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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

Flow visualization study of the horseshoe vortex in a turbine stator cascade

Flow visualization techniques were used to show the behavior of the horseshoe vortex in a large scale turbine stator cascade. Oil drops on the end wall surface flowed in response to local shear stresses, indicating the limiting flow streamlines at the surface. Smoke injected into the flow and photographed showed time averaged flow behavior. Neutrally bouyant helium filled soap bubbles followed the flow and showed up on photographs as streaks, indicating the paths followed by individual fluid particles. Preliminary attempts to control the vortex were made by injecting air through control jets drilled in the end wall near the vane leading edge. Seventeen different hole locations were tested, one at a time, and the effect of the control jets on the path follwed by smoke in the boundary layer was recorded photographically.

Gaugler, R. E.↗
NASA NTRS1983

Containerless electromagnetic levitation melting of Cu-Fe and Ag-Ni alloys

The feasibility of producing silver or copper alloys containing finely dispersed nickel or iron particles, respectively, by utilizing containerless electromagnetic levitation casting techniques was investigated. A levitation coil was designed to successfully levitate and melt a variety of alloys including Nb-Ge, Cu-Fe, Fe-C, and Ag-Ni. Samples of 70 Cu-30 Fe and 80 Ag-20 Ni (atomic %), prepared by mechanical pressing of the constituent powders, were levitated and heated either to the solid plus liquid range of the alloys or to the fully liquid region. The samples were then solidified by passing helium gas into the bell jar or they were dropped into a quenching oil. The structure of the samples which were heated to the solid plus liquid range consists of uniform distribution of Fe or Ni particle in their respective matrices. A considerable amount of entrapped gas bubbles were contained. Upon heating for longer periods or to higher temperatures, the bubbles coalesced and burst, causing the samples to become fragmented and usually fall out of the coil.

Abbaschian, G. J.↗
NASA NTRS1987

Method and apparatus for generating microshells of refractory materials

A system is described for forming accurately spherical and centered fluid-filled shells, especially of high melting temperature material. Material which is to form the shells is placed in a solid form in a container, and the material is rapidly heated to a molten temperature to avoid recrystallization and the possible generation of unwanted microbubbles in the melt. Immediately after the molten shells are formed, they drop through a drop tower whose upper end is heated along a distance of at least one foot to provide time for dissipation of surface waves on the shells while they cool to a highly viscous, or just above melting temperature so that the bubble within the shell will not rise and become off centered. The rest of the tower is cryogenically cooled to cool the shell to a solid state.

Lee, Mark C.↗
NASA NTRS2013

Investigation of VEGGIE Root Mat

VEGGIE is a plant growth facility that utilizes the phenomenon of capillary action as its primary watering system. A cloth made of Meta Aramid fiber, known as Nomex is used to wick water up from a reservoir to the bottom of the plants roots. This root mat system is intended to be low maintenance with no moving parts and requires minimal crew interface time. Unfortunately, the water wicking rates are inconsistent throughout the plant life cycle, thus causing plants to die. Over-wicking of water occurs toward the beginning of the cycle, while under-wicking occurs toward the middle. This inconsistency of wicking has become a major issue, drastically inhibiting plant growth. The primary objective is to determine the root cause of the inconsistent wicking through experimental testing. Suspect causes for the capillary water column to break include: a vacuum effect due to a negative pressure gradient in the water reservoir, contamination of material due to minerals in water and back wash from plant fertilizer, induced air bubbles while using syringe refill method, and material limitations of Nomex's ability to absorb and retain water. Experimental testing will be conducted to systematically determine the cause of under and over-wicking. Pressure gages will be used to determine pressure drop during the course of the plant life cycle and during the water refill process. A debubbler device will be connected to a root mat in order to equalize pressure inside the reservoir. Moisture and evaporation tests will simultaneously be implemented to observe moisture content and wicking rates over the course of a plant cycle. Water retention tests will be performed using strips of Nomex to determine materials wicking rates, porosity, and absorptivity. Through these experimental tests, we will have a better understanding of material properties of Nomex, as well as determine the root cause of water column breakage. With consistent test results, a forward plan can be achieved to resolve the issue and give valuable insight for the next generation of VEGGIE.

Subbiah, Arun M.↗
NASA NTRS2001

Surfactant Facilitated Spreading of Aqueous Drops on Hydrophobic Surfaces

Microgravity technologies often require aqueous phases to spread over nonwetting hydrophobic solid surfaces. Surfactants facilitate the wetting of water on hydrophobic surfaces by adsorbing on the water/air and hydrophobic solid/water interfaces and lowering the surface tensions of these interfaces. The tension reductions decrease the contact angle, which increases the equilibrium wetted area. Hydrocarbon surfactants; (i.e., amphiphiles with a hydrophobic moiety consisting of an extended chain of (aliphatic) methylene -CH2- groups attached to a large polar group to give aqueous solubility) are capable of reducing the contact angles on surfaces which are not very hydrophobic, but do not reduce significantly the contact angles of the very hydrophobic surfaces such as parafilm, polyethylene or self assembled monolayers. Trisiloxane surfactants (amphiphiles with a hydrophobe consisting of methyl groups linked to a trisiloxane backbone in the form of a disk ((CH3)3-Si-O-Si-O-Si(CH3)3) and an extended ethoxylate (-(OCH2CH2)a-) polar group in the form of a chain with four or eight units) can significantly reduce the contact angle of water on a very hydrophobic surface and cause rapid and complete (or nearly complete) spreading (termed superspreading). The overall goal of the research described in this proposal is to establish and verify a theory for how trisiloxanes cause superspreading, and then use this knowledge as a guide to developing more general hydrocarbon based surfactant systems which superspread. We propose that the trisiloxane surfactants superspread because their structure allows them to strongly lower the high hydrophobic solid/aqueous tension when they adsorb to the solid surface. When the siloxane adsorbs, the hydrophobic disk parts of the molecule adsorb onto the surface removing the surface water. Since the cross-sectional area of the disk is larger than that of the extended ethoxylate chain, the disks can form a space-filling mat on the surface which removes a significant amount of the surface water. In this presentation, we report the results of measurements of the molecular packing and rates of kinetic exchange of the trisiloxane surfactants at the air/water interface in order to confirm our picture of trisiloxane packing, and provide additional insight into the superspreading process. We used the pendant bubble technique as a Langmuir trough to measure the trisiloxane equation of state which relates the tension to the surface concentration. From these measurements we obtain accurate values for the maximum packing density. We find that trisiloxanes with 4 and 8 ethoxylate groups have the same maximum packing concentration, indicating that the maximum packing is controlled by the cross section of the head group. For trisiloxanes with larger than eight ethoxylates, the maximum packing increases with ethoxylate number, indicating that the disposition of the ethoxylate chain (i.e., its effective size) is controlling. This supports our picture of superspreading: The superspreading ability of trisiloxanes decreases considerably for trisiloxanes with larger than eight ethoxylates; the packing measurements indicate that for the higher ethoxylate number trisiloxanes, the compact nonpolar head groups are pushed apart by the ethoxylate chain. They leave spaces of surface water on adsorption and do not lower the solid tension as much as their lower chain analogues. Finally the report measurements of the dynamic tension reduction accompanying the adsorption of trisiloxanes onto an initially clean interface using the pendant bubble technique, and we obtain from these relaxations, the equation of state and a mass transfer model, the rate constants for kinetic exchange. We find that the rate constants for desorption of trisiloxanes are generally much slower than for analogous aliphatic polyethoxylate surfactants with identical ethoxylate chain lengths. When an aqueous drop of a superspreader solution is placed on a hydrophobic surface and begins to spread, the lower desorption rates allows the tension at the drop center to remain reduced relative to the tension of the expanding periphery, thus strengthening Marangoni forces which can assist the spreading. Marangoni forces can be especially significant in the case of superspreaders because their maximum equilibrium reduction in tension is several dynes/cm lower than for aliphatic surfactants.

Kumar, Nitin↗
NASA NTRS1985

Fusion Target Technology

In order to produce the high quality spherical shells that are required, three parameters must be controlled accurately: the shell dimensions, shell sphericity and concentricity, and the surface topology of the shell. Attempts to conduct experiments on the dynamics of liquid bubbles (molten shells) in laboratories are limited by a strong coupling among the three parameters, time, gravity, and temperature. These limitations are circumvented and detailed study of each of the important processes is carried out through the use of low gravity environments collectively available in drop towers, in KC-135 flights, in a neutrally buoyant immiscible system, and in an acoustic levitation system.

Wang, T. G.↗
NASA NTRS1997

Development of a Device to Deploy Fluid Droplets in Microgravity

A free-floating droplet in microgravity is ideal for scientific observation since it is free of confounding factors such as wetting and nonsymmetrical heat transfer introduced by contact with surfaces. However, the technology to reliably deploy in microgravity has not yet been developed. In some recent fluid deployment experiments, droplets are either shaken off the dispenser or the dispenser is quickly retracted from the droplet. These solutions impart random residual motion to deployed droplet, which can be undesirable for certain investigations. In the present study, two new types of droplet injectors were built and tested. Testing of the droplet injectors consisted of neutral buoyancy tank tests, 5-sec drop tower tests at the NASA Lewis Zero Gravity Facility, and DC-9 tests. One type, the concentric injector, worked well in the neutral buoyancy tank but did not do well in low-gravity. However, it appeared that it makes a fine apparatus for constructing bubbles in low-gravity conditions. The other type, the T-injector, showed the most promise for future development. In both neutral buoyancy and DC-9 tests, water droplets were formed and deployed with some control and repeatability, although in low-gravity the residual velocities were higher than desirable. Based on our observations, further refinements are suggested for future development work.

Robinson, David W.↗
NASA NTRS2001

Investigation of Capillary Limit in a Loop Heat Pipe

This paper presets an experimental study on the capillary limit of a loop heat pipe (LHP) at low powers. The slow thermal response of the loop at low powers made it possible to observe interactions among various components after the capillary limit was exceeded. The capillary limit at low powers was achieved by imposing additional pressure drops on the vapor line through the use of a metering valve. A differential pressure transducer was also used to measure the pressure drop across the evaporator and the compensation chamber (CC). Test results show that when the capillary limit is exceeded, vapor will penetrate the primary wick, resulting in a partial dry-out of the evaporator and a rapid increase of the CC temperature. Because the evaporator can tolerate vapor bubbles, the LHP will continue to function and may reach a new steady state at the higher temperature. Thus, the LHP will exhibit a graceful degradation in performance rather than a complete failure. Moreover, the loop can recover from a partial dry-out by reducing the heat load without a re-start.

Ku, Jentung↗
NASA NTRS1990

Heat transfer in space systems; Proceedings of the Symposium, AIAA/ASME Thermophysics and Heat Transfer Conference, Seattle, WA, June 18-20, 1990

Theoretical and experimental studies of heat-tranfer in a space environment are discussed in reviews and reports. Topics addressed include a small-scale two-phase thermosiphon to cool high-power electronics, a low-pressure-drop heat exchanger with integral heat pipe, an analysis of the thermal performance of heat-pipe radiators, measurements of temperature and concentration fields in a rectangular heat pipe, and a simplified aerothermal heating method for axisymmetric blunt bodies. Consideration is given to entropy production in a shock wave, bubble-slug transition in a two-phase liquid-gas flow under microgravity, plasma arc welding under normal and zero gravity, the Microgravity Thaw Experiment, the flow of a thin film on stationary and rotating disks, an advanced ceramic fabric body-mounted radiator for Space Station Freedom phase 0 design, and lunar radiators with specular reflectors.

Chan, S. H.↗
NASA NTRS1990

Isothermal gas-liquid flow at reduced gravity

Research on adiabatic gas-liquid flows under reduced gravity condition is presented together with experimental data obtained using a NASA-Lewis RC 100-ft drop tower and in a LeRC Learjet. It is found that flow patterns and characteristics remain unchanged after the first 1.5 s into microgravity conditions and that the calculated time for a continuity wave to traverse the test section is less than 1.2 s. It is also found that the dispersed bubbles move at the same velocity as that of the front of the slug and that the transition between bubbly and slug flow is insensitive to diameter. Both the bubbly and the slug flows are suggested to represent a continuum of the same physical process. The characteristics of annular, slug, and bubbly flows are compared.

Dukler, A. E.↗
NASA NTRS2004

Enhanced Boiling on Micro-Configured Composite Surfaces Under Microgravity Conditions

Two experimental setups: High Heat Flux Pool Boiling Setup and Optical system of Measuring Contact Angle and Spreading Parameters were established and a series of experiments was conducted. The experimental work on the nucleate boiling performance of both Freon-113 and water on the composite surfaces has been finished and the results show that the composite surface with 25% volume fraction of graphite fibers in the copper matrix has the best enhancing performance. Stronger enhancement was obtained for water compared to Freon-113. The wall superheat initiating boiling was reduced 40% and 35% and the heat flux of the nucleate boiling was augmented up to ten times and 6.7 times, respectively. A bubble departure model has been presented to explain the enhancement mechanism of the boiling heat transfer on the composite surfaces. A powerful optical method to measure contact angle and spreading parameters of liquids on solid surfaces, including both transparent and non-transparent substrates, has been developed and successfully used in the measurements for various liquid-solid systems. The experimental work on identification of profiles near three-phase line by laser shadowgraphy method has been finished and the characteristics of the three-phase line for different liquid-solid systems were unveiled, which is very important to understand the mechanism of boiling under microgravity conditions. The four basic patterns of sessile profile were discovered through caustics and caustic-diffraction analysis by applying wave theory in shadowgraphy technology, which contributes to clearly explain the different characteristics of wetting and spreading of various liquids on a solid surface, and therefore to further understand the bubble departure mechanisms. A new working pattern of heat pipes using working fluids with positive surface-tension gradient against temperature was discovered and analyzed, and then the new heat pipe systems using this kind of working fluids have been presented. Two patent devices, i.e. Shadowgraphic Method to Measure Properties of Sessile Drops and Heat Pipe Systems Using New Working Fluids, have been developed; the former has been approved by The United States Patent & Trademark Office and the latter is being examined.

Source record↗
NASA NTRS2012

Microgravity Passive Phase Separator

A new invention disclosure discusses a structure and process for separating gas from liquids in microgravity. The Microgravity Passive Phase Separator consists of two concentric, pleated, woven stainless- steel screens (25-micrometer nominal pore) with an axial inlet, and an annular outlet between both screens (see figure). Water enters at one end of the center screen at high velocity, eventually passing through the inner screen and out through the annular exit. As gas is introduced into the flow stream, the drag force exerted on the bubble pushes it downstream until flow stagnation or until it reaches an equilibrium point between the surface tension holding bubble to the screen and the drag force. Gas bubbles of a given size will form a front that is moved further down the length of the inner screen with increasing velocity. As more bubbles are added, the front location will remain fixed, but additional bubbles will move to the end of the unit, eventually coming to rest in the large cavity between the unit housing and the outer screen (storage area). Owing to the small size of the pores and the hydrophilic nature of the screen material, gas does not pass through the screen and is retained within the unit for emptying during ground processing. If debris is picked up on the screen, the area closest to the inlet will become clogged, so high-velocity flow will persist farther down the length of the center screen, pushing the bubble front further from the inlet of the inner screen. It is desired to keep the velocity high enough so that, for any bubble size, an area of clean screen exists between the bubbles and the debris. The primary benefits of this innovation are the lack of any need for additional power, strip gas, or location for venting the separated gas. As the unit contains no membrane, the transport fluid will not be lost due to evaporation in the process of gas separation. Separation is performed with relatively low pressure drop based on the large surface area of the separating screen. Additionally, there are no moving parts, and there are no failure modes that involve fluid loss. A patent application has been filed.

Paragano, Matthew↗
NASA NTRS2004

Centrifugal Adsorption Cartridge System

The centrifugal adsorption cartridge system (CACS) is an apparatus that recovers one or more bioproduct(s) from a dilute aqueous solution or suspension flowing from a bioreactor. The CACS can be used both on Earth in unit gravity and in space in low gravity. The CACS can be connected downstream from the bioreactor; alternatively, it can be connected into a flow loop that includes the bioreactor so that the liquid can be recycled. A centrifugal adsorption cartridge in the CACS (see figure) includes two concentric cylinders with a spiral ramp between them. The volume between the inner and outer cylinders, and between the turns of the spiral ramp is packed with an adsorbent material. The inner cylinder is a sieve tube covered with a gas-permeable, hydrophobic membrane. During operation, the liquid effluent from the bioreactor is introduced at one end of the spiral ramp, which then constrains the liquid to flow along the spiral path through the adsorbent material. The spiral ramp also makes the flow more nearly uniform than it would otherwise be, and it minimizes any channeling other than that of the spiral flow itself. The adsorbent material is formulated to selectively capture the bioproduct(s) of interest. The bioproduct(s) can then be stored in bound form in the cartridge or else eluted from the cartridge. The centrifugal effect of the spiral flow is utilized to remove gas bubbles from the liquid. The centrifugal effect forces the bubbles radially inward, toward and through the membrane of the inner cylinder. The gas-permeable, hydrophobic membrane allows the bubbles to enter the inner cylinder while keeping the liquid out. The bubbles that thus enter the cylinder are vented to the atmosphere. The spacing between the ramps determines rate of flow along the spiral, and thereby affects the air-bubble-removal efficiency. The spacing between the ramps also determines the length of the fluid path through the cartridge adsorbent, and thus affects the bioproduct-capture efficiency of the cartridge. Depending on the application, several cartridges could be connected in a serial or parallel flow arrangement. A parallel arrangement can be used to increase product-capturing and flow capacities while maintaining a low pressure drop. A serial arrangement can be used to obtain high product-capturing capacity; alternatively, series-connected cartridges can be packed with different adsorbents to capture different bioproducts simultaneously.

Gonda, Steve R.↗
NASA NTRS1994

Light transmission and reflection in perennially ice-covered Lake Hoare, Antarctica

We have investigated the transmission and albedo of the perennial ice cover on Lake Hoare, Antarctica. Our database consists of year-round measurements of the photosynthetically active radiation (400-700 nm) under the ice, measurements of the spatial variation of the under-ice light in midsummer, and spectrally resolved measurements from 400 to 700 nm of the albedo and transmission of the ice cover in early (November) and in midsummer (January). Our results show that the transmission decreases in the first part of summer, dropping by a factor of approximately 4 from November to January. We suggest that this is due to heating in the upper layers of the ice cover and the formation of Tyndall figures. Later in the summer when a significant liquid water fraction occurs within the ice cover, the transmission increases. In the fall when the ice cover freezes solid the transmission drops markedly. The spectrally resolved measurements from 400 to 700 nm show that approximately 2-5% of the incident light in this spectral region penetrates the 3.5-m thick ice cover. We have analyzed the spectral data using a two-stream scattering solution to the radiative transfer equation with three vertical layers in the ice cover. A surficial glaze of scattering ice 1 cm thick overlies a layer of sandy, bubbly ice about a meter thick, and below this is a thick layer of sand-free ice with bubbles. We find that the ice cover is virtually opaque at wavelengths longer than 800 nm. The net transmission of solar energy is approximately 2%. Significant changes in the thickness of the ice cover have been reported at Lake Hoare. These are due primarily to changes in the thickness of the bottom layer only. Because this layer is relatively clear, the effect on the transmission through the ice cover from these changes is less than would be predicted assuming a homogeneous ice cover.

Mckay, C. P.↗
NASA NTRS2004

NASA Tech Briefs, July 2004

Topics: Optoelectronic Sensor System for Guidance in Docking; Hybrid Piezoelectric/Fiber-Optic Sensor Sheets; Multisensor Arrays for Greater Reliability and Accuracy; Integrated-Optic Oxygen Sensors; Ka-Band Autonomous Formation Flying Sensor; CMOS VLSI Active-Pixel Sensor for Tracking; Lightweight, Self-Deploying Foam Antenna Structures; Electrically Small Microstrip Quarter-Wave Monopole Antennas; A 2-to-28-MHz Phase-Locked Loop; Portable Electromyograph; Open-Source Software for Modeling of Nanoelectronic Devices; Software for Generating Strip Maps from SAR Data; Calibration Software for use with Jurassicprok; Software for Probabilistic Risk Reduction; Software Processes SAR Motion-Measurement Data; Improved Method of Purifying Carbon Nanotubes; Patterned Growth of Carbon Nanotubes or Nanofibers; Lightweight, Rack-Mountable Composite Cold Plate/Shelves; SiC-Based Miniature High-Temperature Cantilever Anemometer; Inlet Housing for a Partial-Admission Turbine; Lightweight Thermoformed Structural Components and Optics; Growing High-Quality InAs Quantum Dots for Infrared Lasers; Selected Papers on Protoplanetary Disks; Module for Oxygenating Water without Generating Bubbles; Coastal Research Imaging Spectrometer; Rapid Switching and Modulation by use of Coupled VCSELs; Laser-Induced-Fluorescence Photogrammetry and Videogrammetry; Laboratory Apparatus Generates Dual-Species Cold Atomic Beam; Laser Ablation of Materials for Propulsion of Spacecraft; Small Active Radiation Monitor; Hybrid Image-Plane/Stereo Manipulation; Partitioning a Gridded Rectangle into Smaller Rectangles; Digital Radar-Signal Processors Implemented in FPGAs; Part 1 of a Computational Study of a Drop-Laden Mixing Layer; and Some Improvements in Signal-Conditioning Circuits.

Source record↗
NASA NTRS2001

First Protein Crystallization Experiments on The International Space Station: Sweet Success in Space With Thaumatin

We determined the room temperature 1.2 A structure of thaumatin using a crystal grown in the first protein crystallization experiment conducted aboard the International Space Station (ISS). The crystals were grown in the Enhanced Gaseous Nitrogen Dewar (EGN) developed by Alexander McPherson and co-workers. EGN transports frozen solutions contained in tygon tubing in a liquid nitrogen Dewar to ISS where the tubes then thaw. Batch, free interface diffusion (FID), or vapor diffusion crystallization occurs after thawing. EGN was flown to the ISS on STS-106 on September 8, 2000. This was a "risk mitigation" flight that tested EGN performance and the process of conducting experiments on ISS. We focused on how to map a hanging drop crystallization recipe to the EGN FID method. Thaumatin was chosen as the test system. Three series of crystallization recipes were set-up. Each series tested different volume ratios of protein-rich solution to precipitant-rich solution. The series differed from each other by fixing either the protein concentration or the amount of protein in the solutions. Upon return of the samples to Earth on October 24 by STS-92, bubbles that spanned the diameter of the tubing were observed in all tubes. Such bubbles interrupt liquid-liquid diffusion and force vapor diffusion equilibration to occur instead. Nonetheless, crystals grew in 9 of 30 tubes. Many large crystals were grown, the largest being 2.0 x 1.1 x 1.0 cubic mm. The largest crystal was used to collect data at room temperature on beamline 7-1 of the Stanford Synchrotron Radiation Source to a maximum resolution of 1.2 A. The structure was refined anisotropically using SHELX with a data to parameter ratio of 4.5 to give an R(sub factor) of 15.8% (R(sub free) = 18.2%) for ail reflections without generated hydrogens. This refinement is proceeding. Comparisons of this 1.2 A microgravity structure to previous reports of the thaumatin structure at 1.75 A and to ground control crystals will be presented.

Kundrot, Craig E.↗
NASA NTRS1961

An Experimental Study of Boiling in Reduced and Zero Gravity Fields

A pool boiling apparatus was mounted on a counterweighted platform which could be dropped a distance of nine feet. By varying the size of the counterweight, the effective gravity field on the equipment was adjusted between zero and unity. A study of boiling burnout in water indicated that a variation in the critical heat flux according to the one quarter power of gravity was reasonable. A consideration of the transient burnout process was necessary in order to properly interpret the data. A photographic study of nucleate boiling showed how the velocity of freely rising vapor bubbles decreased as gravity was reduced. The bubble diameters at the time of breakoff from the heated surface were found to vary inversely as gravity to the 1/3.5 power. Motion pictures were taken to illustrate both nucleate and film boiling in the low gravity range.

Usiskin, C. M.↗
NASA NTRS1984

Analysis of dynamic characteristics of fluid force induced by labyrinth seal

Flow patterns of the labyrinth seal are experimentally investigated for making a mathematical model of labyrinth seal and to obtain the flow induced force of the seal. First, the flow patterns in the labyrinth chamber are studied on the circumferential flow using bubble and on the cross section of the seal chamber using aluminum powder as tracers. And next, the fluid force and its phase angle are obtained from the measured pressure distribution in the chamber and the fluid force coefficients are derived from the fluid force and the phase angle. Those are similar to the expression of oil film coefficients. As a result, it is found that the vortices exist in the labyrinth chambers and its center moves up and down periodically. The pressure drop is biggest in the first stage of chambers and next in the last stage of chambers.

Iwatsubo, T.↗