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At least 505 records · Page 28
All sourcesNASA NTRSDOE OSTI
NASA NTRS2022

Hybrid simulations of a tangential discontinuity-driven foreshock bubble formation in comparison with a hot flow anomaly formation

Hot flow anomalies (HFAs) and foreshock bubbles (FBs) are significant foreshock transients that can accelerate particles and disturb the magnetosphere-ionosphere system. Yet, their early formation mechanisms are still not fully understood. To investigate the formation of tangential discontinuity (TD)-driven FBs and HFAs, we use 2-D local hybrid simulations where a reflected or an injected warm foreshock ion beam can interact with a TD whose half-thickness is comparable to the ion inertial scale. We show that the foreshock ions perform a partial gyration within, or across, the TD. Bulk motion differences between partially-gyrating foreshock ions and fluid-electrons lead to the generation of currents. As the trigger, these foreshock-driven currents change the magnetic field topology around the TD and force the frozen-in solar wind plasma to redistribute along with the field lines, shaping the foreshock transient. This confirms a recently proposed kinetic formation model. The extent of the magnetic field direction change across the TD within the foreshock ion gyromotion determines the current profile and thus the type of foreshock transient that forms. For a thin TD, the foreshock ions generate a current that is much stronger on the upstream side than the downstream side, forming an FB with one upstream compressional boundary. For the same foreshock ion gyroradius and magnetic shear, a thick TD yields comparable foreshock-driven currents on the upstream and downstream sides, forming an HFA with two compressional boundaries. Our study suggests that the TD thickness is one of the factors that determine the formation of FBs and HFAs

Andrew Vu↗
NASA NTRS1992

Compressibility effects on dynamic stall of airfoils undergoing rapid transient pitching motion

The research was carried out in the Compressible Dynamic Stall Facility, CDSF, at the Fluid Mechanics Laboratory (FML) of NASA Ames Research Center. The facility can produce realistic nondimensional pitch rates experienced by fighter aircraft, which on model scale could be as high as 3600/sec. Nonintrusive optical techniques were used for the measurements. The highlight of the effort was the development of a new real time interferometry method known as Point Diffraction Interferometry - PDI, for use in unsteady separated flows. This can yield instantaneous flow density information (and hence pressure distributions in isentropic flows) over the airfoil. A key finding is that the dynamic stall vortex forms just as the airfoil leading edge separation bubble opens-up. A major result is the observation and quantification of multiple shocks over the airfoil near the leading edge. A quantitative analysis of the PDI images shows that pitching airfoils produce larger suction peaks than steady airfoils at the same Mach number prior to stall. The peak suction level reached just before stall develops is the same at all unsteady rates and decreases with increase in Mach number. The suction is lost once the dynamic stall vortex or vortical structure begins to convect. Based on the knowledge gained from this preliminary analysis of the data, efforts to control dynamic stall were initiated. The focus of this work was to arrive at a dynamically changing leading edge shape that produces only 'acceptable' airfoil pressure distributions over a large angle of attack range.

Chandrasekhara, M. S.↗
NASA NTRS1999

Evaluation of Factors Affecting Powdered Drug Reconstitution in Microgravity

Owing to the high cost of transporting mass into space, and the small volume available for equipment in the Space Shuttle Orbiter and the International Space Station, refrigeration space is extremely limited. For this reason, there exists strong motivation for transporting certain drugs in powdered form so that they do not require refrigeration. When needed, the powdered drug will be mixed with saline to obtain a liquid form that may be injected intravenously. While this is a relatively simple task in a 1-G environment, there are some difficulties that may be encountered in 0-G. In non-accelerated spaceflight, gravitational and inertial forces are eliminated allowing other smaller forces, such as capillary forces and surface tension, to dominate the behavior of fluids. For instance, water slowly ejected from a straw will tend to form a sphere, while fluid in a container will tend to wet the inside surface forming a highly rounded meniscus. Initial attempts at mixing powdered drugs with saline in microgravity have shown a tendency toward forming foamy emulsions instead of the desired homogeneous solution. The predominance of adhesive forces between the drug particles and the interface tensions at the gas/liquid and solid/liquid interfaces drastically reduce the rate of deaggregation of the drug powder and also reduce the rate of absorption of saline by the powder mass. In addition, the capillary forces cause the saline to wet the inside of the container, thus trapping air bubbles within the liquid. The rate of dissolution of a powder drug is directly proportional to the amount of surface area of the solid that is exposed to liquid solvent. The surface area of drug that is in contact with the liquid is greatly reduced in microgravity and, as a result, the dissolution rate is reduced as well. The KC-135 research described here was aimed at evaluating the extent to which it is possible to perform drug reconstitution in the weightlessness of parabolic flight using standard pharmacological supplies. The experiment included a parametric assessment of possible factors affecting the reconstitution process. The specific questions that we wished to answer were: (1) Is it possible to reconstitute powdered drugs in weightlessness using standard pharmacological equipment? (2) What are the differences between drug reconstitution in a 1-G and a 0-G environment? (3) What techniques of mixing the drug powder and diluent are more successful? (4) What physical and chemical factors play a role in determining the success of mixing and dissolution? (5) Is it necessary to employ crewmember and equipment restraints during the reconstitution process?

Schaffner, Grant↗
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.↗
DOE OSTI2020

Amphiphilic Block Copolymers for Flocculation and Hydrophobization of Legacy Waste Suspensions in Flotation Driven Dewatering Operations

There exists a degrading legacy fuel pond at the Sellafield site (UK), known as the First-Generation Magnox Storage Pond (FGMSP). After being placed into a passive care and maintenance regime resulting in a long storage period, the fuel rods, primarily their cladding, corroded in the pond forming magnesium hydroxide based sludges and suspended material. These ponds are a grave concern to the British government in terms of hazard and risk reduction. Therefore, decommissioning of these ponds is a top priority beginning with the contaminant retrievals process [1]. The pond has accumulated significant quantities of waste materials amongst the skips of fuel, including but not limited to: large inventories of corroded Magnox sludge, fuel rod fragments, metal fragments (from fuel skips), concrete degradation products (from the pond infrastructure), wind-blown sand, and other materials such as bird guano and animal remains. This challenge requires a chemically robust technology to complete sludge retrievals [2]. As nuclear is different, a more stringent process operation criteria is required. From the criteria, flotation was selected as a viable technology. Flotation involves the application of collector molecules which modify the hydrophobicity of suspended particles allowing them to adsorb to rising bubbles. As some particles lack inertia for flotation due to their size, dual flocculant/collector agents can be deployed for greater particle recovery, in this case, amphiphilic diblock copolymers. Two copolymers of Poly(acrylic acid)-b-poly(n-butyl acrylate) (or PAA-b-PnBA), of different hydrophobic chain lengths (PBA) were synthesized for flotation campaigns. Flotation has shown promise to be a valuable rapid dewatering strategy for decommissioning of legacy waste ponds whilst upholding the required operational criteria. This research has shown: PAA-b-PnBA copolymers promote flocculation of Mg(OH){sub 2} particulates. Diblock copolymers retain more fluid than traditional surfactant based collectors wrt. relative particulate recovery performance- where longer PnBA chain length polymers performed best. Performance appears to be hydrodynamically limited due to over-flocculation of Mg(OH){sub 2}. Potential to combine with sedimentation for high particle recovery with low fluid carryover.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

Fluid Flow Observations of The Spray Near-Field Using High-Speed X-Ray Imaging

Sprays are important to may industrial processes, but the near-field region where spray formation takes place is difficult to visualize and characterize through visible light imaging because this region is typically optically dense. X-ray imaging is one technique that can penetrate this optically dense region and provide unique observations of the spray formation process. This study uses high-speed white beam X-ray imaging conducted at the Advanced Photon Source to capture spray formation dynamics from a canonical airblast atomizer. In this work, a range of momentum flux ratios are visualized by varying the gas flow rate while the liquid flow rate is held constant. The use of X-rays show overlapping flow structures including bags, ligaments, mushrooms, and webs. Air bubbles are captured within the liquid regions, and a very dynamic crown forms at the liquid needle exit at higher momentum flux ratios. Finally, at the highest momentum flux ratios, air bubbles and liquid droplets are observed migrating upstream in the center of the crown, and this motion is attributed to a toroidal recirculation cell at the nozzle exit.

47 OTHER INSTRUMENTATION↗
NASA NTRS1991

An evaluation of three two-dimensional computational fluid dynamics codes including low Reynolds numbers and transonic Mach numbers

Full-potential, Euler, and Navier-Stokes computational fluid dynamics (CFD) codes were evaluated for use in analyzing the flow field about airfoils sections operating at Mach numbers from 0.20 to 0.60 and Reynolds numbers from 500,000 to 2,000,000. The potential code (LBAUER) includes weakly coupled integral boundary layer equations for laminar and turbulent flow with simple transition and separation models. The Navier-Stokes code (ARC2D) uses the thin-layer formulation of the Reynolds-averaged equations with an algebraic turbulence model. The Euler code (ISES) includes strongly coupled integral boundary layer equations and advanced transition and separation calculations with the capability to model laminar separation bubbles and limited zones of turbulent separation. The best experiment/CFD correlation was obtained with the Euler code because its boundary layer equations model the physics of the flow better than the other two codes. An unusual reversal of boundary layer separation with increasing angle of attack, following initial shock formation on the upper surface of the airfoil, was found in the experiment data. This phenomenon was not predicted by the CFD codes evaluated.

Hicks, Raymond M.↗
NASA NTRS2007

Polymethylmethacrylate (PMMA) Material Test Results for the Capillary Flow Experiments (CFE)

In support of the Capillary Flow Experiments (CFE) program, several polymethylmethacrylate (PMMA) flight vessels were constructed. Some vessels used a multipiece design, which was chemically welded together. Due to questions regarding the effects of the experiment fluid (silicone oil) on the weld integrity, a series of tests were conducted to provide evidence of the adequacy of the current vessel design. Tensile tests were conducted on PMMA samples that were both in the as-received condition, and also aged in air or oil for up to 8 weeks. Both welded and unwelded samples were examined. Fracture of the joints was studied using notched tensile specimens and Brazilian disk tests. Results showed that aging had no effect on tensile properties. While the welded samples were weaker than the base parent material, the weld strength was found to be further degraded by bubbles in the weld zone. Finally a fracture analysis using the worst-case fracture conditions of the vessel was performed, and the vessel design was found to have a factor of three safety margin.

Lerch, Bradley A.↗
NASA NTRS1971

Development of a space activity suit

The development of a series of prototype space activity suit (SAS) assemblies is discussed. The SAS is a new type of pressure suit designed especially for extravehicular activity. It consists of a set of carefully tailored elastic fabric garments which have been engineered to supply sufficient counterpressure to the body to permit subjects to breath O2 at pressures up to 200 mm Hg without circulatory difficulty. A closed, positive pressure breathing system (PPBS) and a full bubble helmet were also developed to complete the system. The ultimate goal of the SAS is to improve the range of activity and decrease the energy cost of work associated with wearing conventional gas filled pressure suits. Results are presented from both laboratory (1 atmosphere) and altitude chamber tests with subjects wearing various SAS assemblies. In laboratory tests lasting up to three hours, the SAS was worn while subjects breathed O2 at pressures up to 170 mm Hg without developing physiological problems. The only physiological symptoms apparent were a moderate tachycardia related to breathing pressures above 130 mm Hg, and a small collection of edema fluid in the hands. Both problems were considered to be related to areas of under-pressurization by the garments. These problems, it is suggested, can ultimately be corrected by the development of new elastic fabrics and tailoring techniques. Energy cost of activity, and mobility and dexterity of subjects in the SAS, were found to be superior to those in comparable tests on subjects in full pressure suits.

Annis, J. F.↗
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 NTRS2012

Development of Two Color Fluorescent Imager and Integrated Fluidic System for Nanosatellite Biology Applications

Nanosatellites offer frequent, low-cost space access as secondary payloads on launches of larger conventional satellites. We summarize the payload science and technology of the Microsatellite in-situ Space Technologies (MisST) nanosatellite for conducting automated biological experiments. The payload (two fused 10-cm cubes) includes 1) an integrated fluidics system that maintains organism viability and supports growth and 2) a fixed-focus imager with fluorescence and scattered-light imaging capabilities. The payload monitors temperature, pressure and relative humidity, and actively controls temperature. C. elegans (nematode, 50 m diameter x 1 mm long) was selected as a model organism due to previous space science experience, its completely sequenced genome, size, hardiness, and the variety of strains available. Three strains were chosen: two green GFP-tagged strains and one red tdTomato-tagged strain that label intestinal, nerve, and pharyngeal cells, respectively. The integrated fluidics system includes bioanalytical and reservoir modules. The former consists of four 150 L culture wells and a 4x5 mm imaging zone the latter includes two 8 mL fluid reservoirs for reagent and waste storage. The fluidic system is fabricated using multilayer polymer rapid prototyping: laser cutting, precision machining, die cutting, and pressure-sensitive adhesives it also includes eight solenoid-operated valves and one mini peristaltic pump. Young larval-state (L2) nematodes are loaded in C. elegans Maintenance Media (CeMM) in the bioanalytical module during pre-launch assembly. By the time orbit is established, the worms have grown to sufficient density to be imaged and are fed fresh CeMM. The strains are pumped sequentially into the imaging area, imaged, then pumped into waste. Reagent storage utilizes polymer bags under slight pressure to prevent bubble formation in wells or channels. The optical system images green and red fluorescence bands by excitation with blue (473 nm peak) and amber (587 nm peak) LEDs it achieves 8 m lateral resolution using a CMOS imaging chip (as configured for serial data speeds) or 4 m resolution using USB imaging chips. The imager consists of a modified commercial off-the-shelf CMOS chip camera, amber, blue and white LEDs, as well as a relay lens and dual-band filters to obviate moving parts while supporting both fluorescence wavelengths.

Wu, Diana Terri↗
DOE OSTI2022

Ephemeral antibubbles: Spatiotemporal evolution from direct numerical simulations

Antibubbles, which consist of a shell of a low-density fluid inside a high-density fluid, have several promising applications. We show, via extensive direct numerical simulations (DNSs), in both two and three dimensions, that the spatiotemporal evolution of antibubbles can be described naturally by the coupled Cahn-Hilliard-Navier-Stokes (CHNS) equations for a binary fluid. Our DNSs capture elegantly the gravity-induced thinning and breakup of an antibubble via the time evolution of the Cahn-Hilliard scalar-order-parameter field $\phi$, which varies continuously across interfaces, so we do not have to enforce complicated boundary conditions at the moving antibubble interfaces. To ensure that our results are robust, we supplement our CHNS simulations with sharp-interface volume-of-fluid DNSs. We track the thickness of the antibubble and calculate the dependence of the lifetime of an antibubble on several parameters; we show that our DNS results agree with various experimental results; in particular, the velocity with which the arms of the antibubble retract after breakup scales as σ 1/2 , where σ is the surface tension.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2012

Performance of Reynolds Averaged Navier-Stokes Models in Predicting Separated Flows: Study of the Hump Flow Model Problem

Separation can be seen in most aerodynamic flows, but accurate prediction of separated flows is still a challenging problem for computational fluid dynamics (CFD) tools. The behavior of several Reynolds Averaged Navier-Stokes (RANS) models in predicting the separated ow over a wall-mounted hump is studied. The strengths and weaknesses of the most popular RANS models (Spalart-Allmaras, k-epsilon, k-omega, k-omega-SST) are evaluated using the open source software OpenFOAM. The hump ow modeled in this work has been documented in the 2004 CFD Validation Workshop on Synthetic Jets and Turbulent Separation Control. Only the baseline case is treated; the slot flow control cases are not considered in this paper. Particular attention is given to predicting the size of the recirculation bubble, the position of the reattachment point, and the velocity profiles downstream of the hump.

Cappelli, Daniele↗
DOE OSTI2020

Investigating biomass composition and size effects on fast pyrolysis using global sensitivity analysis and CFD simulations

It is notoriously difficult to build an accurate universal model for biomass pyrolysis due to its sensitivity to a wide number of critical material attributes such as chemical species and physical sizes. In this work, a biomass pyrolysis kinetics with 32 heterogeneous reactions and 59 species was implemented in an open-source multiphase computational fluid dynamics (CFD) software MFiX and validated against two different experimental pyrolysis data sets that provided detailed data describing chemical component yields. The reaction scheme was then used to build a surrogate model and assess the sensitivity of pyrolysis yields to feedstock compositions. The sensitivity analysis determined that the yield of bio-char showed a strong positive sensitivity to the carbon-rich lignin and tannin pseudo-species in the reaction scheme while the bio-oil and bio-gas were correlated to oxygen-rich lignin pseudo-species. The reaction scheme was then integrated into a coarse-grained discrete element model to simulate fast pyrolysis in a bubbling fluidized bed over a range of feedstock particle sizes. The reactor simulations showed further sensitivity to particle size and hydrodynamics. Notably, particles under 0.5 mm have small heat transfer limitations but left the reactor before completely converting and thus reduced the bio-oil yield. Results from this study can be used to guide future development of highly accurate models for fast pyrolysis reactors with a variety of feedstock properties and operating conditions.

09 BIOMASS FUELS↗
NASA NTRS1999

Microgravity Two-Phase Flow Transition

Two-phase flows under microgravity condition find a large number of important applications in fluid handling and storage, and spacecraft thermal management. Specifically, under microgravity condition heat transfer between heat exchanger surfaces and fluids depend critically on the distribution and interaction between different fluid phases which are often qualitatively different from the gravity-based systems. Heat transfer and flow analysis in two-phase flows under these conditions require a clear understanding of the flow pattern transition and development of appropriate dimensionless scales for its modeling and prediction. The physics of this flow is however very complex and remains poorly understood. This has led to various inadequacies in flow and heat transfer modeling and has made prediction of flow transition difficult in engineering design of efficient thermal and flow systems. In the present study the available published data for flow transition under microgravity condition are considered for mapping. The transition from slug to annular flow and from bubbly to slug flow are mapped using dimensionless variable combination developed in a previous study by the authors. The result indicate that the new maps describe the flow transitions reasonably well over the range of the data available. The transition maps are examined and the results are discussed in relation to the presumed balance of forces and flow dynamics. It is suggested that further evaluation of the proposed flow and transition mapping will require a wider range of microgravity data expected to be made available in future studies.

Parang, M.↗
DOE OSTI2026

Modeling and Experimental Validation of a Direct-Contact Counter-Flow Fluidized Bed Heat Exchanger for Thermal Energy Storage (TES) Applications

Particle-based thermal energy storage (TES) systems are an emerging energy storage technology. The technological advances have reduced costs, making TES more competitive and reliable in the marketplace but an efficient and reliable operation is heavily dependent on coherent heat transfer between air to particles or vice versa. The particle-based TES technologies provide an intermediate system that can store energy for short (0-10 h), long (10-200 h) and seasonal (> 200 h) timescales. The TES systems store energy by converting electricity to thermal energy; electricity can be directly sourced intermittent generation technologies and/or the grid, helping manage peak loads and other mismatches in supply and demand. The overall efficiency of the TES system depends on the performance of system components (particle storage silos and particle transfer mechanism etc.). The particle heat exchanger is one of the key system components that affects the system efficiency. The pressurized fluidized bed heat exchanger (PFB HX) performance is challenging to predict due to the chaotic behavior of particle and fluid interaction. This research presents a computational study of a novel direct-contact, counter-flow and air-to-particles PFB HX, that contributes in advancing the particle-based long-duration TES technologies. For the current analysis an unsteady Eulerian-Eulerian CFD model was developed and validated against experiments performed at the National Laboratory of the Rockies for two particle sizes (600 ..mu..m and 825 ..mu..m ). Following validation, parametric simulations were conducted to evaluate the effects of interphase drag models (Syamlal-O'Brien and Gidaspow), particle size, bed height and the influence of a frictional-viscosity term on hydrodynamics and heat transfer between the air & particles. The key findings from the analysis are: (1) for the studied operating window Syamlal-O'Brien provides superior agreement with measured gas temperatures (errors generally < 10%) while Gidaspow shows large deviations for the coarse particle case; (2) model predictions are most sensitive in the lower 0.2 m above the air distributor where bubble initiation and local mixing dominate interphase heat transfer; (3) representation of the distributor (number of inlet ports) materially affects predicted local mixing and temperature stratification; and (4) the Eulerian-Eulerian framework reproduces bulk thermal trends but shows regime dependent limitations for coarse particles, motivating mesoscale informed closures for scale-up analysis for future studies. These results provide validated guidance for drag selection and distributor design in particle-based thermal energy storage applications. Collectively, the validated model and parametric results quantify key drivers of PHB-HX performance and provide practical guidance for design and optimization. The results provide confidence in the model predictability and provide a step forward to improve on heat exchange performance. The demonstrated performance and modeling approach support the deployment and further development of this novel PHB-HX concept for robust, particle-based long-duration thermal energy storage systems.

25 ENERGY STORAGE↗
NASA NTRS1992

Some aspects of unsteady separation

Unsteady separation can be forced in a variety of ways and in this presentation two fundamental means will be considered: (1) the introduction of convected vorticular disturbances into the flow; and (2) the influence of a specific type of three-dimensional geometry. In both situations a response of the viscous flow near the wall is provoked wherein the fluid near the surface abruptly focuses into a narrow region that erupts from the surface into the mainstream. In two-dimensional flows, the eruption takes the form of a narrow, explosively-growing spike, while in three-dimensional situations, examples are presented which indicate that the eruption is along a narrow zone in the shape of a crescent-shaped plume. The nature of the three-dimensional flow near a circular cylinder, which is mounted normal to a flat plate, is also examined in this study. Here the three-dimensional geometry induces complex three-dimensional separations periodically. The dynamics of the generation process is studied experimentally in a water channel using hydrogen bubble wires and a laser sheet, and the main features of the laminar regime through to transition are documented.

Smith, C. R.↗
NASA NTRS1992

The kinematics of buoyancy induced mixing

A model problem to study mixing driven by buoyancy flow fields due to a time dependent body force which consists of a steady and an oscillatory component is considered. Flow fields generated by a time dependent body force, which consists of a steady and an oscillatory component from vibrations or g-jitter, mix two fluids inside a cavity by stretching and folding the interface into various morphological patterns. These patterns show two basic structures depending on the dominant components of the body force. These structures are whirls and tendrils, corresponding to the dominance of either the steady or oscillatory component, respectively. A combination of these structures also occurs in the interaction region. In this region the effect of the steady component opposes the oscillatory component and the result is to smooth the interface, and prevent breakup of the interface. For the parametric range considered, two basic flow regimes occur: convective and chaotic. In the convective regime, the morphological patterns are topological. In the chaotic regime, mixing occurs by a repetitive sequence of bubble formation, necking, and breakup which spreads the concentration field throughout the cavity. The length stretch of the interface increases exponentially with time. The dynamical system characteristics show that in the convective regime, at a point in space, the flow field is oscillatory with elliptical phase space trajectories, and its power spectrum indicates that the flow field responds to the corresponding input frequency. Whereas, in the chaotic regime, the flow field is aperiodic, the phase space trajectories show irregular patterns, and the power spectrum shows a broadband distribution.

Duval, Walter M. B.↗