mm in diam-

Fig. 1. Schematic drawing of the computational field showing the geometry of the boundaries. The dimensions of the boundaries are in mm, given inparentheses.

eter, located concentrically around the delivery tube measur-ing 10.36mm in diameter. The AS-HPGA nozzle was de-signed to have the same total jet exit area as the DJ-HPGA,thus the gap distance between the inner and outer walls ofthe AS-HPGA is 0.254mm, i.e., smaller than the jet diam-eter.Pressure transducers were located in the melt delivery tube

and the atomizer manifold to measure the aspiration pressureat the melt delivery tube orifice and the actual atomizationgas delivery pressure to the annular slit, respectively. Thisprocedure has been discussed previously in detail [1].

3. Computational modeling procedure

A CFD program called Rampant© (manufactured by Flu-ent Inc., Lebanon, New Hampshire) was used in this study.An unstructured triangular grid mesh density was created todelineate reasonable (non-interacting) gas flow field bound-aries for the atomizer nozzle. The coordinates of the meshboundaries and overall calculation space are depicted inFig. 1. Since the modeling involved an annular-slit HPGAtype atomizer, possessing a rotational symmetry, the compu-tational domain was simplified into modeling one half of acentral cross-section of the atomizer and the melt feed tube(e.g., see Fig. 2). The atomization flow field is oriented hor-izontally with the atomizer melt feed and gas supply on theleft and the axis of symmetry boundary on the bottom ofthe computational domain, respectively, as shown in Fig. 1.A grid refinement was applied during the CFD calculationsto regions containing large pressure gradients and close tosolid walls. An additional conservation equation for the tur-bulent kinetic energy and its dissipation rate was also solvedto account for the effects of turbulence. The compressibil-ity effect, included in the turbulence model, used Sarkar’sdilatation dissipation method [14]. The turbulent model clo-sure and its specific handling are discussed in detail in an-other article [11]. Atomization gas pressures of 0.69, 2.07,3.45, 4.82, 6.20, and 7.58MPa were used in the CFD modelto initialize the pressure in the manifold, upstream of theannular slit exit. The thermodynamic constants of argon gaswere used.


Fig. 2. CFD model of the AS-HPGA nozzle at gas atomization pressure of 0.69MPa in the open-wake condition: (a) the global velocity output and themirroring schematics of the gas flow structures; (b and c) the velocity, and static pressure profiles, respectively, along the geometric centerline of theAS-HPGA nozzle.

4. Results

4.1. CFD modeling results

Since the AS-HPGA atomizer nozzle was modeledaxis-symmetrically, the calculated images of the velocityprofiles can be reflected about the axis of symmetry to givethe full flow field of the AS-HPGA nozzle. The resultinganalyses of the dominant shock structures in the modeledpressure conditions are presented as schematic drawingsmirroring (below) the CFD outputs. It must be noted that

the velocity magnitude increases with decreasing shades ofdarkness in the CFD figures.The velocity flow field modeled at an atomization gas

pressure of 0.69MPa is given in Fig. 2a. The rapidly expand-ing gas exiting the annular gas opening forms a small obliqueshock near the edge of the ceramic melt delivery tube tip,slowing down the gas velocity. The velocity re-acceleratesthen decelerates across a set of Prandtl–Meyer waves [15]before combining with the other gas streams to form a uni-fied flow field of enhanced Prandtl–Meyer expansion wavesalong the central axis. A diminutive recirculation zone is


located adjacent to the melt orifice surrounded by the gasflow field mentioned above. Located 0.6 nozzle diameterlength (NDL) units downstream, at the terminus of the recir-culation zone, is the stagnation front where the gas velocityis zero. Delineating the recirculation zone is the sonic line[17], separating it from the surrounding atomizing gas. Theturbulent layer (or viscous layer) [17] lies in the recirculationzone near the sonic boundary. In the recirculation zone, therecirculation gas is observed to flow upstream from the stag-nation front toward the melt orifice, along the central axis.At the melt orifice, the recirculating gas turns laterally (ra-dially outward) toward the circumferential edge of the melt

Fig. 3. CFD model of the AS-HPGA nozzle at gas atomization pressure of 2.07MPa in the open-wake condition: (a) the global velocity output and themirroring schematics of the gas flow structures; (b and c) the velocity, and static pressure profiles, respectively, along the geometric centerline of theAS-HPGA nozzle.

tip. At the edge, it encounters the sonic boundary, forcingit to turn and flow downstream, contained within the sonicboundary. In this case, a turbulent layer is found separatingthe gas that flows upstream within the core of the recircu-lation zone, from the gas that flows downstream along theinner perimeter of the sonic line. This turbulent layer is anal-ogous to the recirculation eddies described by a proposedcontrol volume model [2] (this is discussed in Section 5.1).As the modeled pressure increases to 2.07MPa, the stag-

nation front extends downstream to about 1.8 NDL unitsfrom the melt orifice, lengthening the recirculation zone(Fig. 3a). With the gas flow expansion and acceleration


process, the recirculation zone forms a projected hourglasscontour, due to the influence of a recompression shock thatgains strength.At a pressure of 3.45MPa, the gas flow expansion down-

stream of the melt orifice begins to contract the elongatedrecirculation zone, exaggerating the hourglass contour(Fig. 4a). The stagnation front is at 2.75 NDL units, and therecirculation zone has a total length of 3.4 NDL units.A closed wake condition is observed at 4.82MPa (Fig. 5a).

At this pressure, a Mach disk forms and truncates the exag-

Fig. 4. CFD model of the AS-HPGA nozzle at gas atomization pressure of 3.45MPa in the open-wake condition, near to wake-closure pressure: (a) theglobal velocity output and the mirroring schematics of the gas flow structures; (b and c) the velocity, and static pressure profiles, respectively, along thegeometric centerline of the AS-HPGA nozzle.

gerated hourglass recirculation zone, giving rise to a short-ened primary recirculation zone. The internal shock is seento terminate at the edges of the “bowed” Mach disk; while, arecompression shock and a trailing shock are formed off theedge of the primary recirculation zone and off the edge ofthe Mach disk, respectively. The stagnation front associatedwith the primary recirculation zone is seen at only 1.0 NDLunit downstream, and the “bowed” Mach disk is located2.5 NDL units downstream. There are two other stagnationpoints observed immediately downstream of the Mach disk


Fig. 5. CFD model of the AS-HPGA nozzle at gas atomization pressure of 4.82MPa in the closed-wake condition: (a) the global velocity output andthe mirroring schematics of the gas flow structures; (b and c) the velocity, and static pressure profiles, respectively, along the geometric centerline of theAS-HPGA nozzle.

within the secondary recirculation zone (Fig. 5a). The firstof the two stagnation points, that is smaller, is close to theMach disk, only 2.75 NDL units downstream. The larger (instatic pressure) stagnation point is located 3.4 NDL unitsdownstream and is very visible in the CFD velocity flowfield (Fig. 5a).Since the CFD models of the AS-HPGA for a moderate

pressure range above 4.82MPa have gas flow features simi-lar to that at 4.82MPa, at wake-closure, only a CFD modelof 4.82MPa will be presented here.

4.2. Velocity profile along the axis of symmetry

The calculated centerline velocity at each modeled atom-ization gas pressure, starting from the melt orifice position,is plotted below the CFD figures to help quantify the gasvelocity magnitude, the flow direction, the length of the re-circulation zones, and the location of the stagnation frontsand stagnation points. A negative magnitude in the gas ve-locity in the figures indicates that the gas is flowing towardsthe melt orifice (i.e., upstream), while a positive velocity


magnitude indicates that the gas is flowing away from themelt orifice (i.e., downstream). Stagnation fronts (locationsof peaked stagnation pressure) are located where centerlinevelocities are equal to zero.The velocity profile at 0.69MPa is depicted in Fig. 2b.

A stagnation front that bounds the recirculation zone is lo-cated 0.6 NDL units from the orifice. Within the recircula-tion zone, all the centerline flow is upstream, except for theimmediate orifice area where it goes to zero. Downstreamof the stagnation front, the gas accelerates along the cen-terline to 400m/s at 1.8 NDL and, then oscillates, reachingvelocities as high as 390m/s. The velocity oscillation, how-ever, is less apparent for the downstream velocity profile at2.07MPa (Fig. 3b) because the (Prandtl–Meyer) wavelengthis too large for the computational field of view. The maxi-mum negative velocity within the recirculation zone reaches250m/s and the maximum positive velocity downstream ofthe recirculation zone is 400m/s at 4.5 NDL.At a pressure of 3.45MPa, the stagnation front is 2.75

NDL units downstream from the orifice. A negative velocityoscillation is noted within the recirculation zone (Fig. 4b),possibly associated with the exaggerated hourglass shape ofthe recirculation zone. Beyond the stagnation front, the ve-locity increases, reaching 425m/s at 4.8 NDL. At the pres-sure of 4.82MPa, the length of the primary recirculationzone is truncated to 1.0 NDL unit (Fig. 5b). The veloc-ity profile curve is seen to cross the zero velocity axis inthree instances, indicating the occurrence of three stagnationfronts within the wake region. The first stagnation front isjust downstream of the melt orifice in the primary recircu-lation zone, as mentioned above. The downstream gas ve-locity immediately after this reaches close to 400m/s over avery short distance before it abruptly drops to zero velocity(at 2.7 NDL). A precipitous drop in velocity from 400m/sto zero occurs across the “bowed” Mach disk (Fig. 5b). Asecondary recirculation zone is established, located between2.5 and 4.5 NDL downstream. Bounding the secondary re-circulation zone are the two other stagnation points, located2.8 and 3.4 NDL, respectively. Between these two stagnationpoints, the gas flow is reversed, flowing upstream. Beyondthe third stagnation point, located 3.4 NDL, the gas realignsits flow in the downstream direction and reaches a top ve-locity greater than 450m/s before exiting the computationalfield.

4.3. Pressure profile along the axis-symmetry

At an atomization pressure of 0.69MPa (Fig. 2c), thestatic pressure within the recirculation zone ranges between130 and 255 kPa, with the highest pressure being at the stag-nation front located at 0.6 NDL units. Beyond this recircu-lation zone, the static pressure oscillates above and belowthe atmospheric pressure, 101 kPa. The pressure oscillationis anti-phased to the velocity oscillation profile (Fig. 2b).The Prandtl–Meyer wave oscillations compress and expandthe gas, causing it to decelerate and accelerate, respectively.

At an atomization pressure of 2.07MPa (Fig. 3c), the initialpositive pressure peak is located at the stagnation front, i.e.,zero velocity point, at 1.8 NDL downstream. A second pos-itive static pressure peak is also found 1 NDL downstreamfrom the first. Beyond this point, the static pressure, again,oscillates above and below atmospheric pressure.When the modeled atomization pressure reaches 3.45MPa

(Fig. 4c), the recirculation zone is 2.7 NDL units long, buthas a minor static pressure peak before reaching the stag-nation pressure peak at the stagnation front. At this minorpeak the static pressure is 120 kPa, while the pressure at thestagnation front is 250 kPa. Downstream from the stagnationfront, the static pressure is again found to oscillate, similarto the 2.07MPa case.When the modeling pressure is 4.82MPa (Fig. 5c), two

recirculation zones are apparent. The stagnation pressure ofthe primary recirculation zone is 120 kPa. Within the gapbetween the zones, the static pressure gradually falls until the2.5 NDL point. Over a very short distance, the static pressureabruptly rises to 225 kPa, as the atomizing gas crosses the“bowed” Mach disk, reaching the first of two downstreamstagnation points at 2.8 NDL. Further downstream, the staticpressure continues to rise, reaching a second peak staticpressure of 310 kPa at 3.6 NDL downstream. After reachingthe second peak pressure, the static pressure drops below theatmospheric pressure. Due to the length of the computationaldomain, one cannot observe the subsequent oscillation ofthe pressure caused by the Prandtl–Meyer waves.

4.4. Computational aspiration profile

The calculated aspiration pressures are determined fromaveraging the static pressures located across the melt orificedivided by the concentric areas of the melt orifice at eachpressure location (Fig. 6). The aspiration pressure at 0.69is over-ambient, and at 2.07MPa the aspiration is approx-imately ambient. The calculated aspiration pressures above2.07MPa are all sub-ambient. The deepest subambient

Fig. 6. Computational and experimental aspiration pressure measured withrespect to manifold pressure of the ASJ-HPGA nozzle.

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aspiration pressure is achieved at 3.45MPa, followed by agradual rising trend.

4.5. Experimental aspiration profile

The aspiration curve of the annular-slit HPGA nozzleshows that the aspiration pressure is subambient for all theatomization pressure values. The aspiration pressure initiallydecreases as the manifold pressure increases (Fig. 6), un-til the wake-closure pressure of 5.5MPa is reached, and theaspiration pressure drops abruptly. Above 5.5MPa in theclosed-wake condition, the aspiration curve gradually in-creases as manifold pressure increases, as observed in theCFD modeled pressures.

5. Discussion

5.1. CFD images

Typically, the gas exiting a solid (full bore) cylindri-cal (or convergent) jet under high pressure (greater than0.15MPa) in a free expansion condition forms a normalshock (Mach disc) near its exit [16,17]. The shock assiststhe rapidly expanding gas in adjusting to the ambient sur-rounding pressure. The AS-HPGA model shows a similarbehavior, but because of the presence of the melt feed tube,a wake region is established in addition to the typical gasjet dynamics. At 0.69MPa, the gas expands downstreamfrom the nozzle, and the normal Mach disk, existing in thefree stream condition, becomes an attached oblique shockthat extends downstream from the feed tube tip (Fig. 2a).The location of the attached oblique shock can be relatedto the location at which “boundary layer” separation be-gins on the exterior surface of the melt feed tube. Thiswas investigated by Espina and Piomelli [10], who showedthat the boundary layer separation can be retarded at ahigher operating pressure, thus pushing the oblique shockfurther down the exterior surface of the feed tube. As seenin the cylindrical jet studies [16], the Prandtl–Meyer ex-pansion waves in the model are found downstream of theoblique shock. After the second series of Prandtl–Meyerwaves, the individual gas jets from the opposing sides ofthe annular slit-jet coalesce to form a unified gas flow fieldwith enlarged Prandtl–Meyer wave structures, resemblingthe “diamond” patterns often seen in Schlieren imagining[1,13,16,17].At a higher pressure (2.07MPa), the contour of the recir-

culation zone lengthens into an hourglass shape (Fig. 3a).Here, the atomizing gas expands into the recirculationzone, constricting it. As the modeling pressure increases to3.45MPa (Fig. 4a), the recompression shock composed ofPrandtl–Meyer compression shocks becomes fully devel-oped, emanating from the elongated “waist” of the recircu-lation zone. Due to expansion of the atomizing gas pushinglaterally into the recirculation zone, an exaggerated hour-

glass contour results. The flow patterns generated in theCFD models of these open wake cases are similar to thoseobserved in Schlieren imaging [5].As the modeling pressure increases to 4.82MPa (Fig. 5a),

a closed-wake condition is observed, revealing a Machdisk structure. However, unlike the flat Mach disk seenin Schlieren images [18], this computed Mach disk has a“bowed” geometry. Such a shape results from the fact thatthe gas velocity is unlikely to be uniform and normal acrossthe Mach disk surface when an uneven gas stream existsimmediately upstream from the Mach disk. The recircula-tion zone would contour the streamlines of the atomizinggas, such that the velocity vectors immediately in front ofthe Mach disk (on the upstream side) would have radialvelocity components to them. This would give rise to the“bowed” shaped Mach disk. A “bowed” shaped Mach diskhas been observed by Giel and Mueller [19] in a trun-cated plug nozzle that had a gas geometry similar to theASJ-HPGA nozzle investigated. In fact, the “bowed” shapeof the Mach disk implies that there is a velocity profile withmagnitudes that are greater along the centerline than at theedge of the Mach disk.Previously, the gas flow dynamics of the recirculation

zone of an HPGA nozzle, in gas-only operation, had beenrepresented in the form of a simple control volume [1]. Al-though the proposed two-dimensional triangular control vol-ume is an over-simplification of a real three-dimensionalrecirculation zone, the simple control volume model ade-quately serves to represent the general events in the recircu-lation zone; but, in light of the results from this CFD study,the model needs to be refined. According to the model [1],the gas enters the wake from the stagnation front and exitsthe wake along the circumferential edge of the melt tip base,and a series of turbulent eddies line the boundary of the re-circulation zone (see Fig. 7a). From the results of this CFDstudy, however, the recirculation eddies are located withinthe sonic boundary (Fig. 7b), and are represented as a tur-bulent layer. Giel and Mueller also observed this turbulentlayer within the sonic boundary [19]. The turbulent layeris essentially a series of adjoining recirculation eddies thatform the lateral perimeter of the recirculation zone withinthe sonic boundary. The turbulent layer delineates the up-stream flowing gas in the core of the recirculation zone fromthe downstream flowing gas that is found external to the re-circulation zone. The gas velocity magnitude in the turbu-lent layer is low because the turbulent layer sees reversal ingas flow direction across its profile (see Figs. 2–5, and rel-ative velocity magnitude in Fig. 8); however, the mass ex-changes across the layer could be significant. In most cases,though, the mass exchanges across the turbulent layer maybe equal, i.e., the gas mass entering and exiting across theturbulent layer are comparable. Compared to the gas massentering the stagnation front and its influence on aspirationpressure, the gas mass exchange across the turbulent layerboundary may not have a significant effect on aspirationpressure. The sonic boundary in this refined control volume


Fig. 7. (a) Control volume model reproduced from Ting et al. [2]; (b) refined control volume showing the recirculation zone within the sonic boundary(recirculation wake).

model (Fig. 7b) separates the supersonic gas flow externalto the boundary and the subsonic flow gas within it.In this study, the subsonic gas flowing along the circum-

ferential edge was abducted to flow downstream betweenthe turbulent layer and the sonic boundary (see Fig. 7b).Most of the gas does not cross the sonic boundary fromthe subsonic-side into the supersonic-side of the atomizingfree-stream. This is because it is difficult for the abductedsubsonic gas to accelerate itself to supersonic speed in or-der to enter the supersonic free-stream gas on the other sideof the sonic boundary. However, the atomizing supersonicfree-stream gas can more readily lose its kinetic energy, de-celerating to subsonic velocity, in order to cross the sonicboundary and to enter into the subsonic recirculation wake.Some of this decelerated, entrained gas from the supersonicfree-stream ends up at the stagnation front, feeding into therecirculation zone via the stagnation front. Subsequently,

Fig. 8. A schematic depiction of the gas velocity profile across the turbulent layer (M ∼ 0) and the sonic boundary (M = 1). V denotes velocity and Mdenotes Mach number of the gas velocity.

this gas addition is pushed upstream along the central axisof the wake until it eventually affects the aspiration pressureat the melt orifice. At the stagnation front, the remainingbalance of the entrained gas exits the wake, accelerating tosupersonic velocity to cross again the sonic boundary intothe free-stream.The gas–mass flux across the sonic boundary occurs in a

direction nearly parallel to this boundary, analogous to vehi-cles that smoothly exit and enter a high-speed highway. Thevelocity gradient across the sonic boundary resembles theshear layer profile of a supersonic flow across a parallel sta-tionary boundary (see Fig. 8), with the stationary boundarybeing the turbulent layer. Meanwhile the mass-flux acrossthe turbulent layer occurs essentially in a direction perpen-dicular to the turbulent layer (see Fig. 8). This is a resultof the numerous toroidal vortices (or, turbulent eddies) thatgive the gas its circular momentum as each vortex rotates.


Since the gas behaves as a vortex within the turbulent layer,the net mass-flux across the turbulent layer is negligible.

5.2. Stagnation pressures and aspiration pressures

Theoretically based turbulence models have been success-ful in predicting features in incompressible, free shear layers[14]. However, attempts to extend these models to super-sonic speeds and compressible shear layers have been lesseffective. Although the compressible dissipation model pro-posed by Sarkar et al. demonstrated relative agreement be-tween normalized turbulence intensities and shear stresseswith convective gas flows in a simple shear layer geometry,this is still only qualitative agreement and for a simple freeshear layer geometry [14]. An accurate turbulence model isdifficult to formulate, and the computations are made morecomplicated by the fact that a turbulence model is most accu-rately developed when using a highly refined computationalmesh. Therefore, a trade-off between accuracy and compu-tational time associated with a refined computational meshmust be reached.In the present study, a reduced stagnation pressure at the

stagnation front, specifically in the primary recirculationzone, reduces the aspiration pressure at the melt orifice. Forexample, at an atomization gas pressure of 4.82MPa the re-duced static pressure at the primary stagnation front (about1.0 NDL downstream in Fig. 5c) gives rise to the deep sub-ambient aspiration pressure shown in Fig. 6. On the otherhand, a higher primary stagnation front pressure (at about1.8 NDL in Fig. 3c) for 2.07MPa, gives a slightly sub-ambient aspiration in Fig. 6. The stagnation front pressureis 115 kPa after wake-closure (at 4.82MPa), while beforewake-closure, it is 195 kPa, at 2.07MPa. This stagnation andaspiration pressure relationship agrees with a previous inves-tigation; whereby it was found, in general, that a reductionin the static pressure (mass of gas) at the wake front corre-lated to a reduced aspiration pressure at the melt orifice [1].Contrary to expectations, the modeled aspiration pres-

sures, given in Fig. 6, show a rising trend from a manifoldpressure of 3.45 to 4.82MPa, even though the CFD imagein Fig. 4a shows no Mach disk formed at 3.45MPa, i.e., theCFD flow image shows an open-wake condition. Not untilthe manifold pressure is raised to 4.82MPa does the CFDmodel reveal a Mach disk, or closed-wake condition, as in-dicated in Fig. 5a. This ambiguity may be due to the inherentapproximations in the turbulent model used, resulting in aninaccuracy in modeled aspiration pressures in these highlyenergetic gas flow conditions.The highly elongated hourglass shaped recirculation zone

at 3.45MPa (see Fig. 4a) adds to the computational aspira-tion inaccuracy within the recirculation zone, particularly atthis manifold pressure. The narrow section of the recircu-lation zone inhibits the recirculating gas from reaching themelt orifice and influencing the aspiration pressure. This in-hibition can be seen in the static pressure rise within the re-circulation zone between 0.8 and 1.8 NDL downstream from

the orifice (Fig. 4c), and in the slowing of the gas velocitymagnitude within this same narrow section (Fig. 4b). Theconstriction, compounding the inaccuracy of the turbulentmodel, diminishes the influence of the stagnation front pres-sure on the aspiration pressure at the melt orifice. Becausethe mass of gas is constricted at the neck, less recirculatedgas is able to reach the melt orifice. This gives rise to an in-crease in static pressure in the recirculation zone (Fig. 4c).Thus, the aspiration at 3.45MPa is deeply subambient, arti-ficially resembling that of a closed-wake condition.As Fig. 6 illustrates, the total variation in computed

aspiration pressures is greater than those experimentallymeasured for the open-wake and closed-wake conditions,which also suggests the inaccuracy of the turbulence modelused in the CFD calculations. Espina and Piomelli [10]have also observed similar correlation deficiencies betweencalculated and experimental aspiration pressure values. Theatomization gas (manifold) pressure for CFD-computedwake-closure conditions appears to be lower (4.82MPa,or less) than the experimentally measured value of about5.5MPa. Although both computational models and ex-perimental measurements are based on the DJ-HPGA de-sign, the effective annular-slit gas exit areas are differentbetween the computed and experimental configurations.The computed AS-HPGA model has an effective jet areaof 25.7mm2 that is 300% larger than the experimentalAS-HPGA jet area: 8.52mm2. The larger annular slit areamay contribute, along with a sub-optimal turbulence model,to the production of a lower wake closure pressure in theCFD model. However, experimental verification is neededto confirm this possible explanation.

5.3. Closed wake and mach disk instability

In the closed-wake condition, at 4.82MPa, the maximumstagnation front static pressure downstream of the Machdisk (see Fig. 5c) is 28% greater (320 kPa versus 250 kPa)than the maximum stagnation front static pressure (seeFig. 4c) in the open-wake condition at 3.45MPa. Further-more, the maximum (third) stagnation point observed inthe closed-wake condition (at about 3.5 NDL downstreamin Fig. 5c) is considerably larger than the stagnation frontpressure in all the other open-wake conditions modeled.Interestingly, at 4.82MPa, the stagnation front pressure(120 kPa) in the primary recirculation zone (at about 1.0NDL in Fig. 5c) is approximately 40–50% lower than thestagnation front pressures at all the open-wake conditionsmodeled. Although this is not an average of the pressurein the recirculation zone, it however, as mentioned before,represents the gas mass entering the recirculation zone andinfluencing the aspiration pressure. In other words, in theclosed-wake condition (Fig. 5c), there are stagnation pres-sures upstream and downstream of the Mach disk that arelower and higher than all the computed stagnation pressuresin the open-wake conditions (Figs. 2c, 3c and 4c). Thisdichotomy in stagnation front pressures lends support for


the existence of a high instability in the Mach disk that wasproposed in the pulsatile atomization model [3,4,6].An intense recirculation zone is observed immediately

downstream of the Mach disk, as indicated in Fig. 5a. Itis formed as a result of having a strong gas velocity dis-parity (Fig. 5b) between the gas immediately upstream anddownstream of the “bowed” Mach disk. The retarded gasvelocity downstream of the Mach disk causes the formationof this secondary recirculation zone and the two stagnationpoints within this recirculation zone (Fig. 5). In addition,at the closed-wake condition the primary recirculation zoneis isolated from the secondary recirculation zone, and the“bowed” Mach disk blocks the flow of gas upstream fromthe secondary recirculation zone to the primary recirculationzone. One notices that the upstream flowing gas in the sec-ondary recirculation zone is turned downstream as it nearsthe Mach disk (Fig. 5). Therefore, one observes a deep sub-ambient aspiration pressure in the closed-wake due to the“gas-starved” stagnation front in the primary recirculationzone. According to a previous study, an aspiration discon-tinuity was observed across the wake-closure pressure [6].It was hypothesized that the state of entropy of the atom-izing gas increases with the formation of the Mach diskwhen the atomizing gas transitions from an open-wake toa closed-wake condition. However, the increased entropy isaccompanied by a decrease in total energy of the gas flowpattern which prevents reversion back to an open wake con-dition. Thus, it is reasonable to claim that the physical conti-nuity of the shock structures, between the internal shock andthe “bowed” Mach disk, is necessary for the stability of theclosed-wake condition. In other words, the Mach disk, in theclosed-wake condition, would be destroyed if the internalshock structures were displaced from their equilibrium po-sition by a strong disruptive force, i.e., when a high-densitymelt is introduced into the primary recirculation zone duringthe melt atomization process.

5.4. Atomization implications

As proposed in the pulsatile atomization model, the meltflowing from the delivery tube orifice acts as a movingboundary that could disrupt the stability of the closed-wakestructure by displacing the internal shock. In this instance,the Mach disk vanishes, the stagnation pressure from thesecondary recirculation zone rushes into the “opened” pri-mary recirculation zone, pushes upwards against the meltorifice, and temporarily halts the melt flow. This scenariois supported by the fact that the magnitude of the stag-nation front pressure in the secondary recirculation zoneof the closed-wake condition is considerably higher thanthe stagnation front pressure in the primary recirculationzone. This pressure gradient would drive the gas in the sec-ondary recirculation zone to flow towards the melt orificewhen the “bowed” Mach disk is disrupted by the melt flow.Subsequently, the melt flow is briefly halted by the strongupstream gas flow. Next, as described in the pulsatile at-

omization model [3,4,6], the disrupted melt flow enablesthe reestablishment of the Mach shock structures. The deepaspiration pressure of the reestablished closed-wake con-dition vigorously draws the melt down the ceramic pourtube, reinitiating melt flow once again. The whole intermit-tent melt atomization process would repeat itself, pulsating,until the melt is exhausted.

6. Conclusions

This study provided additional insight into the relation-ship between aspiration pressure at the melt orifice and stag-nation pressure in the primary recirculation zone under bothopen-wake and closed-wake conditions. This study also de-scribed the anatomical gas profile within the conical shearlayer arrangement in the sonic boundary and also explainedthe different methods of gas transport occurring across thesonic boundary and the turbulent layer. In the open-wakecondition, the calculated aspiration pressure reveals that thestagnation pressure is decreased as manifold pressure is in-creased to the onset point of stable atomization, i.e., whenaspiration pressure drops to one atmosphere. Over all threeopen wake calculations, the stagnation front position movesdownstream as the manifold pressure is increased.The deep subambient aspiration pressure at the wake-

closure condition is due to the existence of a relativelylow-pressure stagnation front in the primary recirculationzone. The study also reveals that there exists a secondaryrecirculation zone downstream of the Mach disk structure,in the closed-wake condition, bounded by two relativelyhigh-pressured stagnation points. These pressures are sig-nificantly greater than the static pressure in the primaryrecirculation zone of the closed-wake condition, and thestagnation pressures in all the open-wake conditions mod-eled. The high-pressured recirculating gas behind the Machdisk flows rapidly upstream towards the melt orifice if theMach disk is destabilized during melt atomization. Thiscalculated finding lends support to the governing effects ofthe proposed pulsatile atomization model [3,4,6].

Acknowledgements

The CFD work was funded by the Materials Science Divi-sion of DOE-BES at Ames Laboratory under contract num-ber W-7405-Eng-82. The authors would like to thank Jia Mifor developing and performing the CFD model calculationsand Murielle Ting for reviewing the manuscript.

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A Computational Fluid Dynamics (CFD) Investigation of the Wake Closure Phenomenon