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DOE OSTI2020

Probing the Effects of NO x and SO x Impurities on Oxy-Fuel Combustion in Supercritical CO 2 : Shock Tube Experiments and Chemical Kinetic Modeling

The direct-fired supercritical carbon dioxide cycles are one of the most promising power generation methods in terms of their efficiency and environmental friendliness. Two important challenges in implementing these cycles are the high pressure (300 bar) and high CO 2 dilution (>80%) in the combustor. The design and development of supercritical oxy-combustors for natural gas require accurate reaction kinetic models to predict the combustion outcomes. The presence of a small amount of impurities in natural gas and other feed streams to oxy-combustors makes these predictions even more complex. During oxy-combustion, trace amounts of nitrogen present in the oxidizer is converted to NO x and gets into the combustion chamber along with the recirculated CO 2 . Similarly, natural gas can contain a trace amount of ammonia and sulfurous impurities that get converted to NO x and SO x and get back into the combustion chamber with recirculated CO 2 . In this work, a reaction model is developed for predicting the effect of impurities such as NO x and SO x on supercritical methane combustion. The base mechanism used in this work is GRI Mech 3.0. H 2 S combustion chemistry is obtained from Bongartz et al. while NOx chemistry is from Konnov. The reaction model is then optimized for a pressure range of 30–300 bar using high-pressure shock tube data from the literature. It is then validated with data obtained from the literature for methane combustion, H 2 S oxidation, and NO x effects on ignition delay. The effect of impurities on CH 4 combustion up to 16 atm is validated using NO x -doped methane studies obtained from the literature. In order to validate the model for high-pressure conditions, experiments are conducted at the UCF shock tube facility using natural gas identical mixtures with N 2 O as an impurity at ~100 bar. Current results show that there is a significant change in ignition delay with the presence of impurities. A comparison is made with experimental data using the developed model and predictions are found to be in good agreement. The model developed was used to study the effect of impurities on CO formation from sCO 2 combustors. It was found that NO x helps in reducing CO formation while the presence of H 2 S results in the formation of more CO. The reaction mechanism developed herein can also be used as a base mechanism to develop reduced mechanisms for use in CFD simulations.

Energy & Fuels↗

DOE OSTI2023

Numerical Study of Solar Receiver Tube With Modified Surface Roughness for Enhanced and Selective Absorptivity in Concentrated Solar Power Tower

Abstract Concentrated solar power (CSP) is a reliable renewable energy source that is progressively lowering its cost of energy. However, the heat loss due to reflected and emitted radiation hinders the maximum achievable thermal efficiency for solar receiver tubes on the solar tower. Current solar selective coatings cannot withstand the high temperatures that come with state-of-the-art CSP towers often needing to be recoated soon after initial operation. We intend to use Inconel 718 with different additive manufacturing (AM) practices to construct surfaces that allow for more light-trapping to occur. By adjusting printing parameters, we can tailor a surface to allow for more absorption while diminishing emitted radiation heat loss. By using COMSOL Multiphysics, we can generate these theoretical surfaces to emulate a printed surface, and using the coupled Multiphysics we can simulate how the surface dictates radiation properties. Our results show that by having a rougher surface we can enhance the absorptivity of Inconel 718 (IN718) by 38.8%. We expect this work to transform how solar absorber tubes are manufactured without using selective coatings and supplement the US Department of Energy (DOE) 2030 SunShot Initiative.

14 SOLAR ENERGY↗

DOE OSTI2025

Nonseeded linewise temperature measurements by resonantly ionized photoemission thermometry in a Mach 4 Ludwieg tube

A one-dimensional (1D) thermometry using oxygen-tagging resonantly ionized photoelectron thermometry (O 2 RIPT) was employed to investigate thermal gradients within a Mach 4 Ludwieg tube. The Ludwieg tube is pulsed with a test duration of approximately 100 ms, providing a cold supersonic flow at Mach 4 ideal for studying aerothermal effects. This study focused on measuring freestream temperatures, capturing shock-induced heating behind a detached bow shock from a blunt cylinder, and resolving sharp temperature variations across a bow shock generated by a cylinder. The O 2 RIPT technique produced strong emission signals extending approximately 4 cm long, demonstrating its capability for precise temperature measurements in high-speed wind tunnel environments. The results confirm that O 2 RIPT is well-suited for applications in large-scale aerodynamic testing facilities, particularly in regions with strong compression effects, enabling the resolution of sharp thermal gradients. This method presents a promising solution for thermometry in dynamic flow conditions relevant to various experimental ground-test facilities.

McCord, Walker (ORCID:0000000179747550)↗

DOE OSTI2025

Upgrade to Fixed and Translating Scintillation-based Loss Detector System in the Fermilab Drift Tube Linac

The closed-off structure of the Fermilab Drift Tube Linac precludes a robust array of instrumentation from directly monitoring the H- beam that is accelerated from 750 keV to 116 MeV. To improve beam tuning and operational assessment of Drift Tube Linac performance, scintillator-based loss monitors were previously installed along the exterior of the first two accelerating cavities to assess low energy beam losses. Here we present a recent upgrade to the loss monitor system, including significant improvements in analog signal processing to address baseline-interfering noise; digitization of the signals to enable regular operational use and tuning; and a new remote operation upgrade of the translating loss monitor with precise positioning of the loss monitor along its nine-foot track. Data from the fixed and translating detectors collected under varying beam conditions validate the utility of the upgrade.

Chen, E. V. [Fermilab]↗

DOE OSTI2020

A Novel Low-Cost Method of Manufacturing Nb3Sn Superconductors with Multiple-Tin-Tube Sources (CRADA FRA-2008-0001 Final Report)

In order to successfully sustain a fusion reaction, peak magnetic fields on the order of 12-13 Tesla will be required. Magnetic fields of this magnitude can only be accomplished by advanced superconductors such as Nb3Sn. However, the economic success of a fusion machine will depend on further improvements in the cost-performance of the Nb3Sn conductor. This project will develop a novel, low-cost, multiple-tin-tube process as a new manufacturing approach for large-scale Nb3Sn-conductor production. The process will be suitable for the efficient production of larger strands (0.83 mm), consistent with ITER (International Thermonuclear Experimental Reactor) specifications. In Phase I, Cu/Nb composites were manufactured and shaped into sub-elements. These sub-elements were tin-coated by electroplating, assembled into a precise-fit restack billet tube, and drawn to 0.83 mm diameter. In Phase II, the process will be scaled-up to full production levels. The improved Nb3Sn conductor should have an immediate benefit for high-field magnet applications. A prototype fusion machine, based on a cost effective Nb3Sn conductor, would have enormous economic and social benefits. In addition, the conductor should be applicable to nuclear magnetic resonance (NMR), which has requirements for use in chemical research, biochemistry, pharmaceutical chemistry, polymer science, petroleum research, agricultural chemistry, and medicine. Leszek Motowidlo, Principal Investigator, will be responsible for the overall coordination of the effort. He and others of SupraMagnetics staff will design and fabricate protoype PIT Nb3Sn conductors for evaluation at Fermilab. Emanuela Barzi will be responsible for the Fermilab subcontract and will coordinate and supervise critical current testing Nb3Sn strands and cable fabrication and evaluation.

43 PARTICLE ACCELERATORS↗

DOE OSTI2021

HFIR SiC-SiC Composite Clad Tube Bowing Test: Pre-Irradiation Characterization

This report describes the pre-irradiation characterization of the SiC-SiC composite clad tube bowing experiment that will be irradiated in the High Flux Isotope Reactor (HFIR). There are concerns that SiCSiC fuel cladding in light water reactors could undergo bowing because of the non-uniform fast neutron flux profiles. This experiment is combined with the SiC-SiC channel box experiment, which has similar concerns regarding control blade movements in boiling water reactors. The HFIR experiment aims to validate the predicted deformation and stresses in the composite clad specimen after the exposure of fast neutron flux gradients. Significant radial fast neutron flux gradients that exist in the permanent reflector of HFIR were thoroughly characterized by using detailed 3D neutronic calculations. The 3D displacement damage dose rate profile and the resulting volumetric swelling in SiC were used as inputs to structural analyses to determine the predicted deformation that will affect the specimens. The tube specimens were characterized by using traditional dimensional inspection and surface profilometry to provide detailed information regarding the pre-irradiation condition as the first step to evaluate the radiation-induced deformation. Furthermore, fine engraving markers were inscribed along all outer surfaces of the specimen and mapped by using a digital microscope and a multidimensional stage. This allows marker spacings to be accurately measured and compared with similar measurements that will be made post-irradiation to provide local radiation-induced strain mapping. The experiment successfully completed two HFIR cycle irradiations, cycles 492 and 493, which finished on July 25, 2021.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2023

High-Temperature Creep Behavior of Thin-Walled FeCrAl Alloy Tubes

This report summarizes measured creep properties for FeCrAl alloy C26M measured using subsized specimens machined from prototypic thin-walled tubes. A representative tube fabricated in a previous large batch production effort was machined into dual-gauge axial specimens using electrical-discharge machining. Creep tests, comprising strain-rate jump tests (SRJ), jump stress (JS) and constant-stress (CS) tests, were conducted at temperatures ranging from 600-900ºC to determine creep mechanisms (elucidated from stress exponents) and activation energies to compare with prior data available in the literature at temperatures up to 650ºC. It was found that the results from the SRJ tests indicated that the highest stress exponent of 5.8 occurred at 600ºC, which decreased to the lowest stress exponent of 2.5 at 700ºC. At higher temperatures, the stress exponents increased slightly to a range of 2.9 to 4.3 between 750ºC and 900ºC. The high stress exponent value of 5.8 suggested dislocation glide creep mechanisms dominated creep deformation at 600ºC since high stress values were measured. The low stress exponent of 2.5 at 700ºC suggested diffusional creep mechanisms start to occur that aid in dislocation cross-slip and climb mechanisms. The slightly higher stress exponents of 2.9 to 3.9 may suggest different contributions of creep deformation mechanisms based on diffusional processes associated with Nabarro-Herring and Coble creep and dislocation creep that involve thermally activated cross-slip and climb mechanisms. These deformation mechanisms could have also been affected by the development of recovery and/or recrystallization processes in the microstructure of the C26M2 specimens. From the SJ and single CS tests, two sets of creep activation energies were calculated. The steady state creep values obtained from the SJ tests showed several abnormalities especially with the data at 850ºC. The comparison of the creep activation energies between the data from the SJ and CS tests showed higher creep rates for the SJ tests than the CS tests, indicating microstructure softening occurred in the C26M2 specimens during the SJ tests that led to the higher creep rates at stresses above the initial stress of 10 MPa. For the CS tests, the results showed steady increases in MCR with increasing temperature at each stress. The best linear fit to the MCR values at each stress was with data obtained at 800ºC, 850ºC and 900ºC. The lowest Q c value of 130.8 KJ/mole was observed with the highest stress of 25 MPa. As stress was lowered, the Q c values increased continuously to the highest value of 188.2 KJ/mole at 10 MPa. This trend suggests that the dominant creep mechanism is diffusional based dislocation climb since the decreasing activation energies with increasing stress promotes easier dislocation climb around obstacles. The comparison between the SJ and CS tests indicates that the best type of creep test performed on FeCrAl alloys such as C26M2 is the single CS test.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Hot rolling of ZK60 magnesium sheet with isotropic tensile properties from tubing made by Shear Assisted Processing and Extrusion (ShAPE)

In order to evaluate the viability of ShAPE processed Mg alloys as a feedstock for fabricating lightweight sheet material, tubes consisting of ShAPE-extruded Mg alloy ZK60 were flattened into plates and hot rolled at 450 °C to reductions of 37%, 68%, and 93%. The mechanical properties and microstructure of the rolled material were characterized through tensile testing and electron backscattered diffraction (EBSD). ZK60 specimens rolled to 68% reduction had tensile properties similar to published properties of rolled ZK60 sheets fabricated using conventional processes, and exhibited negligible tensile anisotropy referenced to the rolling direction. Additional rolling from 68% to 93% reduced the ultimate tensile stress in the rolling direction from 341.74±5.96 MPa to 260.76±22.4MPa. The yield stress and elongation to failure of the material also decreased from 292.16±1.11 MPa to 256.93±18.4 MPa and 6.95±1.94% to 3.38±0.51%, respectively, but negligible little anisotropy was observed with respect to loading direction. EBSD mapping indicated that the as-extruded ZK60 had texture rotated away from the basal direction which developed into a strong basal texture over numerous hot rolling steps. This evolution in texture has been observed after rolling for hot-rolled ZK60 fabricated through conventional extrusion processes. The initial grain structure was found to have experienced noticeable twinning from flattening the tube into plate. After hot rolling, the grain structure became more equiaxed, but the average grain diameter did not change appreciably from 5.15 ± 3.39 µm in the ShAPE extruded material, to 5.27 ± 12.44 µm in the 93% hot rolled sheet. This response to hot rolling is similar to the response of ZK60 fabricated using other methods such as Equal Channel Angular Processing (ECAP). Therefore, this work demonstrates ShAPE has the potential as an alternative method to producing feedstock for Mg alloy sheets. Modifications to the experimental procedure which could lead to improvements in observed properties are briefly discussed.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Optimizing the Heisenberg Vortex Tube for Hydrogen Cooling (Final Technical Report)

Hydrogen utilization at Plug Power sites ranges between 70-93% with the remainder vented and lost to the atmosphere. The goal of this project was to improve hydrogen utilization at Plug Power fulfillment centers via the patented Heisenberg vortex tube (HVT). The HVT combines conventional counterflow vortex tubes with para-orthohydrogen conversion catalyst to allow the cooling of hydrogen flows with no moving parts or external energy inputs. In year 1 of this project the HVT was evaluated to improve hydrogen utilization via the following concepts: 1) increasing liquid hydrogen pump volumetric efficiency by 20% through vapor separation and subcooling of the liquid, 2) reducing liquid hydrogen storage tank boil-off losses by 20% through thermal vapor shielding (TVS), and 3) increase isentropic efficiency of supercritical hydrogen expansion at 40-50 K, from 31% to over 40%. The TVS concept was selected as the most favorable application for further development. While the conceptual analysis was underway, the cryocatalysis hydrogen experiment facility (CHEF) was retrofitted with a new cryocooler, higher pressure condenser tanks, and in-situ fiber-optic Raman probes for ortho-parahydrogen composition analysis at the inlets and outlets of the HVT. To our knowledge this is the first in-situ implementation of cryogenic Raman probes for ortho-parahydrogen analysis. Subsequent testing of catalyzed and non-catalyzed HVT identified a low flow rate, high-conversion efficacy regime well suited for TVS development. Computational fluid dynamics (CFD), Reduced order modeling (ROM), and quantum Monte Carlo atomistic simulations were applied to optimize the design of the HVT implemented for TVS. The simulations and analysis identified a ruthenium-based catalyst as the most optimal for high conversion with little pressure losses and was matched to experimental measurements. These results indicated the design could achieve the 20% boil-off reduction target. An HVT field-trial was designed and constructed by Plug Power and implemented at a customer site. However, budget limitations reduced the amount of catalyst that could be applied to the HVT. With the reduced amount of catalyst, CFD analysis estimated about 3% reduction in boil-off. A similar amount of boil-off reduction was observed during preliminary measurements during tank commissioning. However, the results have a large margin for error and were operated at relatively low tank temperatures when the HVT has the lowest potential for improvement. This project demonstrated the use of para-orthohydrogen catalysis for reducing liquid hydrogen tank boil-off losses. The field trial system is anticipated to provide long-term experimental measurements on tank operational performance that will allow Plug Power to instrument additional tanks in the future. Recommendations for future work include the development of higher activity, lower cost para-orthohydrogen conversion catalyst for use in the HVT. Tank process optimizations could maximize the efficacy of the HVT and further improve hydrogen utilization.

08 HYDROGEN↗

DOE OSTI2024

3D Printing of Inconel 718 with Enhanced Boron Composition as a Novel Solar Absorber Tube Material in the Concentrated Solar Power (CSP) System

The growing demands for elevated efficiency in the solar energy industry led researchers to focus on the development of functional solar absorber tube material in concentrated solar power (CSP) systems, when molten salts are adopted as the heat transfer fluid. In this study, the typical solar absorber tube material, Inconel 718, was enhanced with boron to achieve a higher solar absorptivity in the visible light spectrum. Combined with an additive manufacturing (AM) method, the boron composition exceeded the traditional manufacturing limit of 60 ppm without microstructural defects. The boron-enhanced Inconel 718 exhibited a high solar absorptivity of nearly 90 % while maintaining a high thermal cycle fatigue resistance after thermal cycling treatment between 550°C and 720°C. The boron composition was increased to the manufacturing failure point, and the effects of different boron compositions on mechanical properties, microstructure, and optical properties were studied. The provided microstructure-property map in this study delivers high potentials of functional AM-printed alloy material in CSP applications.

13 HYDRO ENERGY↗

DOE OSTI2025

Euler equations and the Sod shock tube problem

The Euler equations are a subset of the magnetohydrodynamic (MHD) equations in the infinitely collisional, unmagnetized limit. MHD modeling is central to many areas of plasma physics, ranging from low-temperature glow discharges to inertial confinement fusion. An important aspect of the Euler equations is their ability to describe states with discontinuities, such as shock waves. A standard benchmark test for numerical implementation of the Euler equations is the Sod shock tube. In this test, the system is initialized at rest with a pressure and density discontinuity, which results in a shock wave traveling into the low-pressure region and a rarefaction wave traveling into the high-pressure region. Starting with the presentation of the Euler equations, a numerical algorithm is presented here to solve these equations in one dimension. This is followed by an overview of the Sod shock tube problem that includes the precise initial setup and the analytic solution. Finally, the analytic solution is compared with results from numerical simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Upgrade to Fixed and Translating Scintillation-Based Loss Detector System in the Fermilab Drift Tube Linac

The closed-off structure of the Fermilab Drift Tube Linac precludes a robust array of instrumentation from directly monitoring the H- beam that is accelerated from 750 keV to 116 MeV. To improve beam tuning and op-erational assessment of Drift Tube Linac performance, scintillator-based loss monitors were previously installed along the exterior of the first two accelerating cavities to assess low energy beam losses. Here we present a recent upgrade to the loss monitor system, including significant improvements in analog signal processing to address baseline-interfering noise; digitization of the signals to enable regular operational use and tuning; and a new remote operation upgrade of the translating loss monitor with precise positioning of the loss monitor along its nine-foot track. Data from the fixed and translating de-tectors collected under varying beam conditions validate the utility of the upgrade.

Chen, Erin V. [Fermilab] (ORCID:0000000215467899)↗

DOE OSTI2026

Magnetic Mapping of MAGIS-100 Tubes to Guide Experimental Redesign

The MAGIS-100 atom interferometer requires an exceptionally uniform, low-magnetic-field environment along its 100-meter baseline. While characterization of the raw structural tubes established a clean baseline, the original surrounding experimental design proved overly complex, ultimately introducing complications that degraded data precision. To resolve these systemic issues, a comprehensive redesign of the surrounding apparatus is underway. This poster details our magnetometry data collection efforts on the baseline tubes and highlights how these measurements are being used to guide a streamlined external design. By leveraging this background data, the new configuration aims to eliminate the complexities of the initial setup and ensure the environmental stability required for high-precision quantum sensing.

Savoia Cooley, Patricia [North Central Coll.]↗

DOE OSTI2026

Short Circuit Detection and Voltage Sense for High Voltage Ionization Tube Power Supplies

Fermilab's PIP-II upgrade requires new rack-mounted power supplies for Beam Loss Monitor (BLM) ionization tubes compatible with the microTCA 4.1 standard, supporting high-side current measurement for short circuit detection, voltage sense telemetry, and low-side current measurement for beam loss readout. This work presents the design and preliminary schematic of such a supply. A resistive current sensing approach was chosen over inductive, optical, and Hall-effect alternatives for its independence from cable length and component availability. A 500 mΩ inline shunt steps the 2 kV common mode voltage down to roughly 70 V, producing a ~27 μV pulse during a short, which is amplified 500x, compared against a 14-bit DAC threshold, and latched to drive a fault line. Voltage sense steps the 2 kV output down at a 1V/1000V ratio, buffers it with a low bias current amplifier, and digitizes it via a 24-bit ADC over SPI. Onboard power is regulated from 12 V down to isolated 5 V and 3.3 V rails, with capacitive isolation on FPGA communication lines. Lumped parameter models were developed for the ionization tube (0.327 nF, 20 to 200 GΩ dynamic resistance) and the RG-58 coaxial cable to support the design. Component selection is complete and a preliminary schematic has been drawn in Altium Designer, forming the foundation for future prototyping and validation.

Yu, Kellen [Cornell U.]↗

DOE OSTI2023

Cross-flow separation characteristics and piloting of graphene oxide nanofiltration membrane sheets and tubes for kraft black liquor concentration

Dewatering of weak black liquor (WBL) in the kraft cycle by evaporation is highly energy intensive. Membranes are an attractive alternative for energy-efficient dewatering, but existing commercial polymeric or ceramic membranes are either degraded in BL or have high capital costs. Our recent works have demonstrated the engineering of graphene oxide (GO) nanofiltration membranes, their stability and promising performance in BL conditions, and preliminary scale-up into sheets and tubes. Here, we describe in detail the separation characteristics of GO membrane sheets and tubes under real BL conditions and crossflow operation. Recycle-mode piloting of a GO tubular membrane showed average “production flux” of 16 L/m2/h (LMH) and high rejections of lignin (98.3%), total solids (66%), and total organic carbon (83%), with no signs of irreversible fouling identified. A corresponding GO sheet membrane produced an average flux of ~25 LMH and maintained high lignin rejection of ~97% during a slipstream pilot at a kraft mill site using WBL with ~16 wt% total solids (TS). Finally, we piloted a Dow/DuPont XUS1808 polyamide composite reverse osmosis (RO) membrane for last-mile processing of the GO nanofiltration membrane permeate. The RO membrane showed a steady state flux of 19 LMH at 65 bar and produced ~0.02 wt% TS water product, which is highly suitable for reuse in pulp washing operations in the kraft process. The results have strong positive implications for the industrial application of GO membranes in BL concentration and other related applications.

Materials Science↗

DOE OSTI2023

Hot Rolling of ZK60 Magnesium Alloy with Isotropic Tensile Properties from Tubing Made by Shear Assisted Processing and Extrusion (ShAPE)

In the present work, we utilized Shear Assisted Processing and Extrusion (ShAPE), a solid-phase processing technique, to extrude hollow tubes of ZK60 Mg alloy. Hot rolling was performed on these as-extruded tubes (after slitting them longitudinally) to thickness reductions of 37%, 68%, and 93% to investigate their viability as rolling feedstock material. EBSD analysis showed the formation of twinned grains in the ShAPE processed material and a gradual re-orientation of the basal texture parallel to the extrusion direction with each rolling step. Moreover, an equiaxed grain size of 5.15 ± 3.39 μm was obtained in the ShAPE extruded material, and the microstructure was retained even after 93% rolling reduction. The rolled sheets also showed excellent tensile strengths and no mechanical anisotropy, a critical characteristic for formability. The unique microstructures developed and their excellent mechanical properties, combined with the ease of scalability of the process, make ShAPE a promising alternative to existing methods for producing rolling feedstock material.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Nanostructured Tube Wakefield Accelerator

Unprecedented $\rm TeVm^{-1}$ acceleration gradients are modeled to be realizable using a nonlinear surface crunch-in mode in nanostructured tubes. This mode is realizable using advances in nanofabrication and solid energy density attosecond bunch compression. Three dimensional computational and analytical modeling demonstrates GeV energy gain in sub-millimeter long tubes with effective wall densities $n_{\rm t}\sim10^{22-24}\rm cm^{-3}$ and hundreds of nanometer core radius when driven by submicron near solid electron beams, $n_{\rm b}\sim0.05n_{\rm t}$. Besides the many $\rm TVm^{-1}$ average gradients, strong self-focusing and nanomodulation of the beam which increases its peak density and the wakefield strength also opens up controlled high-energy photon production.

43 PARTICLE ACCELERATORS↗

DOE OSTI2020

Spouted bed with venturi draft tube and method for improved gas-solid contacting

A Venturi draft tube spouted bed and method are disclosed that enables scale-up with small particles and improves heat and mass transfer by increasing material turnover rate. A Venturi-style eductor has been incorporated into the spouted bed draft tube to provide suction at the bottom of the bed to better entrain material and reduce the propensity for dead zones at the bottom of the narrow conical section.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗