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NASA NTRS2004

Assessment and Control of Spacecraft Charging Risks on the International Space Station

The International Space Station (ISS) operates in the F2 region of Earth's ionosphere, orbiting at altitudes ranging from 350 to 450 km at an inclination of 51.6 degrees. The relatively dense, cool F2 ionospheric plasma suppresses surface charging processes much of the time, and the flux of relativistic electrons is low enough to preclude deep dielectric charging processes. The most important spacecraft charging processes in the ISS orbital environment are: 1) ISS electrical power system interactions with the F2 plasma, 2) magnetic induction processes resulting from flight through the geomagnetic field and, 3) charging processes that result from interaction with auroral electrons at high latitude. Recently, the continuing review and evaluation of putative ISS charging hazards required by the ISS Program Office revealed that ISS charging could produce an electrical shock hazard to the ISS crew during extravehicular activity (EVA). ISS charging risks are being evaluated in an ongoing measurement and analysis campaign. The results of ISS charging measurements are combined with a recently developed model of ISS charging (the Plasma Interaction Model) and an exhaustive analysis of historical ionospheric variability data (ISS Ionospheric Specification) to evaluate ISS charging risks using Probabilistic Risk Assessment (PRA) methods. The PRA combines estimates of the frequency of occurrence and severity of the charging hazards with estimates of the reliability of various hazard controls systems, as required by NASA s safety and risk management programs, to enable design and selection of a hazard control approach that minimizes overall programmatic and personnel risk. The PRA provides a quantitative methodology for incorporating the results of the ISS charging measurement and analysis campaigns into the necessary hazard reports, EVA procedures, and ISS flight rules required for operating ISS in a safe and productive manner.

Koontz, Steve↗

NASA NTRS2001

Standardization of Rocket Engine Pulse Time Parameters

Plumes of bipropellant thrusters are a source of contamination. Small bipropellant thrusters are often used for spacecraft attitude control and orbit correction. Such thrusters typically operate in a pulse mode, at various pulse lengths. Quantifying their contamination effects onto spacecraft external surfaces is especially important for long-term complex-geometry vehicles, e.g. International Space Station. Plume contamination tests indicated the presence of liquid phase contaminant in the form of droplets. Their origin is attributed to incomplete combustion. Most of liquid-phase contaminant is generated during the startup and shutdown (unsteady) periods of thruster pulse. These periods are relatively short (typically 10-50 ms), and the amount of contaminant is determined by the thruster design (propellant valve response, combustion chamber size, thruster mass flow rate, film cooling percentage, dribble volume, etc.) and combustion process organization. Steady-state period of pulse is characterized by much lower contamination rates, but may be lengthy enough to significantly conh'ibute to the overall contamination effect. Because there was no standard methodology for thruster pulse time division, plume contamination tests were conducted at various pulse durations, and their results do not allow quantifying contaminant amounts from each portion of the pulse. At present, the ISS plume contamination model uses an assumption that all thrusters operate in a pulse mode with the pulse length being 100 ms. This assumption may lead to a large difference between the actual amounts of contaminant produced by the thruster and the model predictions. This paper suggests a way to standardize thruster startup and shutdown period definitions, and shows the usefulness of this approach to better quantify thruster plume contamination. Use of the suggested thruster pulse time-division technique will ensure methodological consistency of future thruster plume contamination test programs, and allow accounting for thruster pulse length when modeling plume contamination and erosion effects.

Larin, Max E.↗

NASA NTRSDate not supplied

Analysis of Supercooled Large Drop Velocity Measurement in the NASA Icing Research Tunnel

An experiment was conducted in the Icing Research Tunnel (IRT) at the NASA Glenn Research Center to measure the velocity of supercooled large drops (SLD) in the test section of the tunnel. Previous experiments in the IRT suggested that supercooled large drops passing through the test section of the tunnel do not move at the same velocity as the surrounding air flow. The difference between drop velocity and tunnel air velocity is called slip velocity. The slip velocity is important for determining the exact nature of SLD icing simulation in the IRT. It can impact the ice growth process because of its effect on drop cooling rate during transit from the spray bars to the test section. It can also affect the amount of splashing that occurs upon impact. Slip velocity is an important flow parameter to determine how far the current facility capabilities can be extended into the SLD regime. Initial measurement data analysis of the drop velocities indicates that drops with diameter larger than about 100 to 200 µm experience velocity slip.

SLD↗

NASA NTRS2024

Finite Element Simulation of the Direct Energy Deposition using Comsol Multiphysics

Direct Energy Deposition (DED) is an emerging technology extensively employed in metal Additive Manufacturing (AM). Despite its widespread industrial application, mathematical modeling in this domain remains challenging. This complexity arises from the intricate nature of the modeling approach and the nonlinear behavior of material parameters across a broad temperature range. Consequently, experimentalists often resort to a trial-and-error method to achieve structures with desired properties. However, this approach can be time-consuming and may not always yield parts with the requisite characteristics, highlighting the necessity for mathematical modeling to enhance manufacturing success. This study focuses on thin-walled manufacturing with a single bead thickness, adjusting laser parameters to produce such structures. The laser cladding speed, typical for DED manufacturing, is considered to be on the order of centimeters per second. The various wall thicknesses and heights are explored to discern the general characteristics of walls manufactured via this DED approach. Our modeling approach diverges from the conventional DED modeling based on activation-deactivation of predefined mesh domains, commonly implemented in many finite element codes. Instead, a method is proposed that effectively models layer cladding and melt pool dynamics, enabling predictions of the microstructure in the resulting structures. The formation mechanisms of cellular, dendritic columnar, and stray (equiaxed) grains, which arise from the interplay between nucleation and growth from the surface is analyzed. The study also examines the feasibility of microstructure formation to demonstrate the various thermal characteristics inherent in wall manufacturing. Our results illustrate how different process parameters influence the temperature gradient and cooling rate of the molten pool, subsequently affecting the primary dendrite arm spacing (PDAS). This modeling technique allows for the investigation of diverse thermal conditions, facilitating the prediction of microstructure and residual stresses in the manufactured parts.

modeling↗

NASA NTRS1985

Effect of Undercooling in a Low-Gravity Containerless Environment on the Structure and Properties of Alloys

The 30 meter and 100 meter drop tubes at the Marshall Space Flight Center offer a unique opportunity to study solidification in a containerless, microgravity environment. Samples are melted in a furnace at the top of the drop tube and solidify during a 4.5 second free fall in the 100 meter drop tube or a 2.6 second free fall in the 30 meter drop tube. The cooling rate obtained in the drop tubes is lower than cooling rates in atomization and splat-quenching processes. Decoupling the rapid solidification process allows the study of the effects of undercooling and recalescence on alloy morphologies. The research therefore has a three-fold purpose. The first is examination of the limits of undercooling of niobium and niobium-base alloys in the drop tube. The second purpose is the observation of microstructures resulting from the solidification of samples at large undercoolings and moderate cooling rates. The third purpose is the observation of metastable phase formation in highly undercooled samples.

Bayuzick, R. J.↗

NASA NTRS2001

The Effect of the Wall Contact and Post-Growth C001-Down on Defects in CdTe Crystals Grown by Contactless PVT

In crystal growth, the quality of the final material may depend, among other factors, on its interaction with the walls of the ampoule during and after the growth, and on the rate of the crystal cool-down at the end of ate the process. To investigate the above phenomena, a series of CdTe crystal growth processes was carried out, The crystals were grown by physical vapor transport without contact with the side walls of the silica glass ampoules, applying the Low Supersaturation Nucleation technique. The source temperature was 930 C, the undercooling was a few degrees. The crystals, having the diameter of 25 mm, grew at the rate of a few mm per day. The post-growth cool-down to the room temperature was conducted at different rates, and lasted from a few minutes to four days. The crystals were characterized using chemical etching low temperature luminescence, and Synchrotron White Beam X-ray Topography techniques. The dislocation (etch pit) density was measured and its distribution was analyzed by comparison with Poisson curves and with the Normalized Radial Distribution Correlation Function. It was found that the contact of the crystal with silica leads to a strain field and high (in the 105 sq cm range) dislocation (etch pit) density. Similar defect concentrations were found in crystals subjected to fast post-growth cool-down. Typical EPD values for lower cool-down rates and in regions not affected by wall interactions are in the lower 10(exp 4) sq cm range. In some areas the actual dislocation density was about 10(exp 3) sq cm or even less. No apparent effect of the cool-down rate on polygonization was observed. A fine structure could be discerned in low-temperature PL spectra of crystals with low dislocation density.

Palosz, W.↗

DOE OSTI2022

The Influence of Environment on Post-Detonation Chemistry and Debris Formation (Abbreviated Final Report: 20-SI-006)

Predicting, responding to, or interpreting the chemical record preserved in debris derived from nuclear events can be challenging due to chemical fractionation. Chemical fractionation is where different species of the evolving radionuclide inventory segregate and/or are lost from the system over the timescales of debris formation. Both historic data and recent research suggest that the interaction and character of the local environment may exert controls on chemical fractionation by influencing the cooling and evolution of the associated fireball as well as the composition of the vapor term and resultant speciation. Prior to this work, an integrated platform permitting dynamic and concurrent consideration of physical and chemical evolution of early time post-detonation event environments did not exist. Our work merged historic data and experimental approaches to support development of a computational framework able to simulate fundamental processes (e.g., entrainment of local environment, oxidation chemistry, and cooling time scales) that may perturb the radionuclide inventory captured in post-detonation debris. Work with historic debris confirmed that entrained environmental material affect debris composition, structure, and radionuclide incorporation. Complementary work utilizing a readily controllable and tunable benchtop setup (a plasma flow reactor) simulated the late cooling of a nuclear fireball (e.g., T < 6000 K) and bounded the sensitivity of actinide speciation and particle size distribution to variations in oxygen concentration and cooling rates. Concurrent laser ablation and laser heating experiments were used to investigate the chemistry and physics of processes occurring in vaporized and/or rapidly heated actinides and other elements in the presence of oxygen. A more computationally efficient microphysical model was developed for predicting and evolving size distributions of particles forming from mixed vapor terms and simulating particle formation processes under a variety of extreme conditions. Continued study of historic nuclear event film confirmed that shockwave data and physics codes agree to within the uncertainty of the data. Good agreement was achieved for thermal emission from an airburst, however the paucity of low-temperature molecular opacity data for mixtures of air, bomb debris, entrained dirt, and water vapor complicate agreement for more elaborate scenarios. A multiphysics code (ALE3D) was modified to bring the necessary physics and chemistry, including these new data and insights, onto a single platform. Code development included improved initialization of large physical systems, modernization of chemistry capabilities, and modifications to enable inclusion of particle transport.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2022

Mild hybridisation of turboprop engine with high-power-density integrated electric drives

Here this paper shares with the aerospace community a case study of turboprop mild hybridisation using a recently developed integrated drive system in the University of Nottingham, UK, within the ACHIEVE project under EU H2020 CleanSky 2 program (project No. 737814). The developed drive system enables green taxiing of a turboprop aircraft while on the ground with its engine off, and as an electrical generator when the turboprop is in the air. The entire system is designed to be able to integrate within the power auxiliary gear box (PAGB) of a turboprop aircraft. Some of the key features of the developed system include a high-speed permanent magnet machine (up to 14,200rpm) with dual three-phase design, SiC-based high power density (11.8kW/L for the power converter, 35.3kW/L and 7.2kW/kg for the machine active parts), integrated cooling design for high-temperature operation (>130°C ambient temperature), fault tolerance consideration with dual channel operation capabilities and sensorless control for entire operational conditions. This paper is giving an overview of the design process of the electrical machine, power converters, and its cooling of the entire drive. Numerical analysis (FEM and CFD) and some experimental results are presented to demonstrate the effectiveness and the desired performance of the developed integrated drive system.

42 ENGINEERING↗

NASA NTRS2005

Improved Electrolytic Hydrogen Peroxide Generator

An improved apparatus for the electrolytic generation of hydrogen peroxide dissolved in water has been developed. The apparatus is a prototype of H2O2 generators for the safe and effective sterilization of water, sterilization of equipment in contact with water, and other applications in which there is need for hydrogen peroxide at low concentration as an oxidant. Potential applications for electrolytic H2O2 generators include purification of water for drinking and for use in industrial processes, sanitation for hospitals and biotechnological industries, inhibition and removal of biofouling in heat exchangers, cooling towers, filtration units, and the treatment of wastewater by use of advanced oxidation processes that are promoted by H2O2.

James, Patrick I.↗

DOE OSTI2025

On the validity and limitations of 1D model for heat and mass transfer performance evaluation in a multilayer binder-free desiccant dehumidifier: isothermal dehumidification with internal cooling

Efficient humidity control is essential for maintaining indoor thermal comfort, yet conventional vapor-compression-based dehumidifiers are energy-intensive. Employing separate sensible and latent cooling through desiccant-coated heat exchangers (DCHEs) combined with evaporative coolers offers energy savings of up to 80 % compared to conventional systems. However, the dehumidification performance of DCHEs remains limited due to the use of polymer binders for coating desiccant materials onto heat exchange surfaces. In our previous study, we developed a multilayer fixed-bed binder-free desiccant dehumidifier (MFBDD) that demonstrated high dehumidification capacity and low pressure drop compared to rotary desiccant wheels. Nevertheless, its potential for further enhancement through internal cooling and the use of step-shaped adsorption isotherms has not been explored. In this study, a physics-based one-dimensional (1D) transient model is developed and validated to capture the coupled heat and mass transfer processes in the MFBDD and extended to simulate internal cooling using a high-capacity composite metal–organic framework, MIL-101/GO-6 (water uptake ≈1.6 g/g within 35–47 % RH). The model enables detailed analysis of local air and bed temperature dynamics and quantifies how internal cooling affects the dehumidification performance under a wide range of operating conditions. Results show that integrating internal cooling and using MIL-101/GO-6 enhance mass adsorbed, moisture removal capacity, and dehumidification effectiveness by 50 %–99 % compared with the M.S. Gel baseline. The study further reveals that achieving near-isothermal operation requires simultaneous enhancement of the convective heat transfer coefficient and heat exchange surface area. In conclusion, this work provides the first detailed physical insight into the interplay between internal cooling and step-shaped isotherms in a binder-free desiccant device and establishes a validated modeling framework for scaling up and system-level performance evaluation of next-generation energy-efficient dehumidification systems.

Heat and mass transfer↗

DOE OSTI2020

Hail tower for gas-vapor separations

A device and process for removing vapors from a gas is disclosed. A tower is provided. Sub-cooled pellets are distributed by the solids distributor across a horizontal cross-section of the tower. A process gas, comprising a product vapor, passes through the gas inlet. The product vapor and the sub-cooled pellets comprise the same material. The product vapor and the sub-cooled pellets agglomerate as the product vapor desublimates onto the sub-cooled pellets, forming product pellets and a vapor-depleted gas. A crushing device, a screening device, and a solids heat exchanger are provided. A portion of the product pellets are recycled as sub-cooled pellets to the solids distributor by crushing and screening the portion of the product pellets to the size distribution of the sub-cooled pellets and cooling the portion of the product pellets to produce the sub-cooled pellets.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

MSR Fuel Salt Qualification Methodology

This report documents the continuing activities at Oak Ridge National Laboratory (ORNL) in support of the US Nuclear Regulatory Commission (NRC) efforts to develop an efficient, appropriate process for liquid fuel salt system qualification. Fuel qualification for salt-cooled molten salt reactors (MSRs) is part of the ongoing coated particle fuel qualification effort. Fuel qualification is a process which provides high confidence that physical and chemical behavior of fuel is sufficiently understood so that it can be adequately modeled for both normal and accident conditions, reflecting the role of the fuel design in the overall safety of the facility. Uncertainties are defined so that calculated fission product releases include the appropriate margins to ensure conservative calculation of radiological dose consequences. The initial phase of ORNL’s activities is documented in ORNL/LTR-2018/1045 Molten Salt Reactor Fuel Qualification Considerations and Challenges.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS2003

Continuous Magnetic Refrigerators for Cooling in the 0.05 to 10 K Range: Progress and Future Development

Low temperature refrigeration is an increasingly vital technology for NASA s Space Science program since most detectors being developed for x-ray, IR and sub-millimeter missions must be cooled to below 100 mK in order to meet the requirements for energy and spatial resolution. For space applications, magnetic refrigeration has an inherent advantage over alternative techniques because it does not depend on gravity. Adiabatic demagnetization refrigerators, or ADRs, are relatively simple, solid state devices. The basic elements are a magnetocaloric refrigerant (usually an encapsulated paramagnetic salt) located in the bore of a superconducting magne$, and a heat switch linking the salt to a heat sink. The alignment of magnetic spins with the magnetic field causes the refrigerant to warm as the magnetic field increases and cool as the field decreases. Thus the simple process of magnetizing the refrigerant to high field with the heat switch closed, then demagnetizing it with the heat switch open allows one to obtain temperatures well below 100 mK using a heat sink as warm as 4.2 K. The refrigerant can maintain a low temperature for a length of time depending on the applied and parasitic heat loads, its mass, and the initial magnetic field strength. Typically ADRs are designed for 12-24 hours of hold time, after which they must be warmed up and recycled. The drawback to single-shot ADRs is that the cooling power per unit mass is relatively low. Refrigerants that are suitable for low temperature operation necessarily have low magnetic ion density, and therefore low entropy density. Since ADRs store entropy, systems with even modest cooling powers (a few microwatts) at temperatures below 100 mK tend to be massive, averaging 10-15 kg.

Shirron, Peter↗

DOE OSTI2021

Urca Cooling in Neutron Star Crusts and Oceans: Effects of Nuclear Excitations

We report the excited-state structure of atomic nuclei can modify nuclear processes in stellar environments. In this Letter, we study the influence of nuclear excitations on Urca cooling (repeated back-and-forth β decay and electron capture in a pair of nuclear isotopes) in the crust and ocean of neutron stars. We provide for the first time an expression for Urca process neutrino luminosity which accounts for a thermal Boltzmann distribution of excited states in both members of an Urca pair. We use our new formula with state-of-the-art nuclear structure inputs to compute neutrino luminosities of candidate Urca cooling pairs. Our nuclear inputs consist of the latest experimental data supplemented with calculations using the projected shell model. We show that, in contrast to previous results that only consider the ground states of both nuclei in the pair, our calculated neutrino luminosities for different Urca pairs vary sensitively with the environment temperature and can be radically different from those obtained in the one-transition approximation. We find that nuclear excitations can lead to an enhancement in total Urca neutrino luminosities in the accreted neutron star crust by about 5 times as compared with the previous Urca results, which is expected to cause significant observational effects.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Cellular fluidics

The natural world provides many examples of multiphase transport and reaction processes that have been optimized by evolution. These phenomena take place at multiple length and time scales and typically include gas–liquid–solid interfaces and capillary phenomena in porous media. Many biological and living systems have evolved to optimize fluidic transport. However, living things are exceptionally complex and very difficult to replicate, and human-made microfluidic devices (which are typically planar and enclosed) are highly limited for multiphase process engineering. In this paper, we introduce the concept of cellular fluidics: a platform of unit-cell-based, three-dimensional structures—enabled by emerging 3D printing methods—for the deterministic control of multiphase flow, transport and reaction processes. We show that flow in these structures can be ‘programmed’ through architected design of cell type, size and relative density. We demonstrate gas–liquid transport processes such as transpiration and absorption, using evaporative cooling and CO 2 capture as examples. We design and demonstrate preferential liquid and gas transport pathways in three-dimensional cellular fluidic devices with capillary-driven and actively pumped liquid flow, and present examples of selective metallization of pre-programmed patterns. Our results show that the design and fabrication of architected cellular materials, coupled with analytical and numerical predictions of steady-state and dynamic behaviour of multiphase interfaces, provide deterministic control of fluidic transport in three dimensions. Cellular fluidics may transform the design space for spatial and temporal control of multiphase transport and reaction processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2020

Atacama Compact Array Measurements of the Molecular Mass in the NGC 5044 Cooling-Flow Group

The fate of cooling gas in the centers of galaxy clusters and groups is still not well understood, as is also the case for the complex processes of triggering star formation in central dominant galaxies, reheating of cooled gas by active galactic nuclei (AGN), and the triggering or “feeding” of supermassive black hole outbursts. We present CO observations of the early-type galaxy NGC 5044, which resides at the center of an X-ray bright group with a moderate cooling flow. For our analysis we combine CO(2−1) data from the 7 m antennae of the Atacama Compact Array (ACA) and the ACA total power array (TP). We demonstrate, using the 7 m array data, that we can recover the total flux inferred from IRAM 30 m single-dish observations, which corresponds to a total molecular mass of about 4 × 10(exp 7) M⨀ Most of the recovered flux is blueshifted with respect to the galaxy rest frame and is extended on kiloparsec-scales, suggesting low filling factor dispersed clouds. We find eight concentrations of molecular gas out to a radius of 10” (1.5 kpc), which we identify with giant molecular clouds. The total molecular gas mass is more centrally concentrated than the X-ray emitting gas but is extended in the northeast-southwest direction beyond the IRAM 30 m beam. We also compare the spatial extent of the molecular gas to the Hα emission: The CO emission coincides with the very bright Hα region in the center. We do not detect CO emission in the fainter Hα regions. Furthermore, we find two CO absorption features spatially located at the center of the galaxy, within 5 pc projected distance of the AGN, infalling at 255 and 265 km s(exp −1) relative to the AGN. This indicates that the two giant molecular clouds seen in absorption are most likely within the sphere of influence of the supermassive black hole.

Galaxy clusters↗

NASA NTRS1993

Mixing and transient interface condensation of a liquid hydrogen tank

Experiments were conducted to investigate the effect of axial jet-induced mixing on the pressure reduction of a thermally stratified liquid hydrogen tank. The tank was nearly cylindrical, having a volume of about 0.144 cu m with 0.559 m in diameter and 0.711 m long. A mixer/pump unit, which had a jet nozzle outlet of 0.0221 m in diameter was located 0.178 m from the tank bottom and was installed inside the tank to generate the axial jet mixing and tank fluid circulation. The liquid fill and jet flow rate ranged from 42 to 85 percent (by volume) and 0.409 to 2.43 cu m/hr, respectively. Mixing tests began with the tank pressure ranging from 187.5 to 238.5 kPa at which the thermal stratification results in 4.9 to 6.2 K liquid sub cooling. The mixing time and transient vapor condensation rate at the liquid-vapor interface are determined. Two mixing time correlations, based on the thermal equilibrium and pressure equilibrium, are developed. Both mixing time correlations are expressed as functions of system and buoyancy parameters and compared well with other experimental data. The steady state condensation rate correlation of Sonin et al. based on steam-water data is modified and expressed as a function of jet subcooling. The limited liquid hydrogen data of the present study shows that the modified steady state condensation rate correlation may be used to predict the transient condensation rate in a mixing process if the instantaneous values of jet sub cooling and turbulence intensity at the interface are employed.

Lin, C. S.↗

DOE OSTI2024

Design and Cooling Performance of Additively Manufactured Ceramic Turbine Vanes

Ceramic materials are of significant interest in aviation and power generation gas turbine engines due to their low density and ability to withstand high temperatures. Increased cycle thermal efficiency and higher specific power output is possible by incorporating ceramic components that enable high turbine inlet temperatures and lower required cooling airflow levels. However, ceramics can be difficult and costly to form into the complex shapes used in gas turbine components, often requiring specialized multi-step processes. Furthermore, ceramic components in the hottest areas of a gas turbine, such as vanes or blade shroud seals, will still likely require cooling which is challenging to implement in conventional ceramic manufacturing approaches. Therefore, this study presents a multidisciplinary approach that investigates the design, fabrication, and overall cooling effectiveness evaluation of additively manufactured (AM), polymer derived ceramic (PDC) turbine vanes. A thermo-mechanically optimized vane design was generated, ceramic additive manufacturing of the complex cooling configuration was developed, and quantification of the increase in overall cooling effectiveness was performed in a 1X scale, high-speed facility using infrared thermography. This study produced a PDC AM process, capable of printing complex internal cooling schemes in 1X scale turbine vanes. Furthermore, it was found that the optimized vane more than doubled the overall cooling effectiveness observed in the baseline design, which reasonably agreed with thermomechanical optimization model predictions. Additionally, the optimized ceramic vane outperformed an identical metal vane, in terms of area averaged cooling effectiveness, suggesting that the ceramic vane could operate at reduced coolant flowrates to achieve comparable levels of cooling performance.

Reynolds number↗