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At least 1,495 records · Page 83
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Numerical investigation of a fueled pre-chamber spark-ignition natural gas engine

Pre-chamber spark-ignition (PCSI) is a leading advanced ignition concept for internal combustion engines with the potential to enable diesel-like efficiency in medium-duty/heavy-duty (MD/HD) natural gas (NG) engines. By leveraging distributed ignition sources from multiple turbulent jets, the PCSI technology can deliver extremely short combustion duration in ultra-lean mixtures and significantly improve the engine thermal efficiency. However, in the automotive industry there is a lack of adequate science base and predictive simulation tools required for commercial development of PCSI engines. Here, in this study, Reynolds-Average Navier-Stokes simulations are carried out to describe the combustion process in lean-burn NG engines, focusing on the combustion modeling approach. Two combustion models, multi-zone well-stirred reactor (MZ-WSR) and G-equation, are used to simulate the combustion process in an MD NG engine equipped with a fueled-PCSI system for four operating conditions close to the lean operating limit. A skeletal chemical mechanism and a laminar flame speed tabulation are used to compute the combustion accurately. Simulation results are compared with experimental data regarding measured cylinder pressure, heat release rate, and combustion duration. By dividing the PCSI combustion process into four distinct phases, the difference between the two models’ results for each phase is analyzed in detail. The MZ-WSR model overestimates the combustion duration for early flame kernel growth in the pre-chamber due to the lack of a specific formulation to take turbulence-chemistry interaction into account. Despite the prolonged combustion duration and low pressure built-up inside the pre-chamber, the model matches the combustion rate in the main-chamber. In contrast, the G-equation model delivers good agreements for the pre-chamber combustion and turbulent jet-driven combustion processes. However, the model starts to underestimate the combustion rate in the main-chamber, especially under ultra-lean mixture conditions. Finally, improvements are needed for both models to simulate the later combustion stage that occurred in the near-wall regions.

33 ADVANCED PROPULSION SYSTEMS↗
NASA NTRSDate not supplied

Numerical Simulation of Lean Blowout of Alternative Fuels in 7-element Lean Direct Injector

This research presents the result of numerically simulating 7-element swirl-venturi Lean Direct Injector (SV-LDI) lean blowout (LBO) experiments conducted at NASA Glenn Research Center in May of 2019. After simulating a cold flow case to confirm the pressure drop agrees well with the experiment, additional cases with two different fuels (an average jet fuel and a Gevo alcohol-to-jet fuel) from the National Jet Fuels Combustion Program (NJFCP) were computed to numerically determine the LBO condition. The procedure to approach the LBO follows the method used in the experiment where the air mass flow rate is gradually increased while the fuel supply is maintained. Transient history of global heat release rate as a function of air flow rate is presented, as well as temperature contours at different conditions to give a visual representation of the flame state. The Open National Combustion Code (OpenNCC) used in this research adopted reduced HyChem (Hybrid Chemistry) models along with k-LES turbulence model and a Lagrangian spray model that takes into account droplet internal temperature distribution affected by the shear force on the droplet surface. The transport equations and chemical reaction terms are integrated together to enhance conservation of chemical species that are especially important in the near LBO conditions. After showing the computed range of LBO agrees well with the experimental measurements, time averaged solutions of both fuels at their initial condition and at their limiting condition just before LBO are compared in detail to facilitate the understanding of LBO mechanism.

combustion↗
DOE OSTI2021

A nudged hybrid analysis and modeling approach for realtime wake-vortex transport and decay prediction

Here, we put forth a long short-term memory (LSTM) nudging framework for the enhancement of reduced order models (ROMs) of fluid flows utilizing noisy measurements for air traffic improvements. Toward emerging applications of digital twins in aviation, the proposed approach allows for constructing a realtime predictive tool for wake-vortex transport and decay systems. We build on the fact that in realistic application, there are uncertainties in initial and boundary conditions, model parameters, as well as measurements. Moreover, conventional nonlinear ROMs based on Galerkin projection (GROMs) suffer from imperfection and solution instabilities, especially for advection-dominated flows with slow decay in the Kolmogorov n-width. In the presented LSTM nudging (LSTM-N) approach, we fuse forecasts from a combination of imperfect GROM and uncertain state estimates, with sparse Eulerian sensor measurements to provide more reliable predictions in a dynamical data assimilation framework. We illustrate our concept by solving the two-dimensional vorticity transport equation. We investigate the effects of measurements noise and state estimate uncertainty on the performance of the LSTM-N behavior. We also demonstrate that it can sufficiently handle different levels of temporal and spatial measurement sparsity, and offer a huge potential in developing next-generation digital twin technologies for aerospace applications.

42 ENGINEERING↗
DOE OSTI2024

Computational Analysis of Hydraulic Efficiency of Michigan DOT Cover C

Drainage structures are used to capture stormwater runoff in streets and highways in urban environments. These drainage structures, which typically consist of catch basins with grates, inlets, or combination grates/inlets, collect stormwater runoff and discharge through buried conveyance systems. They are strategically placed for public safety in curb and gutter systems to provide efficient drainage of water from roadways and thus reduce the risk of hydroplaning. The performance of drainage structures is measured in terms of hydraulic efficiency, which is defined as the percentage of flow captured by the basin as compared to the total flow drainage to the structure. Understanding of the performance of these drainage structures helps designers properly space inlets to promote an economic design that ensures the safety of the traveling public. The current design methodology used to determine drainage structure follows guidelines established in the current Michigan Department of Transportation (MDOT) Drainage Manual (2006). The guidelines in the MDOT Drainage Manual were modeled after the Federal Highway Administration’s (FHWA) Hydraulic Engineering Circular 22 “Urban Drainage Design” (HEC-22). HEC-22 includes empirically derived equations to calculate the interception capacity of drainage structures for several commonly used grate configurations, such as the parallel bar, curved vane and tilt bar grates, which are based on a research study performed by Burgi et al. in the 1970s. MDOT uses several drainage structures to capture runoff that are detailed as Standard Plans. Many of these drainage structures utilize sinusoidal type grates that are not described in HEC-22. Physical modeling of these structures has been limited, posing the need to have them analyzed to verify their capture efficiency. Current MDOT practice is to assume a similar sized reticuline grate, as described in HEC-22, for capture efficiencies. Until recently, evaluating the hydraulic performance of drainage structures was limited to physical modeling in a hydraulics laboratory. With advances in engineering software and computing power, computational fluid dynamics (CFD) modeling has become a more cost-effective alternative. The Federal Highway Administration (FHWA) provides states the option to evaluate their drainage structures using CFD through the Transportation Pooled Fund Program. This study, “Computational Analysis of Hydraulic Efficiency of Michigan DOT Cover C,” was carried out using the pooled fund. MDOT’s Cover C was chosen as the first test candidate, given its similar sinusoidal pattern to other MDOT grates, but it is typically used for high-volume, higher speed applications. A similar version, Cover CX, is used on interstate highways but does not have traverse bars for bicycle safety. Additional grates may be considered for evaluation in the future.

42 ENGINEERING↗
DOE OSTI2020

As a Matter of State: The Role of Thermodynamics in Magnetohydrodynamic Turbulence

Turbulence simulations play a key role in advancing the general understanding of the physical properties of turbulence and in interpreting astrophysical observations of turbulent plasmas. For the sake of simplicity, however, turbulence simulations are often conducted in the isothermal limit. Given that the majority of astrophysical systems are not governed by isothermal dynamics, we aim to quantify the impact of thermodynamics on the physics of turbulence, through varying adiabatic index, γ, combined with a range of optically thin cooling functions. Here, we present a suite of ideal magnetohydrodynamics simulations of thermally balanced stationary turbulence in the subsonic, super-Alfvénic, high ${\beta }_{{\rm{p}}}$ (ratio of thermal to magnetic pressure) regime, where turbulent dissipation is balanced by two idealized cooling functions (approximating linear cooling and free–free emission) and examine the impact of the equation of state by considering cases that correspond to isothermal, monatomic, and diatomic gases. We find a strong anticorrelation between thermal and magnetic pressure independent of thermodynamics, whereas the strong anticorrelation between density and magnetic field found in the isothermal case weakens with increasing γ. Similarly, the linear relation between variations in density and thermal pressure with sonic Mach number becomes steeper with increasing γ. This suggests that there exists a degeneracy in these relations with respect to thermodynamics and Mach number in this regime, which is dominated by slow magnetosonic modes. These results have implications for attempts to infer (e.g.,) Mach numbers from (e.g.,) Faraday rotation measurements, without additional information regarding the thermodynamics of the plasma. However, our results suggest that this degeneracy can be broken by utilizing higher-order moments of observable distribution functions.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2012

Anomaly Detection in Test Equipment via Sliding Mode Observers

Nonlinear observers were originally developed based on the ideas of variable structure control, and for the purpose of detecting disturbances in complex systems. In this anomaly detection application, these observers were designed for estimating the distributed state of fluid flow in a pipe described by a class of advection equations. The observer algorithm uses collected data in a piping system to estimate the distributed system state (pressure and velocity along a pipe containing liquid gas propellant flow) using only boundary measurements. These estimates are then used to further estimate and localize possible anomalies such as leaks or foreign objects, and instrumentation metering problems such as incorrect flow meter orifice plate size. The observer algorithm has the following parts: a mathematical model of the fluid flow, observer control algorithm, and an anomaly identification algorithm. The main functional operation of the algorithm is in creating the sliding mode in the observer system implemented as software. Once the sliding mode starts in the system, the equivalent value of the discontinuous function in sliding mode can be obtained by filtering out the high-frequency chattering component. In control theory, "observers" are dynamic algorithms for the online estimation of the current state of a dynamic system by measurements of an output of the system. Classical linear observers can provide optimal estimates of a system state in case of uncertainty modeled by white noise. For nonlinear cases, the theory of nonlinear observers has been developed and its success is mainly due to the sliding mode approach. Using the mathematical theory of variable structure systems with sliding modes, the observer algorithm is designed in such a way that it steers the output of the model to the output of the system obtained via a variety of sensors, in spite of possible mismatches between the assumed model and actual system. The unique properties of sliding mode control allow not only control of the model internal states to the states of the real-life system, but also identification of the disturbance or anomaly that may occur.

Solano, Wanda M.↗
NASA NTRS2017

Validation of a Solid Rocket Motor Internal Environment Model

In a prior effort, a thermal/fluid model of the interior of Penn State University's laboratory-scale Insulation Test Motor (ITM) was constructed to predict both the convective and radiative heat transfer to the interior walls of the ITM with a minimum of empiricism. These predictions were then compared to values of total and radiative heat flux measured in a previous series of ITM test firings to assess the capabilities and shortcomings of the chosen modeling approach. Though the calculated fluxes reasonably agreed with those measured during testing, this exercise revealed means of improving the fidelity of the model to, in the case of the thermal radiation, enable direct comparison of the measured and calculated fluxes and, for the total heat flux, compute a value indicative of the average measured condition. By replacing the P1-Approximation with the discrete ordinates (DO) model for the solution of the gray radiative transfer equation, the radiation intensity field in the optically thin region near the radiometer is accurately estimated, allowing the thermal radiation flux to be calculated on the heat-flux sensor itself, which was then compared directly to the measured values. Though the fully coupling the wall thermal response with the flow model was not attempted due to the excessive computational time required, a separate wall thermal response model was used to better estimate the average temperature of the graphite surfaces upstream of the heat flux gauges and improve the accuracy of both the total and radiative heat flux computations. The success of this modeling approach increases confidence in the ability of state-of-the-art thermal and fluid modeling to accurately predict SRM internal environments, offers corrections to older methods, and supplies a tool for further studies of the dynamics of SRM interiors.

Martin, Heath T.↗
NASA NTRS2017

Validation of a Solid Rocket Motor Internal Environment Model

In a prior effort, a thermal/fluid model of the interior of Penn State University's laboratory-scale Insulation Test Motor (ITM) was constructed to predict both the convective and radiative heat transfer to the interior walls of the ITM with a minimum of empiricism. These predictions were then compared to values of total and radiative heat flux measured in a previous series of ITM test firings to assess the capabilities and shortcomings of the chosen modeling approach. Though the calculated fluxes reasonably agreed with those measured during testing, this exercise revealed means of improving the fidelity of the model to, in the case of the thermal radiation, enable direct comparison of the measured and calculated fluxes and, for the total heat flux, compute a value indicative of the average measured condition. By replacing the P1-Approximation with the discrete ordinates (DO) model for the solution of the gray radiative transfer equation, the radiation intensity field in the optically thin region near the radiometer is accurately estimated, allowing the thermal radiation flux to be calculated on the heat-flux sensor itself, which was then compared directly to the measured values. Though the fully coupling the wall thermal response with the flow model was not attempted due to the excessive computational time required, a separate wall thermal response model was used to better estimate the average temperature of the graphite surfaces upstream of the heat flux gauges and improve the accuracy of both the total and radiative heat flux computations. The success of this modeling approach increases confidence in the ability of state-of-the-art thermal and fluid modeling to accurately predict SRM internal environments, offers corrections to older methods, and supplies a tool for further studies of the dynamics of SRM interiors.

Martin, Heath T.↗
NASA NTRS1986

Magnetized thermal conduction fronts

The evolution of planar thermal conduction fronts in the presence of a dynamically weak, but otherwise self-consistent, magnetic field is considered. The field is assumed to be connected and untangled. In the diffusion limit for the thermal conductivity, these fronts exhibit self-similar behavior, even in the presence of a field. The role of the field is restricted to channeling the heat flux along its lines of force, and it enters into the problem as a dimensionless angle variable. 'Combing' (or opening) of insulating field lines by the evaporative flow is explicitly demonstrated. Unless the field is nearly perpendicular to the front normal in the hot gas, insulating effects are not profound. Self-similarity breaks down if the front becomes saturated, and under certain conditions magnetized saturated conduction fronts cannot propagate: the solution characteristics of the wave equation form caustics. The physical resolution is the advent of two-fluid (nonlocal) heating. Such Coulomb-heated fronts are expected to be relatively rare in typical astrophysical systems. The large-scale effects of a magnetic field on cloud evaporation in the interstellar medium are briefly discussed, and it is suggested that these fields preclude the presence of time-independent evaporative solutions. Thermal interfaces may then continue to evolve until radiative cooling halts their development; large tracts of warm 10,000 K gas may result.

Balbus, S. A.↗
NASA NTRS1999

TADS--A CFD-Based Turbomachinery Analysis and Design System with GUI: User's Manual

The primary objective of this study was the development of a Computational Fluid Dynamics (CFD) based turbomachinery airfoil analysis and design system, controlled by a Graphical User Interface (GUI). The computer codes resulting from this effort are referred to as TADS (Turbomachinery Analysis and Design System). This document is intended to serve as a User's Manual for the computer programs which comprise the TADS system, developed under Task 18 of NASA Contract NAS3-27350, ADPAC System Coupling to Blade Analysis & Design System GUI and Task 10 of NASA Contract NAS3-27394, ADPAC System Coupling to Blade Analysis & Design System GUI, Phase II-Loss, Design and, Multi-stage Analysis. TADS couples a throughflow solver (ADPAC) with a quasi-3D blade-to-blade solver (RVCQ3D) in an interactive package. Throughflow analysis and design capability was developed in ADPAC through the addition of blade force and blockage terms to the governing equations. A GUI was developed to simplify user input and automate the many tasks required to perform turbomachinery analysis and design. The coupling of the various programs was done in such a way that alternative solvers or grid generators could be easily incorporated into the TADS framework. Results of aerodynamic calculations using the TADS system are presented for a highly loaded fan, a compressor stator, a low speed turbine blade and a transonic turbine vane.

Koiro, M. J.↗
NASA NTRS2003

Pulsed Ejector Wave Propogation Test Program

The development of, and initial test data from, a nondetonating Pulse Detonation Engine (PDE) simulator tested in the NASA Glenn 1 x 1 foot Supersonic Wind Tunnel (SWT) is presented in this paper. The concept is a pulsed ejector driven by the simulated exhaust of a PDE. This pro- gram is applicable to a PDE entombed in a ramjet flowpath, i.e., a PDE combined-cycle propulsion system. The ejector primary flow is a pulsed, uiiderexpanded, supersonic nozzle simulating the supersonic waves ema- nating from a PDE, while the ejector secondary flow is the 1 x 1 foot SWT test section operated at subsonic Mach numbers. The objective is not to study the detonation details, but the wave physics including t,he start- ing vortices, the extent of propagation of the wave front, the reflection of the wave from the secondary flowpath walls, and the timing of these events of a pulsed ejector, and correlate these with Computational Fluid Dynamics (CFD) code predictions. Pulsed ejectors have been shown to result in a 3 to 1 improvement in LID (length-to-diameter) and a near 2 to 1 improvement in thrust augmentation over a steady ejector. This program will also explore the extent of upstream interactions between an inlet and large, periodically applied, backpressures to the inlet as would be present due to combustion tube detonations in a PDE. These interactions could result in inlet unstart or buzz for a supersonic mixed compression inlet. The design of the present experiment entailed the use of an 2-t diagram characteristics code to study the nozzle filling and purging timescales as well as a series of CFD analyses conducted using the WIND code. The WIND code is a general purpose CFD code for solution of the Reynolds averaged Navier-Stokes equations and can be applied to both steady state and time-accurate calculations. The first, proof-of-concept, test entry (spring 2001) pressure distributions shown here indicate the simulation concept was successful and therefore the experimental approach is sound.

Fernandez, Rene↗
NASA NTRS1994

Investigation of finite element: ABC methods for electromagnetic field simulation

The mechanics of wave propagation in the presence of obstacles is of great interest in many branches of engineering and applied mathematics like electromagnetics, fluid dynamics, geophysics, seismology, etc. Such problems can be broadly classified into two categories: the bounded domain or the closed problem and the unbounded domain or the open problem. Analytical techniques have been derived for the simpler problems; however, the need to model complicated geometrical features, complex material coatings and fillings, and to adapt the model to changing design parameters have inevitably tilted the balance in favor of numerical techniques. The modeling of closed problems presents difficulties primarily in proper meshing of the interior region. However, problems in unbounded domains pose a unique challenge to computation, since the exterior region is inappropriate for direct implementation of numerical techniques. A large number of solutions have been proposed but only a few have stood the test of time and experiment. The goal of this thesis is to develop an efficient and reliable partial differential equation technique to model large three dimensional scattering problems in electromagnetics.

Chatterjee, A.↗
DOE OSTI2021

Flow reduction of hydrocarbon liquid in silica nanochannel: Insight from many-body dissipative particle dynamics simulations

A modified many-body dissipative particle dynamics (mDPD) model recently developed for realistic mesoscale multiphase flow simulations is rigorously parameterized, calibrated, and applied for elucidating the flow mechanisms of hydrocarbon liquids (i.e., heptane in this work) in amorphous silica cylindrical nanochannels with inner diameters ranging from 4.5 to 22.5 nm. The simulation results suggest the presence of a strong threshold of pressure gradient under which heptane cannot be driven to flow. The threshold for the 4.5 nm diameter pore is 10 to 100 times as high as for the 9–22.5 nm diameter pore, highlighting a remarkable nanoconfinement effect. Fluid viscosity is found to exhibit a shear-thinning phenomenon with intensity to weaken with increasing channel diameter — a phenomenon not observed in nanochannel flow of liquid water and gas in literature. Most remarkably, the radial profiles of average longitudinal flow velocity fitted by the modified Hagen-Poiseuille equation showed a negative slip length (–2.5% to –0.5% relative to the diameter) and a reduction of apparent permeability by 16% to 23%. Furthermore, this finding suggests silica nanochannels tend to deter hydrocarbon flow, a phenomenon that is opposed to the flow enhancement reported in most of the prior nanochannel flow studies in literature.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Implementation of Chemistry in the Athena++ Code

Chemistry plays a key role in many aspects of astrophysical fluids. Atoms and molecules are agents for heating and cooling, determine the ionization fraction, serve as observational tracers, and build the molecular foundation of life. We present the implementation of a chemistry module in the publicly available magnetohydrodynamic code Athena++ . We implement several chemical networks and heating and cooling processes suitable for simulating the interstellar medium (ISM). A general chemical network framework in the KIDA format is also included, allowing users to easily implement their own chemistry. Radiation transfer and cosmic-ray ionization are coupled with chemistry and solved with the simple six-ray approximation. The chemical and thermal processes are evolved as a system of coupled ordinary differential equations with an implicit solver from the CVODE library. We perform and present a series of tests to ensure the numerical accuracy and convergence of the code. Many tests combine chemistry with gas dynamics, including comparisons with analytic solutions, 1D problems of the photodissociation regions and shocks, and realistic 3D simulations of the turbulent ISM. We release the code with the new public version of Athena++ , aiming to provide a robust and flexible code for the astrochemical simulation community.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1992

Using adaptive grid in modeling rocket nozzle flow

The mechanical behavior of a rocket motor internal flow field results in a system of nonlinear partial differential equations which cannot be solved analytically. However, this system of equations called the Navier-Stokes equations can be solved numerically. The accuracy and the convergence of the solution of the system of equations will depend largely on how precisely the sharp gradients in the domain of interest can be resolved. With the advances in computer technology, more sophisticated algorithms are available to improve the accuracy and convergence of the solutions. An adaptive grid generation is one of the schemes which can be incorporated into the algorithm to enhance the capability of numerical modeling. It is equivalent to putting intelligence into the algorithm to optimize the use of computer memory. With this scheme, the finite difference domain of the flow field called the grid does neither have to be very fine nor strategically placed at the location of sharp gradients. The grid is self adapting as the solution evolves. This scheme significantly improves the methodology of solving flow problems in rocket nozzles by taking the refinement part of grid generation out of the hands of computational fluid dynamics (CFD) specialists and place it into the computer algorithm itself.

Chow, Alan S.↗
DOE OSTI2025

Using system identification in modeling the yaw response of tail fins for small wind turbines with bearing friction

Here, we describe three main developments of our previous study of the nonlinear yaw dynamics of the tail fins for small wind turbines [Khedr et al., J. Renewable Sustainable Energy 16, 053305 (2024)]. First, the model constants derived from archived computational and experimental studies are adjusted by employing system identification (SI) to maximize the model's agreement with wind tunnel tests. This adjustment was done for high wind speeds, where yaw bearing friction can be ignored. When starting a turbine at low wind speed, however, friction can become important. Our second development is to implement a model for the frictional resistive torque and use SI to maximize its accuracy. These developments used wind tunnel experiments on generic delta, elliptical, and rectangular planforms that were described by Khedr et al. [J. Renewable Sustainable Energy 16, 053305 (2024)]. Since the aerodynamic and friction models employ a large number of constants, we describe ways to constrain the values using linearized solutions of the response equations for small and large yaw angles. Third, we test the generality of the aerodynamic and friction modeling using the complex planform from a commercial small turbine, for which limited theoretical and computational guidance is available in selecting the model constants. The model implemented with SI is shown to provide an accurate description of the yaw response of the complex planform. Guidelines are given for the use of wind tunnel tests to determine the model constants for tail fins of any planform.

17 WIND ENERGY↗
DOE OSTI2025

CFD modeling of natural circulation in LiCl-KCl molten salt closed loop

Characterizing flow within a molten salt closed-loop system is crucial for assessing system requirements, evaluating performance, and identifying potential flaws. Direct flow measurement using instrumentation is challenging due to extreme environmental conditions and the limitations associated with measuring molten salt flow under natural convection. Here, this study aims to provide comprehensive insights into the thermal-hydraulic behavior of a closed loop, with a particular focus on temperature distribution and velocity prediction. The Computational Fluid Dynamics (CFD) model demonstrated the capability to effectively simulate and predict both temperature distributions and flow velocities within the molten salt loop. The CFD model's predictive capability was validated by its ability to replicate temperature measurements under varying boundary conditions. The analysis revealed that the CFD model tends to underpredict temperatures in the cold leg and overpredict them in the hot leg, highlighting the need for continuous model refinement and acknowledging the limitations of using a steady-state approach. Furthermore, the potential of using external temperature measurements to estimate internal molten salt temperatures and predict flow velocity was explored, revealing that this approach could introduce up to a 5.5% error in flow velocity calculations. Line probes mapping temperature distributions across the tube's cross-section and molten salt provided valuable insights into temperature gradients, emphasizing the need for a thermal conductivity equation for molten salt with lower uncertainty to achieve more accurate temperature predictions of the system.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

The origin of the Stokes–Einstein relation in simple dense liquids

Here, we investigate the origin of the universal relation between structural relaxation and diffusion in simple dense liquids, known as the Stokes–Einstein (SE) relation. The fact that this relation, originally derived from a hydrodynamic model of a macroscopic particle in a viscous medium, can describe the microscopic-scale liquid dynamics still eludes understanding. We introduce a new universal measure of structural relaxation in a system of N identical particles based on an explicit decomposition of the configuration space into N! congruent convex polyhedra. This measure makes it possible to quantify the correlation between two distinct particle configurations in terms of their minimal Euclidean distance, optimized with respect to particle permutations. Using this measure alongside a model of independent random walkers under the single-occupancy constraint, we derive a master equation that quantifies the SE relation. It allows us to demonstrate that the universal relation between structural relaxation and diffusion in simple dense liquids is caused by two conditions: (a) the confinement of the dominant density fluctuations to the first coordination shell, manifested by de Gennes narrowing, and (b) Gaussianity of the diffusion process; the former is shown to be violated in low-density fluids, and the latter is known to be violated in supercooled liquids.

Physics - Condensed matter physics↗