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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 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Evaluation of Hopper Flow Prediction based on Cubical Triaxial Tester Data and FEM

A cubical triaxial tester (CTT) laboratory device was used to collect key bulk flow characteristics of Crumbles® 6mm rotary sheared woody biomass and Crumbles® 2mm rotary sheard corn stover. The flow properties and a CAD model of a hopper and conveyor system to predict the consistency of flow of material from the hopper. Prediction included the likeliness of jamming, bridging, or ratholing. Each material was then loaded into the hopper and the actual bulk flow was measured. Measured flow closely matched the predicted flow.

09 BIOMASS FUELS↗
DOE OSTI2025

Experimental investigation of unsteady flow dynamics in therminol-66 using edge tone-induced oscillations

Recent research has demonstrated that flow oscillations induced by a wedge positioned opposite the jet outlet in edge tones can be effectively utilized for flow measurement purposes. This highlights the necessity for developing advanced instrumentation capable of precise flow measurements in experimental setups exposed to radiation and in challenging fluids such as molten salts. Here, this study contributes to the existing body of knowledge by conducting experiments using Therminol-66, an effective surrogate for FLiBe under appropriate temperature conditions for nuclear applications, across a broad range of Reynolds numbers from 17,700 to 555,000. Experiments were conducted with Therminol-66 at approximately 368.8 K under atmospheric pressure, with varying flow rates. A reliable correlation was established between the generated frequencies, corresponding flow rates, and device geometry parameters. The data were subjected to non-dimensional analysis to reveal the interrelationships among flow rate, fluid properties, device geometry, and their impact on the acoustic tones produced by the edge tone device. These findings contribute to the development of precise flow measurement instrumentation for use in challenging environments.

46 - INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AN↗
DOE OSTI2023

Exact solution of burst pressure for thick-walled pipes using the flow theory of plasticity

This paper develops an exact solution of burst pressure for defect-free, thick-walled pipes using the flow theory of plasticity in terms of the average shear stress yield criterion (or Zhu-Leis yield criterion). The pipe steel is assumed to obey the power-law strain hardening rule, and large plastic deformation is described by the finite strain theory. On this basis, internal pressure is obtained as a power series function of the effective strains on the inside and outside surfaces of the thick-walled pipe with use of the second Bernoulli numbers. At burst failure, the Zhu-Leis flow solution of burst pressure is determined as a power series solution, and the burst effective strains, the burst effective stresses, and the burst pressure are functions of the diameter ratio (D o / D i ), strain hardening exponent (n), and ultimate tensile strength (UTS). Similarly, the Tresca and von Mises flow solutions of burst pressure are also determined as a power series solution in terms of the Tresca and von Mises yield criteria. A general closed-from exact solution of burst pressure is then proposed for the three yield criteria, and the results showed that the proposed exact solution matches well with the power series solution for each yield criterion. Moreover, the von Mises flow solution is an upper bound prediction, the Tresca flow solution is a lower bound prediction, and the Zhu-Leis flow solution is an intermediate prediction that agrees well with the finite element analysis results of burst pressure for thick-walled pipes. Furthermore, two datasets of full-scale burst tests are then utilized to evaluate and validate the proposed flow solutions of burst pressure for both thin and thick-walled pipes.

42 ENGINEERING↗
DOE OSTI2020

Determining the impacts of venoarterial extracorporeal membrane oxygenation on cerebral oxygenation using a one-dimensional blood flow simulator

Venoarterial extracorporeal membrane oxygenation (VA-ECMO) is a mechanical system that provides rapid and short-term support for patients with cardiac failure. In many patients, pulmonary function is also impaired, resulting in poorly-oxygenated cardiac outflow competing against well-oxygenated VA-ECMO outflow, a condition known as North-South syndrome. North-South syndrome is a primary concern because of its potential to cause cerebral hypoxia, which has a critical influence on neurological complications often seen in this patient population. In order to reduce ischemic neurological complications, it is important to understand how clinical decisions regarding VA-ECMO parameters influence blood oxygenation. In our work, we studied the impacts of flow rate and cannulation site on oxygenation using a one-dimensional (1D) model to simulate blood flow. Our model was initially tested by comparing blood flow results to those observed from experimental work in VA-ECMO patients. The 1D model was combined with a two-phase flow model to simulate oxygenation. Additionally, the influence of various other clinician-tunable parameters on oxygenation in the common carotid arteries (CCAs) were tested, including, blood viscosity, cannula position within the insertion artery, heart rate, and systemic vascular resistance (SVR), as well as geometrical changes such as arterial radius and length. Our results indicated that blood oxygenation to the brain strongly depended on the cannula insertion site and the VA-ECMO flow rate with a weaker but potentially significant dependence on arterial radius. During femoral cannulation, VA-ECMO flow rates greater than ~4.9 L/min were needed to perfuse the CCAs. However, axillary and central cannulation began to perfuse the CCAs at significantly lower flow (~1 L/min). These results may help explain the incidence of cerebral hypoxia in this patient population and the common need to change cannulation strategies during treatment to address this clinical problem. While this work describes patient-averaged results, determining these relationships between VA-ECMO parameters and cerebral hypoxia is an important step towards future work to develop patient-specific models that clinicians can use to improve outcomes.

1D blood flow↗
DOE OSTI2024

Flow field design for zero-gap microbial electrolysis cells using synthetic and real wastewater

Increasing performance in microbial electrolysis cells (MECs) requires the development of optimized reactor configurations with minimal internal resistance and capable to operate with real wastewater. Here, the impact of two different flow fields (serpentine and circular) was examined in zero-gap MECs with synthetic and real wastewaters. The serpentine flow field enabled a uniform distribution of the electrolyte in the anode chamber, resulting in larger current densities at lower flow rates compared to the circular flow field. Electrochemical tests using synthetic media with high buffer capacity revealed more stable and higher performance with the serpentine flow field compared to the circular flow path, producing larger current density (23.7 ± 0.8 A/m 2 vs 21.9 ± 5.6 A/m 2 ), hydrogen production rate (75.8 ± 4.1 L/L-d vs 54.3 ± 2.4 L/L-d), cathodic coulombic efficiency (>91 % vs >50 %), and an overall lower internal resistance (12.5 ± 0.5 mΩm 2 vs 14.8 ± 3.7 mΩm 2 ). Continuous operation for over 30 days with real wastewater indicated higher tolerance of the MECs with serpentine flow field toward media with large concentration of suspended solids, producing a current density of 5.4 ± 1.1 A/m 2 and a hydrogen production rate of 22.2 ± 6.2 L/L-d. Furthermore, the results presented here underscore the importance of reactor design and architecture in optimizing MEC performance for hydrogen production from liquid wastes.

flow path↗
DOE OSTI2024

An in situ imaging investigation of the effect of gas flow rates on directed energy deposition

Gas flow rates in Directed Energy Deposition (DED) Additive Manufacturing (AM) can significantly affect the quality of built parts by altering melt pool geometry. Using a DED process replicator and in situ synchrotron radiography, together with analogous experiments in an industrial DED machine, we investigate the impact of carrier gas and shield gas flow rates on build quality. The results reveal that there is a critical shield gas flow rate above which melt pools are flattened, tracks widen, and thus layer thickness decreases. The reduction in layer thickness is most prominent in conditions with low carrier gas flow rate, as the highly turbulent shield gas flow may divert slow moving powder particles away from the melt pool, decreasing capture efficiency. Very high flow rates increase internal porosity, as fast-moving particles impacting the melt pool surface can entrain chamber gas behind them. High gas flow rates also cool the melt pool, creating shallower melt pools with increased thermal gradients near the solidification front, increasing pore entrapment in the solidified track.

Additive manufacturing↗
DOE OSTI2020

Scaling Analysis of Two–Phase Flow in Fractal Permeability Fields

Fluid mixing in permeable media is essential in many practical applications. The mixing process is a consequence of velocity fluctuations owing to geological heterogeneities and mobility contrast of fluids. Heterogeneities in natural rocks are often spatially correlated, and their properties, such as permeability, may be described using fractal distributions. This work models the fractal characteristics of such permeability fields in which the covariance function is expressed as a power-law function. A generalized scaling relation is derived relating various fractal permeability fields using the magnitude of their fluctuations. Here, this relation reveals the self-similar behavior of two-phase flow in such permeable media. To that end, a recently developed, high-resolution numerical simulator is employed to validate the analytically derived scaling relations. Two flow problems are considered in which flow is governed by 1) a linear, and 2) a nonlinear transport equation. Due to the probabilistic representation of the fractal permeability fields, a sensitivity study is conducted for each flow scenario to determine the number of realizations required for statistical convergence. Scaling analysis is performed using ensemble averages of simulated saturation profiles and their mixing lengths. Results support the validity of the developed scaling relation across the range of investigated flow conditions at intermediate times. The dynamics of linear flow in the asymptotic regime is affected by the correlation structure of heterogeneity. In nonlinear flow, scaling behavior appears to be dominated by the degree of nonlinearity.

58 GEOSCIENCES↗
DOE OSTI2022

Morphology of shocked lateral outflows in colliding hydrodynamic flows

Supersonic interacting flows occurring in phenomena, such as protostellar jets, give rise to strong shocks and have been demonstrated in several laboratory experiments. To study such colliding flows, we use the AstroBEAR AMR code to conduct hydrodynamic simulations in three dimensions. Here, we introduce variations in the flow parameters of density, velocity, and cross-sectional radius of the colliding flows in order to study the propagation and conical shape of the bow shock formed by collisions between two, not necessarily symmetric, hypersonic flows. We find that the motion of the interaction region is driven by imbalances in ram pressure between the two flows, while the conical structure of the bow shock is a result of shocked lateral outflows being deflected from the horizontal when the flows are of differing cross sections.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Field validation of an actuated convergent-beam acoustic Doppler profiler for high resolution flow mapping

Abstract Energetic river and tidal flow environments feature complex hydrodynamic conditions. Conventional acoustic Doppler profiling instrumentation typically requires assumptions of flow homogeneity over the spatial scales of the divergent beam separation. This removes the ability to measure spatio-temporal variability within the flow. However, velocity variability within these spatial scales is often important in the design of structures and devices exposed to such flow, informing dynamic and peak hydrodynamic load predictions. The research presented outlines the development and testing of a flow measurement instrument consisting of multiple spatially-separated single beam acoustic Doppler profilers converging on a remote focal point, the location of which can be programmatically adjusted through actuation. This increases the spatial resolution at which remote field measurements can be made in energetic flow environments. Field testing of the instrument was conducted in a tidal channel at Sequim Bay Inlet, WA, USA. Results are compared with independent reference measurements made by a co-located, motion-corrected acoustic Doppler velocimeter. This comparison, across tidal velocities of 0.4–0.7 m s −1 , showed a mean velocity error of 0.5%–13.2% across nine sample locations within a 3.00 m × 2.25 m plane. To the authors’ knowledge, this is the first publication of flow velocity results from non-intrusive acoustic measurements at an off-axis, focal point location that features 3D positional control.

13 HYDRO ENERGY↗
DOE OSTI2022

Mutually promoting or constraining? Disentangling the superimposed effect of velocity and illuminance on fish motion in low-velocity flows with a novel metric

Global climate change, species invasion, and human activities such as the construction of hydraulic facilities are contributing to the worldwide degradation of fish stocks. As a pivotal environmental factor that affects fish migration and population distribution, low-velocity flow has not drawn enough attention despite its extensive presence in various ecoregions. Herein, to understand the behavioural profiles of fish in low-velocity flow, we examined the motility and swimming performance of two representative cyprinids, grass carp (GC, Ctenopharyngodon idella) and silver carp (SC, Hypophthalmichthys molitrix), under the combined effect of different flow velocities and illuminance ranges. The two species were exposed to two flow velocities (0.15 and 0.25 m/s) and three illuminance ranges (100.0 – 0.9 lx, 300.0 – 2.5 lx, and 700.0 – 4.9 lx). A novel behavioural metric, composed of light preference, cruising swimming speed, rheotaxis index (RI), swimming stability (SS), and the probability of moving forwards/backwards over a certain distance (PM f -0.1 and PM b -0.1), was developed to depict the motion strategy of fish fully. By investigating the individual distribution of the fish in light gradient, we confirmed the scototaxis of GC and found the oscillating light preference in SC that changed from 84.4 – 10.2 lx to 6.0 – 2.1 lx and disappeared with increasing illuminance. At the given velocities, the RI and SS increased in both species with a faster flow, and SC was more forward-prone and stable than GC. Despite its fluctuating light preference, the higher illuminances heightened the RI and SS in SC; while in GC, higher illuminances inhibited the SS and had no impact on the RI. The results of PM f -0.1 and PM b -0.1 indicated that a higher flow velocity could facilitate temporary upstream swimming in both species, while illuminance could promote the same effect in SC only. Finally, our study proposed possible moving manoeuvres in fine-scale spatio-temporal scenarios such as attraction flow and untraditional passages and provides valuable insights into fish community dynamics, laying the groundwork for alleviating the threat from invasive species and for future fish population recovery.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Assessment of Machine Learning Wall Modeling Approaches for Large Eddy Simulation of Gas Turbine Film Cooling Flows: An a Priori Study

Here, in this work, a priori analysis of machine learning (ML) strategies is carried out with the goal of data-driven wall modeling for large eddy simulation (LES) of gas turbine film cooling flows. High-fidelity flow datasets are extracted from wall-resolved LES (WRLES) of flow over a flat plate interacting with the coolant flow supplied by a single row of 7-7-7 shaped cooling holes inclined at 30 degrees with the flat plate at different blowing ratios (BR). The WRLES are performed using the high-order Nek5000 spectral element computational fluid dynamics (CFD) solver. Light gradient boosting machine (LightGBM) is employed as the ML algorithm for the data-driven wall model. Parametric tests are conducted to systematically assess the influence of a wide range of input flow features (velocity components, velocity gradients, pressure gradients, and fluid properties) on the accuracy of ML wall model with respect to prediction of wall shear stress. In addition, the use of spatial stencil and time delay is also explored within the ML wall modeling framework. It is shown that features associated with gradients of the streamwise and spanwise velocity components have a major impact on the prediction fidelity of wall model, while the effect of gradients of wall-normal velocity component is found to be negligible. Moreover, adding flow feature information from an x-y-z spatial stencil significantly improves the ML model accuracy and generalizability compared to just using local flow features from the matching location. Overall, highest prediction accuracy is achieved when both spatial stencil and time delay features are incorporated within the data-driven wall modeling paradigm.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2024

A Pseudoreversible Normalizing Flow for Stochastic Dynamical Systems with Various Initial Distributions

Here, we present a pseudoreversible normalizing flow method for efficiently generating samples of the state of a stochastic differential equation (SDE) with various initial distributions. The primary objective is to construct an accurate and efficient sampler that can be used as a surrogate model for computationally expensive numerical integration of SDEs, such as those employed in particle simulation. After training, the normalizing flow model can directly generate samples of the SDE’s final state without simulating trajectories. The existing normalizing flow model for SDEs depends on the initial distribution, meaning the model needs to be retrained when the initial distribution changes. The main novelty of our normalizing flow model is that it can learn the conditional distribution of the state, i.e., the distribution of the final state conditional on any initial state, such that the model only needs to be trained once and the trained model can be used to handle various initial distributions. This feature can provide a significant computational saving in studies of how the final state varies with the initial distribution. Additionally, we propose to use a pseudoreversible network architecture to define the normalizing flow model, which has sufficient expressive power and training efficiency for a variety of SDEs in science and engineering, e.g., in particle physics. We provide a rigorous convergence analysis of the pseudoreversible normalizing flow model to the target probability density function in the Kullback–Leibler divergence metric. Numerical experiments are provided to demonstrate the effectiveness of the proposed normalizing flow model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Opposing Hysteresis Patterns in Flow and Outflow Macroscopic Fundamental Diagrams and Their Implications

Two key aggregated traffic models are the relationship between average network flow and density (known as the network or flow macroscopic fundamental diagram [flow-MFD]) and the relationship between trip completion and density (known as network exit function or the outflow-MFD [o-FMD]). The flow- and o-MFDs have been shown to be related by average network length and average trip distance under steady-state conditions. However, recent studies have demonstrated that these two relationships might have different patterns when traffic conditions are allowed to vary: the flow-MFD exhibits a clockwise hysteresis loop, while the o-MFD exhibits a counter-clockwise loop. One recent study attributes this behavior to the presence of bottlenecks within the network. The present paper demonstrates that this phenomenon may arise even without bottlenecks present and offers an alternative, but more general, explanation for these findings: a vehicle’s entire trip contributes to a network’s average flow, while only its end contributes to the trip completion rate. This lag can also be exaggerated by trips with different lengths, and it can lead to other patterns in the o-MFD such as figure-eight patterns. A simple arterial example is used to demonstrate this explanation and reveal the expected patterns, and they are also identified in real networks using empirical data. Then, simulations of a congestible ring network are used to unveil features that might increase or diminish the differences between the flow- and o-MFDs. Finally, more realistic simulations are used to confirm that these behaviors arise in real networks.

42 ENGINEERING↗
DOE OSTI2022

The influence of intake flow and coolant temperature on gasoline spray morphology during early-injection DISI engine operation

Multi-hole gasoline injectors operating at conditions spanning throttled early-intake stroke operation produce spray plumes that either remained separated or merge and collapse due to flash boiling. Flash boiling occurs due to the sudden expansion of gas bubbles in the liquid fuel at high fuel temperature and low ambient pressure. This study records high-speed images of spray-morphology changes due to in-cylinder flow, thereby revealing operating conditions that do and do not affect the self-induced morphology observed in quiescent vessels. Specifically, in a central-injection, four-valve, high-tumble engine, where the thermodynamic state and in-cylinder cross flow are dynamic. Motivated by cold start and hot restart operation, the fuel pressure, coolant temperature, in-cylinder air pressure, and engine rpm were systematically varied over relevant operating conditions, which bracketed the range from non- to flash-boiling sprays. The results reveal the operating conditions at which the in-cylinder cross flow disrupts the spray morphology as well as the extent of the disruption. At 650 rpm, the spray morphology was similar to that observed in quiescent vessels at nominally equivalent fuel temperature and in-cylinder pressure, indicating that the spray’s self-induced entrainment flow dominated the in-cylinder flow. However, for fuel temperature and ambient pressure near the transition between non- and flash-boiling, the intake cross flow at higher engine speed (1950 rpm) significantly disrupted the spray morphology. The high cross-flow velocity appears to induce plume merging and collapse, whereas none was evident at low rpm (650 rpm). This study led to the postulate that the spray merging and collapse are governed by the rate of atomization near the nozzle exit, presumed to be controlled by either or both aerodynamic atomization and flash-boiling intensity. It would then follow that spray modeling in CFD requires atomization models that blend the effects of both physical processes.

42 ENGINEERING↗
DOE OSTI2022

Integration of Electromagnetic Geophysics Forward Simulation in Coupled Flow and Geomechanics for Monitoring a Gas Hydrate Deposit Located in the Ulleung Basin, East Sea, Korea

We investigate the feasibility of electromagnetic (EM) geophysics methods to detect the dissociation of gas hydrate specifically from a gas hydrate deposit located in the Ulleung Basin, East Sea, Korea via an integrated flow-geomechanics-EM geophysics simulation. To this end, coupled flow and geomechanics simulation is first performed with the multiple porosity model employed, where a mixed formulation with the finite volume (FV) and finite element (FE) methods are taken for the flow and geomechanics, respectively. From the saturation and porosity fields obtained from the coupled flow and geomechanics, the electrical conductivity model is established for the EM simulation. Solving the partial differential equation of electrical diffusion which is linearized using the 3D finite element method (FEM), the EM fields are then computed. For numerical experiments, particularly two approaches in the configuration for the EM methods are compared in this contribution: the surface-to-surface and the surface-to-borehole methods. When the surface-to-surface EM method is employed, the EM is found to be less sensitive, implying low detectability. Especially for the short term of production, the low detectability is attributed to the similarity of electrical resistivity between the dissociated gas (CH4) and hydrate as well as the specific dissociation pattern within the intercalated composites of the field. On the other hand, when the surface-to-borehole EM method is employed, its sensitivity to capture the produced gas flow is improved, confirming its detectability in monitoring gas flow. Hence, the EM geophysics simulation integrated with coupled flow and geomechanics can be a potential tool for monitoring gas hydrate deposits.

depressurization↗
DOE OSTI2020

Determining flow directions in river channel networks using planform morphology and topology

Abstract. The abundance of global, remotely sensed surface water observations has accelerated efforts toward characterizing and modeling how water moves across the Earth's surface through complex channel networks. In particular, deltas and braided river channel networks may contain thousands of links that route water, sediment, and nutrients across landscapes. In order to model flows through channel networks and characterize network structure, the direction of flow for each link within the network must be known. In this work, we propose a rapid, automatic, and objective method to identify flow directions for all links of a channel network using only remotely sensed imagery and knowledge of the network's inlet and outlet locations. We designed a suite of direction-predicting algorithms (DPAs), each of which exploits a particular morphologic characteristic of the channel network to provide a prediction of a link's flow direction. DPAs were chained together to create “recipes”, or algorithms that set all the flow directions of a channel network. Separate recipes were built for deltas and braided rivers and applied to seven delta and two braided river channel networks. Across all nine channel networks, the recipe-predicted flow directions agreed with expert judgement for 97 % of all tested links, and most disagreements were attributed to unusual channel network topologies that can easily be accounted for by pre-seeding critical links with known flow directions. Our results highlight the (non)universality of process–form relationships across deltas and braided rivers.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

The Onset of Nucleate Boiling Prediction in a Mini Channel with the Eulerian Multiphase Flow

The prediction of boiling incipience is a critical issue for a reactor. Vapor lock causes operating instability and undesirable temperature rise, especially for small channels. This study uses the Eulerian multiphase flow boiling model to predict the onset of nucleate boiling in a millimeter scale rectangular channel. Two wall boiling models, namely the RPI (Rensselaer Polytechnic Institute) and the non-equilibrium sub cooled model are applied. Computational fluid dynamics is employed for this study to investigate the impact of operating conditions like liquid flow rate, operating pressure, heat flux, velocity profile, turbulence model, and inlet liquid temperature. Here, the effect of fundamental boiling parameters on the surface wall temperature and vapor volume fraction is also studied. The parameters under consideration are the bubble departure diameter, bubble departure frequency, nucleate site density, quenching time period, and interface heat transfer coefficients. A series of CFD calculations is conducted by varying the considered variables systematically in a wide range of flow conditions covering laminar, transition, and turbulent flows. The sub-component heat fluxes like the liquid convective, the vapor convective, the evaporative, and the quenching terms are monitored to infer the boiling dynamics in the transition region from the single-phase flow to the nucleate boiling zone. It is found that the CFD approach to detecting the boiling incipience point agrees reasonably with available experimental data. However, its limitations, like inaccuracy for lower flow rates and early transition to boiling flow, are also noticed due to the nature of the considered RPI model.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Modeling and simulation of transitional Rayleigh–Taylor flow with partially averaged Navier–Stokes equations

In this work, the partially averaged Navier–Stokes (PANS) equations are used to predict the variable-density Rayleigh–Taylor (RT) flow at Atwood number 0.5 and maximum Reynolds number 500. This is a prototypical problem of material mixing, featuring laminar, transitional, and turbulent flow, instabilities and coherent structures, density fluctuations, and production of turbulence kinetic energy by both shear and buoyancy mechanisms. These features pose numerous challenges to modeling and simulation, making the RT flow ideal to develop the validation space of the recently proposed PANS Besnard–Harlow–Rauenzahn-linear eddy viscosity model closure. The numerical simulations are conducted at different levels of physical resolution and test three approaches to set the parameters $f_\phi$ defining the range of physically resolved scales. The computations demonstrate the efficiency (accuracy vs cost) of the PANS model predicting the spatiotemporal development of the RT flow. Results comparable to large-eddy simulations and direct numerical simulations are obtained at significantly lower physical resolution without the limitations of the Reynolds-averaged Navier–Stokes equations in these transitional flows. The data also illustrate the importance of appropriate selection of the physical resolution and the resolved fraction of each dependent quantity $\phi$ of the turbulent closure, $f_\phi$. These two aspects determine the ability of the model to resolve the flow phenomena not amenable to modeling by the closure and, as such, the computations’ fidelity.

Navier Stokes equations↗