A hyperbaric aerodynamic levitator for containerless materials research

Levitators are useful for studying solidification and vitrification phenomena of ubiquitous importance to materials that undergo solid-liquid phase transitions during their natural history or in industrial processing, and, consequently, levitators boast a strong legacy of materials discovery breakthroughs.^1–4 Researchers have used levitators to synthesize and study some of the earliest known examples of ultra-high purity semiconductors^5,6 and bulk metallic glasses.⁷ Levitators have enabled advances in fundamental science by providing direct evidence of liquid–liquid phase transitions^8–11 and by elucidating the high temperature structural chemistry of corrosive and hazardous materials.^12,13 Levitators serve as sample environments for synchrotron beamlines for the acquisition of atomic structure data while simultaneously probing structural chemistry via high energy x-ray scattering techniques.^3,14–20

Levitators can attain specimen temperatures of 2000 °C or greater using directed energy sources such as lasers, including continuous wave CO₂ lasers (CW CO₂), electron beams, electromagnetic inductive coupling, or combinations thereof. Ambient environments in standard levitators vary from high vacuum to near-atmospheric pressures depending on the requirements of the selected levitation and heating methods and instrument design limitations. For example, maintaining surface charge on electrostatically levitated specimens normally requires the use of vacuum environments, making the technique incompatible with use at elevated pressures. Other levitation techniques, such as electromagnetic levitation, acoustic levitation, and aerodynamic levitation, do not share this intrinsic incompatibility, though instrument designs supporting high pressure operation have not been widely available. However, a small number of special purpose levitators capable of hyperbaric operation (i.e., operating at greater than normal atmospheric pressure) have been reported, as summarized in Table I.

Hyperbaric levitators employing the acoustic principle of levitation are limited by the maximum operating transducer temperature, restricting their use to low-to-intermediate specimen temperatures (as in the cases of the chamber heating design²² and prototype laser-heated acoustic levitator²¹) or to short heating durations (as in the case of the pulsed laser-heated design^23,24). Pulse-heating techniques can attain extreme specimen temperatures, although short (ms) heating times limit the types of measurements that can be made. Hyperbaric levitators employing other techniques such as buoyant levitation or electromagnetic levitation are inherently limited by specimen properties, being restricted to specimens having low densities or high electrical conductivities, respectively. The principle of aerodynamic levitation is not inherently limited by specimen properties and is theoretically compatible with pressurized environments, although hyperbaric aerodynamic levitators capable of operation at pressures much above 1 MPa (10 bars) have not been demonstrated prior to this work.^4,17,25

Containerless experimentation at high gas pressures confers two primary benefits. First, pressurized systems are known to suppress volatilization. For example, when limited by mass transport through an external boundary layer, evaporation rates are proportional to $1/P$ up to a critical pressure on the order of 1–100 MPa.^30,31 With reduced volatile losses, specimen composition can be better preserved. Specimens may also be observed for longer durations, enabling measurements of the properties and/or structural chemistry of highly volatile materials. Second, reactive gas pressures possess increased chemical potentials $Δμi=RT⁡lnfi/fi◦$⁠, where i is a reactive species (e.g., oxygen or nitrogen) whose magnitude may attain ∼100 kJ/mol at elevated temperatures. This increase in chemical potential can dramatically affect phase equilibria, a fact that has been exploited to synthesize new compounds using elevated pressure crystal growth, surface heating, and/or melting.^32–42 

This work describes the design and performance characteristics of a prototype hyperbaric aerodynamic levitator for containerless materials research. The levitation behaviors of two series of spherical specimens of varying sizes and densities were studied as functions of pressure and flow rate. Additionally, the effect of pressure on heat transfer was assessed by comparing the heating and cooling behaviors of levitated liquid Al₂O₃ at pressures up to 10.3 MPa.

The hyperbaric aerodynamic levitator shown in Fig. 1 comprises four major components: a pressure vessel; a diamond window for CO₂ laser admittance; a converging-diverging conical nozzle; and pressurized fluid handling systems. System components and controls were carefully engineered for safe operation. The pressure vessel (Encole LLC, San Jose, CA, USA) consists of a machined billet of 7075-T6 aluminum featuring a vertical through-bore, multiple ports, and internal water-cooling passages. Finite element simulations were conducted to design the pressure vessel for a maximum internal pressure of 17.2 MPa (2500 psi) with a safety factor of four. A pressure-relief valve and burst disk were installed on the outlet and inlet sides of the pressure vessel, respectively. As an additional engineering control, operators were in a separate room from the hyperbaric levitator. The electronic backpressure regulator and mass flow controllers were operated via a computer interface with remote displays.

The converging-diverging levitation nozzle features conical semi-angles of 30°–60° intersecting at a cylindrical orifice whose diameter may vary from 0.5 to 2 mm.²⁰ The nozzle was vertically installed and sealed onto the pressure vessel with an SAE thread identical to that used for the sight glasses. The shallow conical nozzle design allowed for about half of the levitated specimen volume to be visible above the top of the nozzle as viewed from the horizontal sight glasses. During levitation experiments, the specimen was remotely viewed via a camera (acA150-uc, Basler) equipped with a 1.0X f/6-f/25 telecentric lens (Edmund Optics, Inc.) using a white LED backlight. The optical configuration provided a spatial resolution of 4.8 × 4.8 µm²/pixel, and videos were recorded with a frame rate of 150 fps. Levitation stability, as indicated by the vertical displacement of the top of the sphere, was measured using motion tracking software (ProAnalyst, Xcitex Inc.).

A pair of mass flow controllers (SLA5850 Series, Brooks Instrument) independently provided pressurized fluid to the levitation nozzle (maximum volumetric flow rate Q = 5.0 standard liters per minute or SLM) and as a purge flow across the diamond window to abate deposit formation (max. Q = 0.5 SLM). Pressure within the chamber was controlled using an electronic backpressure regulator (SLA5820 Series, Brooks Instrument) located downstream of the pressure vessel outlet. During a typical levitation experiment, the purge flow was maintained at a constant 0.5 SLM until the system attained the ambient pressure setpoint. Flow through the conical nozzle was then increased until the maximum flow rate was attained or instabilities in the specimen position presenting as a lateral movement were observed. Subsequently, levitation height was recorded at different flow rates stepping down in increments of 0.1 SLM until the sphere no longer displayed stable levitation. In this investigation, two series of levitation experiments were conducted: aluminum spheres of varying diameter (2.529, 3.048, 3.575, or 3.979 mm) and 3 mm diameter spheres made from materials of varying density [aluminum: 2.71 g/cm³, alumina (Al₂O₃): 3.95 g/cm³, yttria-stabilized zirconia (YSZ): 6.00 g/cm³, or type 302 stainless steel (SS302): 7.93 g/cm³].

A custom sight glass featuring a 1.3 mm thick × 10 mm clear aperture diamond window (Element Six Technologies, Santa Clara, CA, USA) encased in an SAE-12 fitting made from 17-4PH steel (Encole, LLC). All sight glass housings featured SAE threads coated with WS₂ in accordance with AMS2530 to prevent galling during frequent disassembly. The diamond window provides excellent transmission for the 10.6 µm wavelength CW CO₂ laser (400 W Synrad Firestar i401, Novanta Photonics) used as a heating source in these studies. Diamond is an ideal material for this purpose, given its excellent thermal conductivity and high strength as compared to traditional CO₂ laser window materials such as ZnSe. In this work, the diamond window was uncoated; consequently, approximately one-third of incident laser energy was lost due to Fresnel reflections (i.e., diamond has an index of refraction of 2.376 at 10.6 µm).

Figure 2 shows the effect of volumetric flow rate Q on the stable levitation height of the specimen Z normalized to its diameter d at selected absolute pressures of 3.45 MPa (corresponding to a nitrogen density of 55.5 kg/m³) and 10.3 MPa (corresponding to a nitrogen density of 166.6 kg/m³). From the available data, it is recognized that Z/d increases with Q (at a fixed pressure and specimen density) and decreases with specimen density (at a fixed pressure and flow rate). Deviations from these trends are discernible. For example, an increase in Z/d when Q approaches 3.0 SLM at 10.3 MPa is observed for the 2.529, 3.048, and 3.575 mm diameter aluminum spheres that is not seen for the larger diameter aluminum spheres. Similarly, an increase in Z/d when Q approaches 3.0 SLM at 10.3 MPa is observed for the 3.000 mm diameter aluminum sphere, but not for this same sphere at 3.45 MPa or for 3.000 mm diameter spheres made from denser materials at either pressure. These results suggest that a change in drag force occurs across this flow rate regime whose magnitude is sufficient to displace the stable levitation position of relatively lightweight specimens.

Evaluating expression (10) using observed relative levitation heights as functions of flow rate and fluid density (i.e., pressure) yields computed drag coefficient values as shown in Figs. 3 and 4.

Figures 3 and 4 illustrate the occurrence of two drag coefficient regimes: a primary trendline onto which most observations fall and a secondary trendline that reflects the change in relative levitation height for lightweight samples (i.e., small size and/or low density) at moderate flow rates and high pressures. Highlighted pressure series correspond to the minimum and maximum pressures employed in this work, a selected common trend for comparison, and, where applicable, the pressure at which deviation in the trends first appears, while additional measured data series are grayed out for the sake of clarity. For example, Fig. 3(a) shows a jump in computed C_d values near 3.0 SLM for pressures exceeding 8.96 MPa. Observations fall on secondary trendlines for similar flow rates starting at pressures of 5.52 and 4.14 MPa, as shown respectively in Figs. 3(b) and 3(c), with increasing specimen diameter. The transitional nature of these drag coefficient regimes is captured in the highlighted pressure series at 5.52 MPa in Figs. 3(b) and 3(c), where the calculated C_d deviates from the primary trendline up to the secondary trendline before returning to the primary trendline at higher flow rates.

As shown in Fig. 5, the secondary trendline for lightweight specimens features a statistically different exponential dependence on experimental parameters as compared to the primary trendline. The origin of this difference is not well understood but is speculated to relate to wake turbulence transitions like those reported for spheres in comparable Reynolds and Froude number regimes.⁴⁶ 

The effect of fluid density was also evaluated by comparing hyperbaric aerodynamic levitation behavior in nitrogen vs argon as a function of pressure. Figure 6 illustrates the levitation of 3.000 mm Al₂O₃ spheres at 3.45 MPa (Ar: 55.5 kg/m³, N₂: 39.8 kg/m³) and 10.3 MPa (Ar: 166.6 kg/m³, N₂: 118.7 kg/m³). At each pressure, the heavier fluid imparts more momentum to the sphere, resulting in a higher relative levitation height. As pressure increases and, consequently, flow velocity decreases at any given flow rate, relative levitation heights decrease for both fluids.

A levitated 3.000 mm Al₂O₃ sphere was melted with a 400 W CO₂ laser at atmospheric pressure, 2.07, 4.14, 6.21, 8.27, and 10.3 MPa nitrogen to assess the effect of pressure on heat transfer characteristics. Levitation trials were conducted with a constant volumetric flow rate of 1.5 SLM at ambient pressures up to 4.14 MPa and a constant volumetric flow rate of 3.5 SLM for ambient pressures from 6.21 to 10.3 MPa, with flow rates selected to maximize specimen stability during heating.

Figure 7 shows the molten Al₂O₃ sphere levitated at atmospheric pressure and 10.3 MPa. At elevated pressures, the increased fluid density apparently leads to a concomitant change in the fluid refractive index, thereby allowing the turbulent flow structure to be visualized. Figure 8 shows cooling curves for the 3.000 mm Al₂O₃ sphere as measured by optical pyrometry (IR-CAS, Chino Corp.). Reported apparent temperatures are uncorrected for effects of view factor, specimen emissivity, or window absorption.

The convective-radiative heat balance can be used to estimate the maximum attainable specimen temperatures as a function of absorbed laser energy and specimen surface area. Figure 9 shows calculated equilibrium temperatures using estimated heat transfer coefficients for atmospheric pressure aerodynamic levitation (dashed) and hyperbaric aerodynamic levitation (solid). Assuming a constant 150 W output laser power and a total hemispherical emissivity of 0.9, specimen temperatures above 2100 °C should be attainable for 3.0 mm specimens with absorptivity values greater than 0.6 at 10.6 µm. To attain higher specimen temperatures, additional laser energy must be delivered to the sample, which can likely be achieved via a combination of optimization of beam delivery optics, the use of anti-reflective coatings on the diamond window used for laser admittance, or increasing output laser power.

Concordant with increased convective heat losses, the additional laser power was required to melt the specimen. Figure 10 compares the laser power necessary to overcome convective heat losses for atmospheric pressure aerodynamic levitation vs hyperbaric aerodynamic levitation at 10.3 MPa by plotting measured apparent temperatures sampled every 62 ms as laser power was continuously increased until melting was attained. An increase of ∼15% of the maximum laser power, corresponding to an additional 60 W, was required to attain molten Al₂O₃ at 10.3 MPa. This represents a modest increase relative to the total laser power available, indicating that materials with even greater melting points than Al₂O₃ can be levitation melted in hyperbaric conditions (note: as temperatures increase further above 2000 °C, radiative heat losses are expected to dominate over convective heat losses, such that increased convective heat losses at elevated pressures may become negligible).

A hyperbaric aerodynamic levitator for containerless materials research has been designed and tested. The instrument operates at ambient pressures up to 10.3 MPa and can attain specimen temperatures greater than 2100 °C, depending on material characteristics. Preliminary evaluations of hyperbaric aerodynamic levitation phenomena indicate stable levitation can be attained across a wide range of flow rates and pressures. For the nozzle configuration tested, two stable levitation regimes were observed for lightweight specimens that are speculated to be associated with a change in turbulent wake structure. Additional simulation and experimentation are recommended to better understand the effects of flow turbulence on levitation stability.

Output laser power necessary to melt specimens at elevated pressures increased due to enhanced convective heat transfer with increasing fluid density; however, the magnitude was modest—∼60 W additional output laser power in going from atmospheric pressure to 10.3 MPa flowing nitrogen necessary to melt a 3.000 mm Al₂O₃ sphere. The results demonstrate that hyperbaric aerodynamic levitation is a promising technique for containerless materials research at high gas pressures.

The continued development of hyperbaric aerodynamic levitation is anticipated to enable previously unfeasible experiments. Future levitator designs compatible with high energy x-ray synchrotron beamlines will support in situ measurements of the structural chemistry of materials that would otherwise vaporize too quickly at high temperatures under atmospheric pressure. By suppressing volatilization rates, hyperbaric levitation may better preserve the complex chemistry of technologically important multicomponent systems, such as high entropy materials. Levitation under high reactive gas pressures also creates the possibility of extended redox regimes that may find applications in network glasses and functional ceramics whose properties are sensitive to oxidation states and point defect populations.

The authors gratefully acknowledge the partial financial support for author Sydney E. Boland from the Office of Naval Research (ONR) Naval Engineering Education Consortium (NEEC) Grant No. N00174-21-1-0008. Funding assistance from the College of Engineering and Computing and the Materials Research Center at Missouri University of Science and Technology is gratefully acknowledged. The authors acknowledge the contributions of undergraduate students Brennan Long (Missouri S&T) and Gerald Amory (Morgan State University) for their assistance in early instrument development. We also extend sincere acknowledgment to Professor Mario Affatigato (Coe College) for assistance with prototype testing and stimulating discussions.

S.W. and R.W. disclose financial interests in Materials Development, Inc., a company involved in developing and selling levitation instruments.

Sydney E. Boland: Formal analysis (lead); Investigation (lead); Methodology (equal); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (equal). Stephen K. Wilke: Investigation (supporting); Methodology (equal); Visualization (supporting); Writing – review & editing (equal). Jonathan A. Scott: Methodology (equal). Sarah M. Schlossberg: Investigation (supporting); Visualization (supporting). Alex Ivaschenko: Resources (equal); Writing – review & editing (equal). Richard J. K. Weber: Funding acquisition (supporting); Investigation (supporting); Methodology (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal). David W. Lipke: Conceptualization (lead); Funding acquisition (lead); Methodology (equal); Project administration (lead); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

A

momentum flux constant

C_d

drag coefficient

c_p

heat capacity

D

diameter of nozzle

d

diameter of sphere

Fr

Froude number

g

standard acceleration due to gravity

h

convective heat transfer coefficient

Q

volumetric flow rate

v

velocity

Z/d

relative levitation height

β

cone angle of the nozzle

ε

emissivity

ρ

density of fluid

ρ_s

density of sphere

σ

Stefan–Boltzmann constant