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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

A universal velocity transformation for boundary layers with pressure gradients

The logarithmic law of the wall does not capture the mean flow when a boundary layer is subjected to a strong pressure gradient. In such a boundary layer, the mean flow is affected by the spatio-temporal history of the imposed pressure gradient; and accounting for history effects remains a challenge. This work aims to develop a universal mean flow scaling for boundary layers subjected to arbitrary adverse or/and favourable pressure gradients. Here, we derive from the Navier–Stokes equation a velocity transformation that accounts for the history effects and maps the mean flow to the canonical law of the wall. The transformation is tested against channel flows with a suddenly imposed adverse or favourable pressure gradient, boundary layer flows subjected to an adverse pressure gradient, and Couette–Poiseuille flows with a streamwise pressure gradient. It is found that the transformed velocity profiles follow closely the equilibrium law of the wall.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Improved pressure-gradient sensor for the prediction of separation onset in RANS models

Here, we improve upon two key aspects of the Menter shear stress transport (SST) turbulence model: (1) We propose a more robust adverse pressure gradient sensor based on the strength of the pressure gradient in the direction of the local mean flow; (2) We propose two alternative eddy viscosity models to be used in the adverse pressure gradient regions identified by our sensor. Direct numerical simulations of the Boeing Gaussian bump are used to identify the terms in the baseline SST model that need correction, and a posteriori Reynolds-averaged Navier-Stokes calculations are used to calibrate coefficient values, leading to a model that is both physics driven and data informed. The two sensor-equipped models are applied to two thick airfoils representative of modern wind turbine applications, the FFA-W3-301 and the DU00-W-212. The proposed models improve the prediction of stall (onset of separation) with respect to the prediction of the baseline SST model.

17 WIND ENERGY↗
DOE OSTI2023

Planar turbulent wakes under pressure gradient: Integral and self-similarity analyses

By using a combination of integral and self-similarity analyses, the generalized analytical solutions for the mean transverse velocity and Reynolds shear stress are rigorously derived for the first time for the far field of planar turbulent wakes under arbitrary pressure gradients. Specifically, by assuming self-similarity for the mean axial velocity, the analytical formulation for the mean transverse velocity is obtained from the integral of the mean continuity equation, and the analytical formulation for the Reynolds shear stress is obtained from the integral of the momentum equation. The generalized analytical formulations for the mean transverse velocity and Reynolds shear stress consist of multiple components, each with its unique scale and physical mechanism. In the zero pressure gradient limit, the generalized formulations recover the single-scale equations reported by Wei, Liu, and Livescu. Furthermore, simpler approximate formulations for the mean transverse velocity and Reynolds shear stress are also obtained, and show excellent agreement with the experimental measurements. Here, the findings provide new insights into the properties of planar turbulent wakes under pressure gradients, filling some long-standing gaps in the existing literature.

42 ENGINEERING↗
DOE OSTI2023

Structure of pressure-gradient-driven current singularity in ideal magnetohydrodynamic equilibrium

Abstract Singular currents typically appear on rational surfaces in non-axisymmetric ideal magnetohydrodynamic (MHD) equilibria with a continuum of nested flux surfaces and a continuous rotational transition. These currents have two components: a surface current (Dirac δ -function in flux surface labeling) that prevents the formation of magnetic islands, and an algebraically divergent Pfirsch–Schlüter current density when a pressure gradient is present across the rational surface. On flux surfaces adjacent to the rational surface, the traditional treatment gives the Pfirsch–Schlüter current density scaling as J ∼ 1 / Δ ι , where Δ ι is the difference of the rotational transform relative to the rational surface. If the distance s between flux surfaces is proportional to Δ ι , the scaling relation J ∼ 1 / Δ ι ∼ 1 / s will lead to a paradox that the Pfirsch–Schlüter current is not integrable. In this work, we investigate this issue by considering the pressure-gradient-driven singular current in the Hahm–Kulsrud–Taylor problem, which is a prototype for singular currents arising from resonant magnetic perturbations. We show that not only the Pfirsch–Schlüter current density but also the diamagnetic current density are divergent as ∼ 1 / Δ ι . However, due to the formation of a Dirac δ -function current sheet at the rational surface, the neighboring flux surfaces are strongly packed with s ∼ ( Δ ι ) 2 . Consequently, the singular current density J ∼ 1 / s , making the total current finite, thus resolving the paradox. Furthermore, the strong packing of flux surfaces causes a steepening of the pressure gradient near the rational surface, with ∇ p ∼ d p / d s ∼ 1 / s . In general non-axisymmetric MHD equilibrium, contrary to Grad’s conjecture that the pressure profile is flat around densely distributed rational surfaces, our result suggests a pressure profile that densely steepens around them.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

A streamline coordinate analysis of a turbulent boundary layer subject to pressure gradients and curvature on the windward side of a bump

Direct numerical simulation (DNS) of a turbulent boundary layer over the Gaussian (Boeing) bump is performed. This boundary layer exhibits a series of adverse and favourable pressure gradients and convex and concave curvature effects before separating. These effects on turbulent boundary layers are characterised and compared with a lower-Reynolds-number flow over the same geometry. The momentum budgets are analysed in the streamline-aligned coordinate system upstream of the separation region. These momentum budgets allow the simplification of equations to facilitate an integral analysis. Integral-analysis-based approximations for Reynolds stresses in the inner and outer regions of the boundary layer are also formulated. The shear and wall-normal Reynolds stress profiles normalised by these approximations exhibit a better collapse compared with friction velocity and Zagarola–Smits normalisations in the strong favourable pressure gradient region and in the mild adverse pressure region that precedes it in this flow. Simplification of these Reynolds stress approximations along with results from the DNS are used to obtain semi-empirical approximations that are able to provide stress closure in terms of wall solution fields for the turbulent boundary layer under consideration.

42 ENGINEERING↗
DOE OSTI2024

Pressure-Gradient-Based RANS Model for Predicting Separation in Transitional and Turbulent Flows

Predicting flow separation poses a significant challenge for RANS models, particularly in transitional flows over airfoils. We propose a novel improvement to RANS models to predict incipient separation in both transitional and fully turbulent flows. Our approach modifies the eddy viscosity model in regions indicated by a pressure-gradient criterion that accounts for intermittency - determining whether the boundary layer is laminar or turbulent. This model demonstrates robust generalization across various airfoil shapes and Reynolds numbers. Applied to the NREL Phase VI wind turbine rotor, our model shows improved aerodynamic performance predictions compared to the baseline RANS model.

k-omega SST↗
DOE OSTI2023

Osmotic Pressure Gradient Effects on Water Diffusion in Porous Rock: Can They Pervert Permeability Tests?

Abstract Generation of a large network of hydraulic cracks is of key importance not only for the success of fracking of shale but also for the recent scheme of sequestration of CO2 in deep formations of basalt and peridotite, which are mafic and ultramafic rocks that combine chemically with CO2. In numerical simulation of the creation of a fracture network in porous rock, an important goal is to enhance the rock permeability. The objective of this article is to calculate the effect of osmotic pressure gradients caused by gradients of concentration of the ions of Ca, Mg, Na, etc. on the effective permeability of the rock. The basic differential equations are formulated, and their explicit solutions for appropriate initial and boundary conditions are obtained under certain plausible simplifications. The main result is explicit approximate formulas for the critical time before which no water permeation through a test specimen can be observed. Depending on various parameters, this time can be unacceptably long, which is manifested as a zero water outflow. The solution may also explain the unreasonably small permeability values reported for some shales.

Mechanics↗
DOE OSTI2024

Measurement of pressure gradients near the interface in the viscous fingering instability

The viscous fingering instability, which forms when a less-viscous fluid invades a more-viscous one within a confined geometry, is an iconic system for studying pattern formation. For both miscible and immiscible fluid pairs the growth dynamics change after the initial instability onset and the global structures, typical of late-time growth, are governed by the viscosity ratio. Here we introduce an experimental technique to measure flow throughout the inner and outer fluids. This probes the existence of a new length scale associated with the local pressure gradients around the interface and allows us to compare our results to the predictions of a previously proposed model for late-time finger growth. Published by the American Physical Society 2024

Physics↗
DOE OSTI2023

Figuring Out Gas & Galaxies in Enzo (FOGGIE). VI. The Circumgalactic Medium of L * Galaxies Is Supported in an Emergent, Nonhydrostatic Equilibrium

The circumgalactic medium (CGM) is often assumed to exist in or near hydrostatic equilibrium, with the regulation of accretion and the effects of feedback treated as perturbations to a stable balance between gravity and thermal pressure. We investigate global hydrostatic equilibrium in the CGM using four highly resolved L* galaxies from the Figuring Out Gas & Galaxies in Enzo (FOGGIE) project. The FOGGIE simulations were specifically targeted at fine spatial and mass resolution in the CGM (Δx ≲ 1 kpc h –1 and M ≃ 200M ⊙ ). We develop a new analysis framework that calculates the forces provided by thermal pressure gradients, turbulent pressure gradients, ram pressure gradients of large-scale radial bulk flows, centrifugal rotation, and gravity acting on the gas in the CGM. Thermal and turbulent pressure gradients vary strongly on scales of ≲5 kpc throughout the CGM. Thermal pressure gradients provide the main supporting force only beyond ~0.25R 200 , or ~50 kpc at z = 0. Within ~0.25R 200 , turbulent pressure gradients and rotational support provide stronger forces than thermal pressure. More generally, we find that global equilibrium models are neither appropriate nor predictive for the small scales probed by absorption line observations of the CGM. Local conditions generally cannot be derived by assuming a global equilibrium, but an emergent global equilibrium balancing radially inward and outward forces is obtained when averaging over the nonequilibrium local conditions on large scales in space and time. Approximate hydrostatic equilibrium holds only at large distances from galaxies, even when averaging out small-scale variations.

79 ASTRONOMY AND ASTROPHYSICS↗
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 OSTI2026

Decadal Spiciness Variability in the Subtropical-Tropical Pacific in the CESM2 Large Ensemble

Tropical Pacific decadal variations impact weather and climate around the world and are also connected to variations in the global warming trend. The mechanisms driving these long-term modulations, particularly the role of subsurface ocean dynamics, are still debated. Here, we investigate the dynamics of spiciness (density-compensated temperature and salinity) anomalies in the tropical and subtropical Pacific, which are hypothesized as a possible driving mechanism of decadal climate variability. Based on the analysis of 100 realizations from the Community Earth System Model Version 2 Large Ensemble (CESM2-LE), we demonstrate a coupling between the subtropics and the equatorial Pacific by propagating spiciness anomalies at decadal time scales. The CESM2-LE simulates spiciness variability along a subduction path from the subtropics to the equator with frequency spectra that show the highest power at low frequencies and a power decay proportional to a −4 slope for frequencies greater than 0.01 cycles per months, corresponding to periods smaller than ∼8.5 years. Signals that originate in the Southern Hemisphere (SH) dominate and arrive with a larger magnitude at the equator compared to spiciness anomalies from the Northern Hemisphere (NH). Spiciness anomalies from the SH have shorter propagation times and are strengthened along their pathway as stochastic wind stress curl forcing generates anomalous baroclinic ocean pressure gradients. These pressure gradients generate spiciness anomalies via anomalous advection across climatological spiciness gradients in the SH. We conclude that the observed spiciness variance at decadal time scales is consistent with a forcing by stochastic wind variations that are low-pass filtered by ocean dynamics.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Scalable Simulation of Pressure Gradient-Driven Transport of Rarefied Gases in Complex Permeable Media Using Lattice Boltzmann Method

Accurate representations of slip and transitional flow regimes present a challenge in the simulation of rarefied gas flow in confined systems with complex geometries. In these regimes, continuum-based formulations may not capture the physics correctly. This work considers a regularized multi-relaxation time lattice Boltzmann (LB) method with mixed Maxwellian diffusive and halfway bounce-back wall boundary treatments to capture flow at high Kn. The simulation results are validated against atomistic simulation results from the literature. We examine the convergence behavior of LB for confined systems as a function of inlet and outlet treatments, complexity of the geometry, and magnitude of pressure gradient and show that convergence is sensitive to all three. The inlet and outlet boundary treatments considered in this work include periodic, pressure, and a generalized periodic boundary condition. Compared to periodic and pressure treatments, simulations of complex domains using a generalized boundary treatment conserve mass but require more iterations to converge. Convergence behavior in complex domains improves at higher magnitudes of pressure gradient across the computational domain, and lowering the porosity deteriorates the convergence behavior for complex domains.

42 ENGINEERING↗
DOE OSTI2024

Review: Pre-Darcy flows in low-permeability porous media

The widely used Darcy’s law specifies a linear relation between the Darcy velocity of fluid flow and the pressure gradient that drives the flow. However, studies have shown that Darcy velocity can exhibit a nonlinear dependence on the pressure gradient in low-permeability porous media such as clay and shale when the pressure gradient is adequately low. This phenomenon is referred to as low-velocity non-Darcian flow or pre-Darcy flow. This paper provides a comprehensive review of the theories, experimental data, and modeling methods for pre-Darcy flow in low-permeability porous media. The review begins by outlining the fundamental mechanisms underlying pre-Darcy flow that regulate the unique characteristics such as nonlinear dependence of the Darcy velocity on the pressure gradient and its relevance to fluid–rock interactions. The review then proceeds to present a thorough compilation of experimental investigations performed in various low-permeability geomaterials including tight sandstones, shales, and clays. Next, empirical and theoretical models and simulation methods that have been developed to fit and interpret experimental data are reviewed. Finally, the review underscores the challenges encountered in conducting and interpreting pre-Darcy flow experiments and suggests future research directions. By analyzing previous experimental investigations, this review aims to offer a valuable resource for researchers and practitioners seeking to enhance their understanding of fluid dynamics in low-permeability geomaterials. This provides insights into the application of pre-Darcy flow in numerous natural and engineered processes such as shale oil and gas recovery, contaminant transport in low-permeability aquifers, and geological disposal of nuclear waste.

58 GEOSCIENCES↗
DOE OSTI2024

NREL Marine Energy Desalination R&D Portfolio

The National Renewable Energy Laboratory (NREL), in collaboration with the U.S. Department of Energy's (DOE's) Water Power Technologies Office (WPTO), has developed a unique R&D approach to advance marine energy desalination. Desalination is a foundational investment within WPTO's Powering the Blue EconomyTM portfolio [1], and was the first investment within this portfolio. NREL's marine energy desalination spans techno-economic feasibility studies, numerical modeling, and laboratory testing at the component and subsystem level, as well as development of the Hydraulic and Electric Reverse Osmosis Wave Energy Converter (HERO WEC). This multilayered approach enables an innovative feedback loop where the data and lessons learned from laboratory and field experiments are used to refine modeling tools and analysis techniques, prioritize out-year activities, and refine strategic directions within NREL and across the WPTO portfolio. The primary objective of the NREL-led research is to identify key barriers associated with the commercialization of wave-powered desalination and develop solutions that can be adopted by the marine energy industry. It should be noted, while WPTO's marine energy portfolio includes wave, tidal, ocean current, thermal gradients, and pressure gradients the bulk of the marine energy desalination work has been focused on wave powered desalination. In parallel, these R&D activities can help inform technical assistance and support of industry and academic technologies. These two tracks help build a common solver community approach, while also identifying key stakeholders, government agencies, and other organizations outside of the marine sector that will be necessary for developing a robust industry.

desalination↗
DOE OSTI2023

Demonstration of RANS models with wall functions in the spectral element code Nek5000

The spectral element based computational fluid dynamics (CFD) code Nek5000 has been traditionally used for high-fidelity applications, such as direct numerical simulation (DNS) and large eddy simulation (LES). These techniques require very fine numerical resolution to accurately capture turbulent fluctuations which can be prohibitively expensive for users without access to leadership class computing facilities. For broader application and adoption, significant effort has been invested to develop Reynolds-averaged Navier–Stokes (RANS) capabilities in Nek5000. Here, this work presents details of the implementation and demonstration of the standard wall functions for the κ–τ model in Nek5000. Results using the wall-modeled approach are compared to a wall-resolved approach for cases with negligible pressure gradient, viz., channel flow, pipe flow and flow in a reactor subchannel. Results show reasonably good agreement between the two approaches for friction factor and Nusselt number. Some expected differences are identified near the wall. These cases demonstrate the potential for significant computational savings by using much coarser meshes for the wall-modeled approach, with only minor differences between the predicted result. Additionally, several Reynolds numbers up to 1,000,000 are demonstrated for pipe flow and predicted friction factors and Nusselt numbers compared well to available correlations, with the worst below 10%. As the Reynolds number is increased, better agreement is observed between the correlations and the wall-modeled approach. In addition, flow in a molten salt fast reactor (MSFR) core is considered which features an adverse pressure gradient and flow separation. It showcases the inability of standard wall functions to accurately predict flows with adverse pressure gradients. The results, however, match reasonably well in trend in regions of the flow where the boundary layer is attached. Ongoing research is dedicated to include a pressure gradient correction to wall functions to improve the accuracy of flows with separation or reattachment and adverse or favorable pressure gradients.

42 ENGINEERING↗
DOE OSTI2023

Fundamental study of gas species transport in the oxygen electrode of solid oxide fuel and electrolysis cells

A fundamental analysis of multicomponent gas transport models was performed in application to the oxygen electrodes of solid oxide cells. It is common practice to neglect the effect of pressure gradients within oxygen electrodes, even though a net molar flux at the electrolyte surface implies that a pressure gradient must exist. The influence of both Darcy velocity and Knudsen flux are considered in the context of ordinary (Fickian) diffusion, the dusty gas model, and the binary friction model. Comparisons between the models and different sets of assumptions are made via parametric studies on operating load, oxygen partial pressure, microstructural properties, and electrode thickness. Results show that the pressure gradient will have a significant impact on the oxygen concentration distribution and therefore the concentration overpotential. In electrolysis mode, pressure increases up to 1 atm are predicted, indicating that pressure at the electrode/electrolyte interface could contribute to electrode delamination. Additionally, it is found that Darcy's law is insufficient for calculating the pressure distribution without accounting for the flux due to Knudsen diffusion. Additionally, it is found that for the range of properties typical of oxygen electrodes, there is a negligibly small difference between the dusty gas model and binary friction model from a practical standpoint.

08 HYDROGEN↗
DOE OSTI2024

Characterization of the ELM-free negative triangularity edge on DIII-D

Tokamak plasmas with strong negative triangularity (NT) shaping typically exhibit fundamentally different edge behavior than conventional L-mode or H-mode plasmas. On DIII-D, every plasma with sufficiently negative triangularity (δ < δ crit ≃ -0.12) is found to be inherently free of edge localized modes (ELMs), even at injected powers well above the predicted L-H power threshold. It is also possible to access an ELM free state at weaker average triangularities provided that at least one of the two x-points is still sufficiently negative. Access to the ELM-free NT scenario is found to coincide with the closure of the second stability region for infinite-n ballooning modes, suggesting that ballooning stability may play a role in limiting the accessible pressure gradient in NT plasmas. Despite this, NT plasmas are able to support small pedestals and are typically characterized by an enhancement of edge pressure gradients beyond those found in traditional L mode plasmas. Further, the pressure gradient inside of this small pedestal is unusually steep, allowing access to high core performance that is competitive with other ELM-free regimes previously achieved on DIII-D. Since ELM-free operation in NT is linked directly to the magnetic geometry, NT fusion pilot plants are predicted to maintain advantageous edge conditions even in burning plasma regimes, potentially eliminating reactor core-integration issues caused by ELMs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Evaluation and optimization of flow boiling frictional pressure drop correlations using the data from traditional and next-generation refrigerants in a micro-fin tube

This study presents an experimental evaluation and optimization of flow boiling frictional pressure drop correlations for conventional and next-generation refrigerants in a horizontal micro-fin tube, with particular emphasis on the newly emerging refrigerant blends R-454C and R-455A, for which pressure-drop data in enhanced tubes remain limited. Experiments were conducted with R-410A, R-454C, R-455A, R-134a, R-1234yf, and R-1234ze(E) in a copper micro-fin tube with an inner diameter of 8.468 mm, over mass fluxes ranging from 100 to 300 kg/(m²·s) depending on the refrigerant, and evaporation temperatures of 7, 12, and 14 °C. Frictional pressure gradients were determined from measured total pressure drops after subtracting acceleration pressure drop, and the resulting database was used to assess four existing models: Kuo and Wang (1996), Cavallini et al. (1997), Goto et al. (2001), and Diani et al. (2014). The measured frictional pressure gradient increased with vapor quality and mass flux for all refrigerants and increased further at lower evaporation temperatures, with the overall trend strongly related to liquid viscosity. Among the four correlations, the Goto et al. (2001) model provided the best overall agreement with the measured data before optimization. To further improve prediction accuracy, the Kuo and Wang (1996) and Goto et al. (2001) models were optimized using the complete experimental database. After optimization, both models reduced the overall mean absolute deviation to below 15%, while the optimized Goto et al. (2001) model maintained the best and most consistent overall performance. The results provide new pressure-drop data for next-generation refrigerants and demonstrate that parameter optimization can significantly enhance the applicability of existing micro-fin-tube correlations.

Hu, Yifeng [ORNL] (ORCID:0000000242875185)↗