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At least 127 records · Page 7

Flow rate and pressure profiles for 1 to 4 axially alined orifice inlets

Choked flow rate and pressure profile data were taken on sequential axially alined inlets of the orifice type, with an orifice length-to-diameter ratio of 0.5. The configuration consisted of two to four inlets spaced at 0.66 and 32 orifice diameters apart. At a spacing of 32 diameters the reduced flow rate appeared to follow the simple power-law relation G(sub r)/G(sub r,1) = N (sup-b), where G(sub r,1) is the reduced flow rate for a single inlet, N is the number of inlets, and b, although temperature dependent, is approximately 0.4. At this spacing the instrumented orifices and spacers gave pressure profiles that dropped sharply at the entrance and partially recovered within each inlet, somewhat independent of N. At low inlet temperature jetting through the last orifice was common. At a spacing of 0.66 diameter fluid jetting through all N inlets was prevalent at low temperatures for each configuration studied, as indicated by the flat pressure profiles and flow rates that were nearlly identical to those for a single orifice inlet. A simplifying relation was developed between the friction loss parameters for flow through N sequential tubes and N sequential inlets. The predicted flow rates for N tubes were in reasonable agreement with the N inlet analysis and followed the simple power-law relation.

Hendricks, R. C.↗

Microgravity two-phase fluid flow pattern modeling

When gas and liquid mixtures flow in a pipe, the distribution of the two phases may take many forms. A flow pattern, or flow regime, is the characteristic spatial distribution of the phases of flow in a pipe. Because heat transfer and pressure drop are dependent on the characteristic distribution of phases, it is necessary to describe flow patterns in an appropriate manner so that a hydrodynamic or heat transfer theory applicable to that can be chosen. A theoretical two phase flow regime transition map under a microgravity environment was developed on physical concepts. These transitions use four basic flow patterns: dispersed flow, slug flow, stratified flow, and annular flow. The forces considered are body force, surface tension force, inertial force, friction, and the force from eddy turbulent fluctuation. Three dimensionless parameters were developed. Because these transition boundaries were developed based on physical concepts, they should be applicable to flow regimes occurring in various design conditions. Because the flow pattern data from KC-135 experiments are insufficient to verify these theoretical transition lines completely, an adiabatic experiment for flow regime analysis is recommended.

Lee, Doojeong↗

Mars Secular Obliquity Decrease and the Layered Terrain

Mars may have substantially decreased its average axial tilt over geologic time due to the waxing and waning of water ice caps through the phenomenon of climate friction (also called obliquity-oblateness feedback). Depending upon Mars' climate and internal structure, water caps of the order of 10(exp 17) - 10(exp 18) kg cycling with the obliquity oscillations could have either increased or decreased the average obliquity by possibly tens of degrees over the age of the solar system. Gravity and topography observations by the Mars Global Surveyor indicate that the south polar cap is mostly uncompensated, so that Mars may be largely rigid on the obliquity timescale. Further, Mars may be a water-rich planet, so that there is a large phase angle between insolation forcing and the size of the obliquity-driven water caps. A stiff, water-rich planet implies an obliquity decrease over the eons. Such a decrease might account for the apparent youthfulness of the polar layered terrain. The idea is that fewer volatiles were available to be cycled into and out of the terrain at high mean obliquity, because of the eveness of insolation between equator and pole, and because of small insolation variations as the obliquity oscillated; so that the movement of volatiles and dust produced thin layers or perhaps no layers at all. As the average obliquity decreased, the insolation contrast between high and low latitudes increased, plus the insolation variations over the obliquity cycle grew somewhat bigger, so that more volatiles and dust might have shuttled into and out of the polar regions, forming the observed thick layers late in Mars' history. It may also be that the average tilt has decreased to the point where the climate friction mechanism is starving itself: more and more water has gotten locked up in the polar regions, making less available for cycling with the oscillations. And the layer-forming mechanism may be starving too: not only less water, but also at low average obliquity the atmospheric pressure is lower, so that dust storms become rarer, making less dust available to be deposited in the layers. The rate of water ice sublimation and the atmospheric pressure are both expected to drop sharply for obliquities only slightly lower than the present one. Hence there are qualitative reasons for believing that (a) the mean obliquity may be about as low as it can get, and (b) the mechanism for making the layers may turn off at low average obliquity, so that the layered terrain is a transient phenomenon. Thus the formation of the layered terrain may be intimately connected to a change in the mean axial tilt.

Rubincam, D. P.↗

Flow Trajectories in Friction Stir Welding

In the Friction Stir Welding (FSW) process, a rotating, shouldered tool with a threaded pin is inserted under pressure along the seam of two pieces of metal which are tightly clamped together, and secured against a rigid anvil underneath. The rotating pin travels along the seam and through a combination of pressure and friction heating produces a zone of plastic deformation around the pin within the workpiece on either side of the seam. As the pin is moved in the direction of welding, the plasticised material moves around the tool and bonds together behind it. The elements of the material flow behavior are a combination of three elements. There is a rotational transport of material being carried around the tool, extrusion of material being forced around the pin on both sides into the cavity created behind it, and a lifting and dropping of material as it is stirred and mixed by the rotating action of the pin. It was assumed that rotational motion of the plastic zone is the primary mechanism for transport of material around the welding tool. A kinematic mathematical model was used to compute trajectories of material movement for various distributions of rotational slip within the plastic zone. These trajectories were then compared with the results of an experiment that produced radiographs of markers embedded in a workpiece that was welded with the FSW process. It was assumed that the copper wire markers retained their original length as the aluminum material flowed around them. The kinematic model included a constraint so that the displacements were such that the total length of the wire markers did not increase after deformation. There was good agreement between the calculated trajectories for the case of localized slip at the outer surface of the plastic deformation zone and the radiographs of the copper wire markers. The trajectories differed markedly from the radiograph traces when a distributed slip zone was assumed. It was concluded that the flow field could be described generally by a rotating plug model with slip occurring on the surface at the outer boundary of the plastic zone.

Bernstein, Edward L.↗

Heat transfer and pressure drop in a compact pin-fin heat exchanger with pin orientation at 18 deg to the flow direction

The heat transfer and pressure drop characteristics of a novel, compact heat exchanger in helium gas were measured at 3.5 MPa and Reynolds numbers of 450 to 12,000. The pin-fin specimen consisted of pins, 0.51 mm high and spaced 2.03 mm on centers, spanning a channel through which the helium flows; the angle of the row of pins to the flow direction was 18 deg. The specimen was radiatively heated on the top side at heat fluxes up to 74 W/sq cm and insulated on the back side. Correlations were developed for the friction factor and Nusselt number. The Nusselt number compares favorably to those of past studies of staggered pin-fins, when the measured temperatures are extrapolated to the temperature of the wall-fluid interface.

Olson, D. A.↗

An Approximate Method for Calculation of the Laminar Boundary Layer with Suction for Bodies of Arbitrary Shape

Various ways were tried recently to decrease the friction drag of a body in a flow; they all employ influencing the boundary layer. One of them consists in keeping the boundary layer Laminar by suction; promising tests have been carried out. Since for large Reynolds numbers the friction drag of the laminar boundary layer is much lower than that of the turbulent boundary layer, a considerable saving in drag results from keeping the boundary layer laminar, even with the blower power required for suction taken into account. The boundary layer is kept laminar by suction in two ways: first, by reduction of the thickness of the boundary layer and second, by the fact that the suction changes the form of the velocity distribution so that it becomes more stable, in a manner similar to the change by a pressure drop. There by the critical Reynolds number of the boundary layer (USigma*/V) (sub crit) becomes considerably higher than for the case without suction. This latter circumstance takes full effect only if continuous suction is applied which one might visualize realized through a porous wall. Thus the suction quantities required for keeping the boundary layer laminar become so small that the suction must be regarded as a very promising auxiliary means for drag reduction.

Schlichting, H.↗

Full Length Assembly Testing in PELICAN (Final Report)

In support of the development of the U.S. Department of Energy (DOE) Versatile Test Reactor (VTR), a thermal hydraulics test facility was constructed to generate experimental measurement of the pressure drop across a single full-scale assembly containing prototypic axial reflectors, fuel, and plena components. Constructed and operated at Argonne National Laboratory, the Pressure drop Experimental Loop for Investigations of Core Assemblies in Nuclear reactors (PELICAN) facility was designed to achieve hydraulic conditions identical to those anticipated for a full-scale fuel assembly located in the VTR core in the region with the highest flow rate. Using water as surrogate for liquid sodium, the flow loop was operated at elevated temperatures and pressures to match the thermophysical properties of liquid sodium and ensure matching Reynolds and Euler numbers. The measurement objectives for data generated from this test facility was driven primarily by the validation needs for code calculations and simulations of the reference VTR core. These objectives focused on the need to validate pressure drop results across the various segments of the fuel assembly as they relate directly to the pumping power and safety of the reactor. Presented in this report are experimental results and analytical comparisons based on testing of a full-length assembly in PELICAN. Housed within a hexagonal test section extending 3.4 m in length, the tested assembly features a prototypic lower reflector, grid plates, wire-wrapped rod bundle, upper reflector, and exit region. The rod bundle extends over 1.5 m in length and contains 217 individual wire-wrapped rods with dimensions that best reflect the reference VTR design. The as-tested bundle assembly was fabricated using 316 stainless steel 0.25-inch (6.35-mm) diameter rods wrapped with 0.04-inch (1.016-mm) diameter wire at a helical pitch of 10.51 inch (26.6 cm). Details of the method for in-house wire-wrapping, assembly, and installation are provided later in this report. Experimental measurements of pressure drop at 19 positions along the test assembly were recorded for a range of flow conditions, with special attention paid to key locations within the assembly, including component inlet and outlet, transition, and wire-wrapped rod bundle regions. Testing conditions were based on 110°C water with flow rates ranging from 50 to 450 GPM (3 to 27 kg/s) at the inlet of the test assembly generating Reynolds numbers and velocities up to ~8.0×10 4 and ~7.8 m/s, respectively, within the rod bundle region. Non-dimensional values for the friction factor were then calculated based on these experimental measurements and compared against those predicted by various analytical correlations available from open literature. Predictions by the upgraded Cheng and Todreas, Rehme, and Novendstern correlations fell within 4% to those values measured experimentally.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Active vibration control in microgravity environment

An active control process to reduce vibration transmitted from the Space Station structure to the vibration sensitive payload is evaluated. A low-friction air-bearing table is used to approximate zero gravity in the horizontal plane. An analog control system is described which activates calibrated air jets when displacement of the test mass is sensed. The air jet control system is found to introduce an effective damping factor in controlling the oscillatory response. The air-jet control system is designed such that the thrust force produces less than 10 to the -5th g acceleration of the payload. An analytical model has verified the amount of damping in addition to flow parameters such as the pressure drop across the valve and the air flow rate.

Gerhold, C. H.↗

On the Accuracy of CFD-Based Pressure Drop Predictions for Right-Angle Ducts

The predictive capability of computational fluid dynamics (CFD) codes for turbulent flow through curved ducts is of significant importance to the design and performance analysis of modern rocket engine flowpaths. Code calibration and validation studies for this class of flow are desireable to estimate the performance margin and operating range of components designed using Navier-Stokes methods. Parametric experimental studies such as that of Weske (NACA ARR W-39) provided a wealth of performance data for the design of single- and compound elbow configurations with various cross-sections, curvature and aspect ratios at varying Reynolds numbers. In that work, the majority of data is presented in the form of loss coefficients, characterizing pressure losses due to duct curvature, and including losses due to wall friction. Using measured friction coefficients, losses of equivalent straight lengths of duct are subtracted, resulting in performance curves useful for design computations. These data are currently used in a CFD-based parametric study covering a broad range of operating conditions. Of particular interest for the accuracy of CFD predictions are the effects on pressure loss due to inlet boundary layer thickness (dependent on upstream development length), and the wall treatment for the turbulence equations (conventional wall functions vs. wall integration using a two-layer model). The experimental data are reassessed in the form of an error analysis, and are compared with CFD predictions for 18 computational cases. Grid-independence, grid spacing, and convergence requirements of the cases are discussed. Conclusions regarding the relative importance of the parametric variables will be presented.

Brankovic, Andreja↗

Experimental study of boundary layer transition with elevated freestream turbulence on a heated flat plate

A detailed investigation to document momentum and thermal development of boundary layers undergoing natural transition on a heated flat plate was performed. Experimental results of both overall and conditionally sampled characteristics of laminar, transitional, and low Reynolds number turbulent boundary layers are presented. Measurements were acquired in a low-speed, closed-loop wind tunnel with a freestream velocity of 100 ft/s and zero pressure gradient over a range of freestream turbulence intensities (TI) from 0.4 to 6 percent. The distributions of skin friction, heat transfer rate and Reynolds shear stress were all consistent with previously published data. Reynolds analogy factors for R(sub theta) is less than 2300 were found to be well predicted by laminar and turbulent correlations which accounted for an unheated starting length. The measured laminar value of Reynolds analogy factor was as much as 53 percent higher than the Pr(sup -2/3). A small dependence of turbulent results on TI was observed. Conditional sampling performed in the transitional boundary layer indicated the existence of a near-wall drop in intermittency, pronounced at certain low intermittencies, which is consistent with the cross-sectional shape of turbulent spots observed by others. Non-turbulent intervals were observed to possess large magnitudes of near-wall unsteadiness and turbulent intervals had peak values as much as 50 percent higher than were measured at fully turbulent stations. Non-turbulent and turbulent profiles in transitional boundary layers cannot be simply treated as Blasius and fully turbulent profiles, respectively. The boundary layer spectra indicate predicted selective amplification of T-S waves for TI is approximately 0.4 percent. However, for TI is approximately 0.8 and 1.1 percent, T-S waves are localized very near the wall and do not play a dominant role in transition process.

Sohn, Ki-Hyeon↗

Numerical study to predict the effect of surface roughness on the thermal and hydraulic performance of additively manufactured heat exchangers

Heat exchangers are used in many industries to transfer thermal energy between two or more objects with an associated thermal and hydraulic performance indicated by thermal effectiveness and pressure drop respectively. Many investigations have aimed to enhance the thermal effectiveness of heat exchangers by introducing turbulent flow inducers that increase the heat transfer rate at the expense of increasing pressure drop. Flow inducers like surface roughness can be controlled with advanced manufacturing methods like additive manufacturing for heat exchanger production. Selecting and manufacturing an optimal surface roughness for heat exchangers requires a more comprehensive approach that accounts for the surface roughness effect on the thermal and hydraulic performance of a sample. Since fabricating samples with additive manufacturing to a desired surface roughness can be an extensive experimental process, this study will fundamentally investigate the effect of surface roughness on the thermal and velocity boundary layers for various surface roughness profiles with physics-based computational modeling. To accurately model the surface roughness effect on thermohydraulic performance, correlations like roughness ratio, friction factor, and Nusselt number are investigated. This study expects to indicate correlations for different flow regimes which can successfully predict the effect of surface roughness on thermohydraulic performance. Results generated from modeling surface roughness effect with unique correlations are then compared to experimental data obtained from literature for validation. The results of this study will provide insight to understand the thermal fluid physics associated with surface roughness and design guidelines for heat exchangers produced with additive manufacturing.

36 MATERIALS SCIENCE↗

NASA Tech Briefs, November 2009

Topics covered include: Cryogenic Chamber for Servo-Hydraulic Materials Testing; Apparatus Measures Thermal Conductance Through a Thin Sample from Cryogenic to Room Temperature; Rover Attitude and Pointing System Simulation Testbed; Desktop Application Program to Simulate Cargo-Air-Drop Tests; Multimodal Friction Ignition Tester; Small-Bolt Torque-Tension Tester; Integrated Spacesuit Audio System Enhances Speech Quality and Reduces Noise; Hardware Implementation of a Bilateral Subtraction Filter; Simple Optoelectronic Feedback in Microwave Oscillators; Small X-Band Oscillator Antennas; Free-Space Optical Interconnect Employing VCSEL Diodes; Discrete Fourier Transform Analysis in a Complex Vector Space; Miniature Scroll Pumps Fabricated by LIGA; Self-Assembling, Flexible, Pre-Ceramic Composite Preforms; Flight-speed Integral Image Analysis Toolkit; Work Coordination Engine; Multi-Mission Automated Task Invocation Subsystem; Autonomously Calibrating a Quadrupole Mass Spectrometer; Determining Spacecraft Reaction Wheel Friction Parameters; Composite Silica Aerogels Opacified with Titania; Multiplexed Colorimetric Solid-Phase Extraction; Detecting Airborne Mercury by Use of Polymer/Carbon Films; Lattice-Matched Semiconductor Layers on Single Crystalline Sapphire Substrate; Pressure-Energized Seal Rings to Better Withstand Flows; Rollerjaw Rock Crusher; Microwave Sterilization and Depyrogenation System; Quantifying Therapeutic and Diagnostic Efficacy in 2D Microvascular Images; NiF2/NaF:CaF2/Ca Solid-State High-Temperature Battery Cells; Critical Coupling Between Optical Fibers and WGM Resonators; Microwave Temperature Profiler Mounted in a Standard Airborne Research Canister; Alternative Determination of Density of the Titan Atmosphere; Solar Rejection Filter for Large Telescopes; Automated CFD for Generation of Airfoil Performance Tables; Progressive Classification Using Support Vector Machines; Active Learning with Irrelevant Examples; A Data Matrix Method for Improving the Quantification of Element Percentages of SEM/EDX Analysis; Deployable Shroud for the International X-Ray Observatory; Improved Model of a Mercury Ring Damper; Optoelectronic pH Meter: Further Details; X-38 Advanced Sublimator; and Solar Simulator Represents the Mars Surface Solar Environment.

Source record↗

Exploring the Effects of Guide Vane on Dimpled Cooling Channel of Gas Turbine Blade

Abstract The purpose of the current study is to find out the heat transfer and pressure drop phenomena of the cooling channel with dimples and guide vane and compare the results with the no guide vane dimpled cooling channel. The first leg of the cooling channel is 490 mm, and the second leg is 460 mm. The two legs relate to the 180 deg turn region. The guide vane was inserted at the bend region of the dimpled cooling channel. The study was conducted with two different guide vanes geometry at two different orientations, i.e., U-guide vane with protrusion and depression orientation and curve-guide vane with protrusion and depression orientations both experimentally and numerically. The numerical study was performed with the large eddy simulation method. The result shows that for both stationary and rotational motion, the U-guide vane with depression experiences the highest thermal performance. The friction factor is comparatively higher for curve-guide vane with protrusion under stationary motion. However, under rotation, the curve-protrusion guide encounters the highest friction factor, which is higher compared to the no guide vane cooling channel.

Energy & Fuels↗

Experimental Investigation of Gas-Side Performance of a Compact Finned-Tube Heat Exchanger

Heat-transfer and pressure-drop data were obtained experimentally for the gas side of a liquid-metal to air, compact finned-tube heat exchanger. The heat exchanger was fabricated from 0.185-inch Inconel tubing in an inline array. The fins were made of 310 stainless-steel- clad copper with a total thickness of 0.010 inch, and the fin pitch was 15.3 fins per inch. The liquid used as the heating medium was sodium. The heat-exchanger inlet gas temperature was varied from 5100 to 1260 R by burning JP fuel for airflow rates of 0.4 to 10.5 pounds per second corresponding to an approximate Reynolds number range of 300 to 9000. The sodium inlet temperature was held at 1400 R with the exception of a few runs taken at 1700 and 1960 R. The maximum ratio of surface temperature to air bulk temperature was 1.45. Friction-factor data with heat transfer were best represented by a single line when the density and viscosity of Reynolds number were evaluated at the average film temperature. At the lower Reynolds numbers reported, the friction data with heat transfer plotted slightly above the friction data without heat transfer. The density of the friction factor was calculated at the average bulk temperature. Heat-transfer results of this investigation were correlated by evaluating the physical properties of air (specific heat, viscosity, and thermal conductivity) at the film temperature.

Gedeon, Louis↗

Measurement of heat transfer and pressure drop in rectangular channels with turbulence promoters

Periodic rib turbulators were used in advanced turbine cooling designs to enhance the internal heat transfer. The objective of the present project was to investigate the combined effects of the rib angle of attack and the channel aspect ratio on the local heat transfer and pressure drop in rectangular channels with two opposite ribbed walls for Reynolds number varied from 10,000 to 60,000. The channel aspect ratio (W/H) was varied from 1 to 2 to 4. The rib angle of attack (alpha) was varied from 90 to 60 to 45 to 30 degree. The highly detailed heat transfer coefficient distribution on both the smooth side and the ribbed side walls from the channel sharp entrance to the downstream region were measured. The results showed that, in the square channel, the heat transfer for the slant ribs (alpha = 30 -45 deg) was about 30% higher that of the transverse ribs (alpha = 90 deg) for a constant pumping power. However, in the rectangular channels (W/H = 2 and 4, ribs on W side), the heat transfer at alpha = 30 -45 deg was only about 5% higher than 90 deg. The average heat transfer and friction correlations were developed to account for rib spacing, rib angle, and channel aspect ratio over the range of roughness Reynolds number.

Han, J. C.↗

Instrument for measuring the wall shearing stress of turbulent boundary layers

It is shown that at a smooth wall in a turbulent boundary layer the velocity profile next to the wall is dependent, aside from the material constants of the flowing medium, only on the shearing stress transmitted to the wall, even with pressure rise or with pressure drop. Consequently, the heat transfer of a small element that is built into the wall and has a higher temperature than that of the flowing medium is a measure of the wall shearing stress. Theoretical considerations indicate that the wall shearing stress of the boundary layer can be defined by means of a heat-transfer measurement with an instrument mounted in the wall. Such an instrument is described. The calibration curve and its directional sensitivity curve are indicated. It permits the determination of the wall shearing stress in magnitude and direction.

BOUNDARY LAYER, TURBULENT↗

Heat transfer enhancement in channels with turbulence promoters

Repeated rib-roughness elements have been used in advanced turbine cooling designs to enhance the internal heat transfer. Often the ribs are perpendicular to the main flow direction so that they have an angle-of-attack of 90 degrees. The objective of this investigation was to determine the effect of rib angle-of-attack on the pressure drop and the average heat-transfer coefficients in the fully developed turbulent air flow in a square duct with two opposite rib-roughened walls for Reynolds numbers varied from 7,000 to 90,000. The rib height-to-equivalent diameter ratio was kept at a constant value of 0.063, the rib pitch-to-height ratio was varied from 10 to 20, and the rib angle-of-attack (alpha) was varied from 90 to 60 deg to 45 to 30 deg, respectively. The thermal-performance comparison indicated that the increased heat conductance for the rib with an oblique angle to the flow (alpha = 45 deg - 30 deg) was about 10-20 percent higher than the rib with a 90 deg angle to the flow, and the pumping power requirement for the angled rib was about 20-50 percent lower than the transverse rib. Semi-empirical correlations for friction factor and heat-transfer coefficients were developed to account for rib spacing and rib angle. The correlations can be used in the design of turbine-blade cooling passages.

Han, J. C.↗

Titanium-Oxygen Reactivity Study

A program has been conducted at Astronautics to investigate the likelihood of occurrence of the catastrophic oxidation of titanium alloy sheet under conditions which simulate certain cases of accidental failure of the metal while it is in contact with liquid or gaseous oxygen. Three methods of fracturing the metal were used; they consisted of mechanical puncture, tensile fracture of welded joints, and perforation by very high velocity particles. The results of the tests which have been conducted provide further evidence of the reactivity of titanium with liquid and gaseous oxygen. The evidence indicates that the rapid fracturing of titanium sheet while it is in contact with oxygen initiates the catastrophic oxidation reaction. Initiation occurred when the speed of the fracture was some few feet per second, as in both the drop-weight puncture tests and the static tensile fracture tests of welded joints, as well as when the speed was several thousand feet per second, as in the simulated micrometeoroid penetration tests. The slow propagation of a crack, however, did not initiate the reaction. It may logically be concluded that the localized frictional heat of rapid fracture and/or spontaneous oxidation (exothermic) of minute particles emanating from the fracture cause initiation of the reaction. Under conditions of slow fracture, however, the small heat generated may be adequately dissipated and the reaction is not initiated. A portion of the study conducted consisted of investigating various means by which the reaction might be retarded or prevented. Providing a "barrier" at the titanium-oxygen interface consisting of either aluminum metal or a coating of a petroleum base corrosion inhibitor appeared to be only partially effective in retarding the reaction. The accidental puncturing or similar rupturing of thin-walled pressurized oxygen tanks on missiles and space vehicle will usually constitute loss of function, and may sometimes cause their catastrophic destruction by explosive decompression regardless of the type of material used for their construction. In the case of tanks constructed of titanium alloys the added risk is incurred of catastrophic burning of the tanks. In view of this it is recommended that thin-walled tanks constructed of titanium alloys should not be used to contain liquid or gaseous oxygen.

Chafey, J. E.↗