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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Assessment of asymmetrical rheological behavior of cementitious material for 3D printing application

Among the multiplicity of construction methods based on digital concrete technologies, the most common one remains the extrusion-based process. Two opposed strategies have been developed in order to print a concrete structure using extrusion: the first one emphasizes the ease-of-pumping of material which is massively accelerated to ensure the stability of the structure, when leaving the extruder; the second one uses a firm mortar able to sustain the own weight of the structure during the printing, without requiring any accelerator. Both methods have their pros and cons and don't imply the same rheological requirements. Most of the recent literature assumes that both types of material (fluid and firm) follow the same trend of behavior and obey to the Von Mises plasticity criterion, while it has been demonstrated that firm cement-based materials can exhibit a pressure dependent behavior. Moreover, rheological study is mainly based on shear rheometry, while the extrusion-based printing process requires a description of the rheological behavior in compression to predict the global stability of the structure, and in tension to prevent cracks formation. This paper investigates the fresh behavior of cement paste and mortar under different solicitations (shear, compression, tension) for different water to cement ratios. The analysis of these results allows to describe the transition between a ductile fluid material (symmetrical in tension and compression) that obeys to a Von Mises plasticity criterion, and a brittle and firm material (asymmetrical in tension and compression) that requires a pressure dependent plasticity criterion in order to predict its strength under a given solicitation.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Structural and vibrational behavior of 2 H -NbSe 2 at high pressures

In this work, the high-pressure structural and vibrational properties of a layered transition metal dichalcogenide 2 H -NbSe 2 were investigated using single-crystal x-ray diffraction and Raman spectroscopy, demonstrating its structural stability up to 35 GPa. The lattice compressibility changes character from being highly anisotropic at low pressures to largely isotropic at high pressures. Concomitantly, the interatomic bonds demonstrate highly anisotropic compression behavior with the Se-Se interlayer bonds compressing by >20%, while the intramolecular Se-Se distance shows a nonmonotonic pressure dependence with a maximum at-12 GPa. The nearest-neighbor central force lattice vibrational model yields pressure dependencies of the interatomic forces in qualitative agreement with bond length compression, providing insight into the vibrational properties of 2 H -NbSe 2 at high pressures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

High-pressure elasticity and equation of state of the fluoroelastomer Viton® A-500

Viton® A is a semi-crystalline copolymer of polyvinylidene fluoride and hexafluoropropylene used in various engineering applications due to its mechanical properties and chemical inertness. In situ ultrasonic spectroscopy and x-ray radiography measurements were performed in a Paris–Edinburgh press to measure the pressure dependence of the transverse and longitudinal acoustic velocity of the fluoroelastomer A-500 from 2.7 to 5.7 GPa at 296 K. In addition, we performed high-pressure Brillouin scattering measurements to obtain acoustic velocities from ambient pressure to 5.7 GPa to supplement the ultrasonic measurements, especially at low pressures. The acoustic velocities were then used to calculate a pressure–volume (P–V) equation of state, the bulk and shear moduli, and the Poisson's ratio. These quantities are compared with the reported pressure-dependent properties of related polymers over this range of pressures.

Acoustical properties↗
DOE OSTI2022

Predicted Melt Curve and Liquid Shear Viscosity of RDX up to 30 GPa

Recent grain-scale simulations of HMX and TATB have shown that predictions for hot spot formation in high explosives are particularly sensitive to accurate determinations of the pressure-dependent melt curve and the shear viscosity of the liquid phase. These physics terms are poorly constrained beyond ambient pressure for the explosive RDX. Here we adopt an all-atom modeling approach using molecular dynamics (MD) simulations to predict the melt curve of RDX near to detonation conditions (30 GPa) and determine the shear viscosity of the liquid as a function of temperature and pressure above the melt curve. Phase-coexistence simulations were used to determine the melt curve, which is predicted to vary by almost 1100 K as the pressure increases from 0 GPa to 30 GPa. Equilibrium MD simulations and the Green-Kubo formalism were used to obtain the pressure-temperature-dependent shear viscosity. The shear viscosity of RDX is predicted to be of similar magnitude to the viscosity of TATB at low GPa-range pressures, and to be roughly an order of magnitude lower than the viscosity of HMX. The temperature dependence of the shear viscosity is Arrhenius at a given pressure, and the exponential pre-factor and activation term exhibit a strong, yet complicated, pressure dependence. An empirical pressure-temperature dependent function for RDX shear viscosity is developed that simultaneously captures a wide range of MD predictions while taking an analytic form that extrapolates smoothly beyond the fitted regime. The relative strength of the pressure and temperature dependencies of these two physics terms is found to be of similar magnitude for RDX, HMX, and TATB, which motivates incorporating these results in future RDX grain-scale modeling.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Deflagration to Detonation Transition Update: XDDT Code Modularization

A legacy FORTRAN 77 implementation of the Baer–Nunziato two-phase mixture theory for deflagration-to-detonation transition (DDT) in reactive granular materials—hereafter the XDDT (eXplosive DDT) code—has been modularized to Fortran 90 with modular structure, external input files, and adaptive mesh capability. During validation, two code defects were identified and corrected: an inconsistency in the nodal solid pressure evaluation and a nonphysical burn-front tracking criterion. The ignition criterion was also corrected to use the granular surface temperature from the interface heat transfer model, matching the original Baer implementation. An initial attempt to validate against Figure 3 of the original Baer and Nunziato (1986) paper revealed that the code’s detonation velocity on a 201-node mesh (5.5 km/s) was approximately 21% below the expected Chapman–Jouguet value for 70% TMD HMX (∼7 km/s). Validation was redirected to the piston-driven DDT experiments of McAfee et al. (1989), Shot B-9036, for which well-characterized ionization-pin data are available. With the compaction-burn coefficient calibrated to 𝐶 𝛼 = 75, the XDDT code reproduces the DDT transition time to within 0.4% and produces a steady-state detonation velocity within 4% of the McAfee experimental value of 6.36 km/s. The burn model was generalized to support pressure-dependent exponents, enabling application to nitrocellulose-based ball propellants (TS3659) with a cube-root pressure dependence. Validation against the Sandusky/Baer PDC82 piston-impact experiment yielded a reactive wave velocity of 2.3–2.8 km/s, in good agreement with the experimental value of ∼2.2 km/s, and wave coalescence within 5% of the experimental timing. The mathematical model, input parameter requirements, and a roadmap for extending XDDT to PETN with an autocatalytic burn model are presented.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
NASA NTRS2020

An Improved Plastically Dilatant Unified Viscoplastic Constitutive Formulation for Multiscale Analysis of Polymer Matrix Composites Under High Strain Rate Loading

Polymer matrix composites are commonly used to fabricate energy-absorbing structures expected to experience impact loading. As such, a detailed understanding of the dynamic response of the constituent materials is necessary. Since the rate, temperature, and pressure dependence of carbon fiber reinforced polymer matrix composites are primarily manifestations of the rate, temperature, and pressure dependence of the polymer matrix, it is crucial that the constitutive behavior of the matrix be accurately characterized. In this work, an existing unified viscoplastic constitutive formulation is extended to ensure thermodynamic consistency and to more accurately account for the tension-compression asymmetry observed in the response of polymeric materials. A new plastic potential function is proposed, and elementary loading conditions are utilized to determine relations between model constants to ensure nonnegative plastic dissipation, a necessary thermodynamic requirement. Expressions for plastic Poisson’s ratios are derived and are bounded by enforcing nonnegative plastic dissipation. The model is calibrated against available experimental data from tests conducted over a range of strain rates, temperatures, and loading cases on a representative thermoset epoxy; good correlation between simulations and experimental data is obtained. Temperature rises due to the conversion of plastic work to heat are computed via the adiabatic heat energy equation. The viscoplastic polymer model is then used as a constitutive model in the generalized method of cells micromechanics theory to investigate the effects of matrix adiabatic heating on the high strain rate response of a unidirectional composite. The thermodynamic consistency of the model ensures plastic dissipation can only cause an increase in temperature. Simulation results indicate that significant thermal softening due to the conversion of plastic work to heat is observed in the composite for matrix dominated deformation modes.

Impact loading↗
DOE OSTI2026

Methyl formate oxidation kinetics up to 100 atm

Methyl formate (MF, CH3OCHO), the simplest ester, is a representative oxygenated fuel with high oxygen content, and low sooting tendency. However, its oxidation behavior under high-pressure and intermediate-temperature conditions remains insufficiently understood, especially where low-temperature peroxy radical chemistry, methanol chemistry, and pressure-dependent reaction pathways play a critical role. In this study, MF oxidation experiments were conducted in the Princeton supercritical-pressure jet-stirred reactor (SP-JSR) at 20 and 100 atm over the temperature range of 400–950 K under both fuel-lean and fuel-rich conditions. Based on the experimental results, an updated HP-Mech was developed by incorporating previous MF sub-mechanisms, expanded low-temperature peroxy pathways, and evaluated pressure-dependent decomposition kinetics. The newly updated HP-Mech shows greatly improved performance in predicting the onset temperature, the key intermediate species fractions, methanol formation, and the progression of MF oxidation across all the experimental conditions. Path flux analysis indicates that MF consumption at the onset stage is dominated by H-abstraction at the methyl site, forming CH2OCHO radicals that lead to the formation and isomerization of O2CH2OCHO, driving low-temperature chain propagation. Moreover, H-abstraction at the formate site forms CH3OCO radicals that preferentially decompose to CH3, initiating the methanol formation pathway linked to CH3O2 and HO2 chemistry. At the same time, HO2 formation is strongly coupled to MF oxidation through multiple MF-derived radical pathways. HCO originates from MF oxidation and acts as a key coupling species linking fuel consumption to HO2 buildup, especially under high-pressure and intermediate-temperature conditions. In addition to this dominant channel, supplementary HO2 formation pathways involving CH3, CH3O, CH2OH, and CH3O2 reacting with O2 further connect methanol chemistry and oxygenated radical chemistry to the HO2 pool, indicating the central role of HO2 in governing MF oxidation. Sensitivity analysis identifies MF with OH/HO2/CH3O2 reactions and the HO2/H2O2/OH sequence as the key factors controlling reactivity in the high-pressure and intermediate-temperature regime. MF directly reacts with OH/HO2/CH3O2 to consume the fuel and produce reactive radicals like CH2OCHO and CH3OCO that undergo subsequent oxidation pathways. Moreover, HO2 recombination suppresses oxidation at lower temperatures, while thermal decomposition of H2O2 accelerates OH production and promotes fuel consumption as temperature increases. The direct formation of active OH from HO2 radicals further completes the mechanism, improving its prediction especially during the oxidation onset stage.

Low-temperature Chemistry↗
NASA NTRS2010

High Pressure/Temperature Metal Silicate Partitioning of Tungsten

The behavior of chemical elements during metal/silicate segregation and their resulting distribution in Earth's mantle and core provide insight into core formation processes. Experimental determination of partition coefficients allows calculations of element distributions that can be compared to accepted values of element abundances in the silicate (mantle) and metallic (core) portions of the Earth. Tungsten (W) is a moderately siderophile element and thus preferentially partitions into metal versus silicate under many planetary conditions. The partitioning behavior has been shown to vary with temperature, silicate composition, oxygen fugacity, and pressure. Most of the previous work on W partitioning has been conducted at 1-bar conditions or at relatively low pressures, i.e. <10 GPa, and in two cases at or near 20 GPa. According to those data, the stronger influences on the distribution coefficient of W are temperature, composition, and oxygen fugacity with a relatively slight influence in pressure. Predictions based on extrapolation of existing data and parameterizations suggest an increased pressured dependence on metal/ silicate partitioning of W at higher pressures 5. However, the dependence on pressure is not as well constrained as T, fO2, and silicate composition. This poses a problem because proposed equilibration pressures for core formation range from 27 to 50 GPa, falling well outside the experimental range, therefore requiring exptrapolation of a parametereized model. Higher pressure data are needed to improve our understanding of W partitioning at these more extreme conditions.

Shofner, G. A.↗
NASA NTRS1989

Optical evidence for the metallization of Xenon at 132(5) GPa

Xe has been compressed in a diamond-anvil cell to approximately 200 GPa. The metallization of Xe by band-gap closure was investigated by obtaining optical data in both the metallic and insulating states. In the metallic state, the pressure dependence of the plasma frequency was determined from absorption data fitted with a free-electron model. In the insulating state, the pressure dependence of the band gap was determined from absorption data fitted with an indirect-band-gap model. The optical data indicate that the insulator-to-metal transition in Xe occurs at 132(5) GPa.

Goettel, Kenneth A.↗
DOE OSTI2023

Sound Velocity and Equation of State of Ballistic Gelatin by Brillouin Scattering

Brillouin scattering spectroscopy with diamond anvil cells was used by measuring the pressure dependence of the sound-relevant polymer material, glass-forming liquid, and H 2 O (water and ice VII) velocities of the material from ambient pressure to 12 GPa at room temperature. Measurements of 20%, 10%, and 4% gelatin solutions were performed. For comparison purposes, we also measured the pressure dependence of the sound velocity of animal tissue up to 10 GPa. We analyzed the Brillouin data using the Tait and Vinet equations of state. We discussed the possible influence of frequency dispersion on bulk modulus at low pressure. We compared the elastic moduli obtained for gelatin to those of several other polymers.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Spectroscopic evidence for the Fe3+ spin transition in iron-bearing δ-AlOOH at high pressure

δ-AlOOH has emerged as a promising candidate for water storage in the lower mantle and could have delivered water into the bottom of the mantle. To date, it still remains unclear how the presence of iron affects its elastic, rheological, vibrational, and transport properties, especially across the spin crossover. In this study, we conducted high-pressure X-ray emission spectroscopy experiments on a δ-(Al 0.85 Fe 0.15 ) OOH sample up to 53 GPa using silicone oil as the pressure transmitting medium in a diamond-anvil cell. We also carried out laser Raman measurements on δ-(Al 0.85 Fe 0.15 )OOH and δ-(Al 0.52 Fe 0.48 )OOH up to 57 and 62 GPa, respectively, using neon as the pressure-transmitting medium. Evolution of Raman spectra of δ-(Al 0.85 Fe 0.15 )OOH with pressure shows two new bands at 226 and 632 cm –1 at 6.0 GPa, in agreement with the transition from an ordered ( P 2 1 nm ) to a disordered hydrogen bonding structure ( Pnnm ) for δ-AlOOH. Similarly, the two new Raman bands at 155 and 539 cm –1 appear in δ-(Al 0.52 Fe 0.48 )OOH between 8.5 and 15.8 GPa, indicating that the incorporation of 48 mol% FeOOH could postpone the order-disorder transition upon compression. On the other hand, the satellite peak ( K β') intensity of δ-(Al 0.85 Fe 0.15 )OOH starts to decrease at ~30 GPa and it disappears completely at 42 GPa. That is, δ-(Al 0.85 Fe 0.15 )OOH undergoes a gradual electronic spin-pairing transition at 30–42 GPa. Furthermore, the pressure dependence of Raman shifts of δ-(Al 0.85 Fe 0.15 )OOH discontinuously decreases at 32–37 GPa, suggesting that the improved hydrostaticity by the use of neon pressure medium could lead to a relatively narrow spin crossover. Notably, the pressure dependence of Raman shifts and optical color of δ-(Al 0.52 Fe 0.48 )OOH dramatically change at 41–45 GPa, suggesting that it probably undergoes a relatively sharp spin transition in the neon pressure medium. Together with literature data on the solid solutions between δ-AlOOH and ε-FeOOH, we found that the onset pressure of the spin transition in δ-(Al,Fe)OOH increases with increasing FeOOH content. These results shed new insights into the effects of iron on the structural evolution and vibrational properties of δ-AlOOH. The presence of FeOOH in δ-AlOOH can substantially influence its high-pressure behavior and stability at the deep mantle conditions and play an important role in the deep-water cycle

58 GEOSCIENCES↗
DOE OSTI2022

Pressure-temperature phase diagram of CaK ( Fe 1 – x Mn x ) 4 As 4 ( x = 0.024 )

Resistance measurements on single crystals of CaK(Fe 1–x Mn x ) 4 As 4 (x = 0.024) were performed under hydrostatic pressure up to 5.15 GPa. The pressure dependence of the magnetic and superconducting transition temperatures and that of the superconducting upper critical field are reported. Furthermore, our results show that upon increasing pressure, the magnetic transition temperature T N is suppressed, whereas the superconducting transition temperature T c first increases and then decreases, exhibiting a maximum at a pressure p c corresponding to the intersection of the T N (p) and T c (p) lines. In addition, a minimum in the normalized slope of the superconducting upper critical field as well as a change in the pressure dependence of the inferred superconducting coherence length are observed at p c , suggesting a difference in the Fermi surface of the paramagnetic and antiferromagnetic states. Finally, CaK(Fe 1–x Mn x ) 4 As 4 (x = 0.024) likely goes through a half-collapsed tetragonal phase transition at ~4.3 GPa, further demonstrating that the half-collapsed tetragonal transition pressure in the CaKFe 4 As 4 system is relatively insensitive to transition metal substitution.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

A non-isothermal breakage-damage model for plastic-bonded granular materials incorporating temperature, pressure, and rate dependencies

Plastic-bonded granular materials (PBM) are widely used in industrial sectors, including building construction, abrasive applications, and defense applications such as plastic-bonded explosives. The mechanical behavior of PBM is highly nonlinear, irreversible, rate dependent, and temperature sensitive governed by various micromechanical attributions such as grain crushing and binder damage. This paper presents a thermodynamically consistent, microstructure-informed constitutive model to capture these characteristic behaviors of PBM. Key features of the model include a breakage internal variable to upscale the grain-scale information to the continuum level and to predict grain size evolution under mechanical loading. In addition, a damage internal state variable is introduced to account for the damage, deterioration, and debonding of the binder matrix upon loading. Temperature is taken as a fundamental external state variable to handle non-isothermal loading paths. The proposed model is able to capture with good accuracy several important aspects of the mechanical properties of PBM, such as pressure-dependent elasticity, pressure-dependent yield strength, brittle-to-ductile transition, temperature dependency, and rate dependency in the post-yielding regime. Furthermore, the model is validated against multiple published datasets obtained from confined and unconfined compression tests, covering various PBM compositions, confining pressures, temperatures, and strain rates.

Breakage↗
DOE OSTI2021

Prediction of crystal structures and motifs in the Fe–Mg–O system at Earth’s core pressures

Abstract Fe, Mg, and O are among the most abundant elements in terrestrial planets. While the behavior of the Fe–O, Mg–O, and Fe–Mg binary systems under pressure have been investigated, there are still very few studies of the Fe–Mg–O ternary system at relevant Earth’s core and super-Earth’s mantle pressures. Here, we use the adaptive genetic algorithm (AGA) to study ternary Fe x Mg y O z phases in a wide range of stoichiometries at 200 GPa and 350 GPa. We discovered three dynamically stable phases with stoichiometries FeMg 2 O 4 , Fe 2 MgO 4, and FeMg 3 O 4 with lower enthalpy than any known combination of Fe–Mg–O high-pressure compounds at 350 GPa. With the discovery of these phases, we construct the Fe–Mg–O ternary convex hull. We further clarify the composition- and pressure-dependence of structural motifs with the analysis of the AGA-found stable and metastable structures. Analysis of binary and ternary stable phases suggest that O, Mg, or both could stabilize a BCC iron alloy at inner core pressures.

Wang, Renhai↗
DOE OSTI2022

Fluctuations and power-law scaling of dry, frictionless granular rheology near the hard-particle limit

Here the flow of frictionless granular particles is studied with stress-controlled discrete element modeling simulations for systems varying in size from 300 to 100,000 particles. The volume fraction and shear-stress ratio μ are relatively insensitive to system size for a wide range of inertial numbers I. Second-order effects in strain rate, such as normal stress differences, require large system sizes to accurately extract meaningful results, notably a nonmonotonic dependence in the first normal stress difference with strain rate. The rheological response represented by the μ(I) scalar model works well at describing the lower-order aspects of the rheology, except near the quasistatic limit of these stress-controlled flows. The pressure is varied over five decades, and a pressure dependence of the coordination number is observed, which is not captured by the inertial number. Large fluctuations observed for small systems N≤1000 near the quasistatic limit can lead to the arrest of flow resulting in challenges to fitting the data to rheological relationships. The inertial number is also insufficient for capturing the pressure-dependent behavior of property fluctuations. Fluctuations in the flow and microstructural properties are measured in both the quasistatic and inertial regimes, including shear stress, pressure, strain rate, normal stress differences, volume fraction, coordination number, and contact fabric anisotropy. The fluctuations in flow properties scale self-similarly with pressure and system size. A transition in the scaling of fluctuations of stress properties and contact fabric anisotropy are measured and proposed as a quantitative identification of the transition from inertial to quasistatic flow.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A directional microcrack damage theory for brittle solids based on continuous hyperplasticity

We present a novel microcrack-damage theory for brittle solids under compression. Instead of using internal variables like zeroth, second or fourth rank damage tensors, the state of material damage is represented by an internal function that encapsulates the information of direction, density and size of microcracks. Just like other internal variables, the evolution of this state function must obey the second law of thermodynamics for arbitrary loading paths. This is done by casting the model in the framework of continuous hyperplasticity and enforcing a non-negative dissipation rate functional. The proposed framework offers predictions on the continuous evolution of microcrack density and the induced material anisotropy along with the macroscopic stress-strain curves. The use of continuous damage function grants the model significantly enhanced resolution in characterizing the direction-dependent response of cracked solids compared to classical models that are based on damage tensors. Two scenarios are considered in developing the theory, one assumes frictionless cracks and the other incorporates friction between crack surfaces. The results highlight that inelasticity, pressure dependence, and loading-unloading hysteresis exhibited by brittle solids are natural consequences of frictional microcracks. The proposed theory offers a generic and versatile framework to upscale micromechanical processes operating at individual crack scale to explain the macroscopic behavior of cracked solids.

Materials Science↗
DOE OSTI2023

Automated reaction kinetics and network exploration (Arkane): A statistical mechanics, thermodynamics, transition state theory, and master equation software

The open-source statistical mechanics software described here, Arkane–Automated Reaction Kinetics and Network Exploration–facilitates computations of thermodynamic properties of chemical species, high-pressure limit reaction rate coefficients, and pressure-dependent rate coefficient over multi-well molecular potential energy surfaces (PES) including the effects of collisional energy transfer on phenomenological kinetics. Arkane can use estimates to fill in information for molecules or reactions where quantum chemistry information is missing. The software solves the internal energy master equation for complex unimolecular reaction systems. Inputs to the software include converged electronic structure computations performed by the user using a variety of supported software packages (Gaussian, Molpro, Orca, TeraChem, Q-Chem, Psi4). The software outputs high-pressure limit rate coefficients and pressure-dependent phenomenological rate coefficients, as well as computed thermodynamic properties (enthalpy, entropy, and constant pressure heat capacity) with added energy corrections. Some of the key features of Arkane include treatment of 1D, 2D or ND hindered internal rotation modes, treatment of free internal rotation modes, quantum tunneling effect consideration, transition state theory (TST) and Rice-Ramsperger-Kassel-Marcus (RRKM) rate coefficient computations, master equation solution with four implemented methods, inverse-Laplace transform of high-pressure limit rate coefficients into the energy domain, energy corrections based on bond-additivity or isodesmic reactions, automated and efficient PES exploration, and PES sensitivity analysis. The present work describes the design of Arkane, how it should be used, and refers to the theory that it employs. Arkane is distributed via the RMG-Py software suite (https://github.com/ReactionMechanismGenerator/RMG-Py).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1997

Cellular Structures in the Flow Over the Flap of a Two-Element Wing

Flow visualization information and time dependent pressure coefficients were recorded for the flow over a two-element wing. The investigation focused on the stall onset; particularly at a condition where the flow is attached on the main element but separated on the flap. At this condition, spanwise separation cells were visible in the flow over the flap, and time dependent pressure data was measured along the centerline of the separation cell. The flow visualizations indicated that the spanwise occurrence of the separation cells depends on the flap (and not wing) aspect ratio.

Yon, Steven A.↗