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Results for “Dimensionless Numbers”

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 91 records · Page 5

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NASA NTRS1992

Transition of oscillatory flow in tubes - An empirical model for application to Stirling engines

Attention is given to an empirical model for transition to turbulence in oscillatory flows in straight tubes. Designed after a correlation for transition of a boundary layer on a flat plate, the model yields the laminar flow momentum thickness Reynolds number that must be met before transition to turbulence will occur. The transition point is located by comparing this to the actual momentum thickness Reynolds number. A scheme is proposed for estimating the momentum thickness Reynolds number in terms of the position within the cycle, the maximum value of the diameter Reynolds within the cycle, Re(max), and the dimensionless frequency, Valensi number. Results from an experimental study of oscillatory flow in a tube are employed to develop the model. When the flow is determined to be turbulent, it is proposed that a fully-developed, steady flow friction coefficient be applied. When the flow is laminar, the assumption of fully developed flow cannot be made; thus, a method is suggested for estimating the friction factor.

Simon, T. W.↗

DOE OSTI2025

Probing the Effect of Electrode Thermodynamics on Reaction Heterogeneity in Thick Battery Electrodes

Thick electrodes present a viable strategy for enhancing energy density and reducing manufacturing costs of lithium-ion batteries. However, reaction heterogeneity during cycling compromises their rate capability and cycle life. While this nonuniformity is commonly attributed to sluggish charge transport, it is demonstrated here that the thermodynamic properties of the electrode material play an equally critical role. Through combined X-ray fluorescence microscopy and absorption near-edge structure spectroscopy, reaction distributions in LiFePO 4 (LFP) and LiNi 0.6 Mn 0.2 Co 0.2 O 2 (NMC) thick electrodes with matched porosity and tortuosity are compared. LFP electrodes develop pronounced depth-oriented state-of-charge (SOC) gradients that worsen with increasing discharge rates, whereas NMC maintains much more uniform SOC distributions under such conditions. This difference originates from their distinct SOC dependence of equilibrium potentials and is quantifiable through a dimensionless “reaction uniformity” number. Intriguingly, LFP thick electrodes also exhibit lateral SOC variations that strengthen during slow discharge. In conclusion, the enhanced reaction uniformity in NMC correlates with better active material utilization and slower capacity fade than LFP, highlighting electrode thermodynamics as a key design consideration for thick electrodes.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Enhanced energy conversion efficiency promoted by cavitation in gasoline direct injection

High-pressure direct fuel injection plays the most crucial role in energy conversion and improving engine combustion efficiency and emission. The optimization of turbulent and multiphase fuel injection has focused on controlling hydrodynamic parameters such as injection pressure. While the thermodynamic influence is often considered in the flash boiling situation, we inquire into how gasoline-type fuel’s hydro- and thermodynamic properties impact the injection dynamics by fuel-temperature induced cavitation. The turbulent and cavitating flows emanating from the direct-injection nozzle is visualized by ultrafast x-ray imaging with an unprecedented spatiotemporal resolution. The ultrafast liquid-fuel dynamics are dominated by injection pressure as well as fuel temperature through cavitation, an important thermodynamic parameter but often difficult to control in engine combustion. With the most direct and quantitative measurement, we discovered that the near-nozzle fuel-jet dynamics can be perfectly scaled by a single dimensionless parameter, cavitation number, particularly sensitive to the fuel temperature, in a wide operation range. This universal scaling shows that cavitation can be harnessed to elevate the pneumatic-hydraulic to kinetic energy conversion efficiency, critical for promoting fuel atomization and engine combustion performance. This enhancement effect will have even more impact on engine combustion using alternative low-emission fuels with higher saturated vapor pressure.

30 DIRECT ENERGY CONVERSION↗

DOE OSTI2024

Quantifying electron transport in aggregated colloidal suspensions in the strong flow regime

Electron transport in complex fluids, biology, and soft matter is a valuable characteristic in processes ranging from redox reactions to electrochemical energy storage. These processes often employ conductor–insulator composites in which electron transport properties are fundamentally linked to the microstructure and dynamics of the conductive phase. While microstructure and dynamics are well recognized as key determinants of the electrical properties, a unified description of their effect has yet to be determined, especially under flowing conditions. In this work, the conductivity and shear viscosity are measured for conductive colloidal suspensions to build a unified description by exploiting both recent quantification of the effect of flow-induced dynamics on electron transport and well-established relationships between electrical properties, microstructure, and flow. These model suspensions consist of conductive carbon black (CB) particles dispersed in fluids of varying viscosities and dielectric constants. In a stable, well-characterized shear rate regime where all suspensions undergo self-similar agglomerate breakup, competing relationships between conductivity and shear rate were observed. To account for the role of variable agglomerate size, equivalent microstructural states were identified using a dimensionless fluid Mason number, Mn f , which allowed for isolation of the role of dynamics on the flow-induced electron transport rate. At equivalent microstructural states, shear-enhanced particle–particle collisions are found to dominate the electron transport rate. This work rationalizes seemingly contradictory experimental observations in literature concerning the shear-dependent electrical properties of CB suspensions and can be extended to other flowing composite systems.

Science & Technology - Other Topics↗

DOE OSTI2020

Thermodynamic Origin of Reaction Non-Uniformity in Battery Porous Electrodes and Its Mitigation

The development of non-uniform reaction current distribution within porous electrodes is a ubiquitous phenomenon during battery charging/discharging and frequently controls the rate performance of battery cells. Reaction inhomogeneity in porous electrodes is usually attributed to the kinetic limitation of mass transport within the electrolyte and/or solid electrode phase. In this work, however, we reveal that it is also strongly influenced by the intrinsic thermodynamic behavior of electrode materials, specifically the dependence of the equilibrium potential on the state of charge: the electrode reaction becomes increasingly non-uniform when the slope of the equilibrium potential curve is reduced. We employ numerical simulations and equivalent circuit model to elucidate such a correlation and show that the degree of reaction inhomogeneity and the resultant discharge capacity can be predicted by a dimensionless reaction uniformity number. For electrode materials that have equilibrium potentials insensitive to the state of charge and exhibit significant reaction non-uniformity, we demonstrate several approaches to spatially homogenizing the reaction current inside porous electrodes, including matching the electronic and ionic resistances, introducing graded electronic conductivity and reducing the surface reaction kinetics.

25 ENERGY STORAGE↗

NASA NTRS1982

Jet array impingement flow distributions and heat transfer characteristics. Effects of initial crossflow and nonuniform array geometry

Two-dimensional arrays of circular air jets impinging on a heat transfer surface parallel to the jet orifice plate are considered. The jet flow, after impingement, is constrained to exit in a single direction along the channel formed by the jet orifice plate and the heat transfer surface. The configurations considered are intended to model those of interest in current and contemplated gas turbine airfoil midchord cooling applications. The effects of an initial crossflow which approaches the array through an upstream extension of the channel are considered. Flow distributions as well as heat transfer coefficients and adiabatic wall temperatures resolved to one streamwise hole spacing were measured as a function of the initial crossflow rate and temperature relative to the jet flow rate and temperature. Both Nusselt number profiles and dimensionless adiabatic wall temperature (effectiveness) profiles are presented and discussed. Special test results which show a significant reduction of jet orifice discharge coefficients owing to the effect of a confined crossflow are also presented, along with a flow distribution model which incorporates those effects. A nonuniform array flow distribution model is developed and validated.

Florschuetz, L. W.↗

NASA NTRS1998

Tape-Drop Transient Model for In-Situ Automated Tape Placement of Thermoplastic Composites

Composite parts of nonuniform thickness can be fabricated by in-situ automated tape placement (ATP) if the tape can be started and stopped at interior points of the part instead of always at its edges. This technique is termed start/stop-on-the-part, or, alternatively, tape-add/tape-drop. The resulting thermal transients need to be managed in order to achieve net shape and maintain uniform interlaminar weld strength and crystallinity. Starting-on-the-part has been treated previously. This paper continues the study with a thermal analysis of stopping-on-the-part. The thermal source is switched off when the trailing end of the tape enters the nip region of the laydown/consolidation head. The thermal transient is determined by a Fourier-Laplace transform solution of the two-dimensional, time-dependent thermal transport equation. This solution requires that the Peclet number Pe (the dimensionless ratio of inertial to diffusive heat transport) be independent of time and much greater than 1. Plotted isotherms show that the trailing tape-end cools more rapidly than the downstream portions of tape. This cooling can weaken the bond near the tape end; however the length of the affected region is found to be less than 2 mm. To achieve net shape, the consolidation head must continue to move after cut-off until the temperature on the weld interface decreases to the glass transition temperature. The time and elapsed distance for this condition to occur are computed for the Langley ATP robot applying PEEK/carbon fiber composite tape and for two upgrades in robot performance. The elapsed distance after cut-off ranges from about 1 mm for the present robot to about 1 cm for the second upgrade.

Costen, Robert C.↗

NASA NTRS2004

Sensitivity Studies for In-Situ Automated Tape Placement of Thermoplastic Composites

This modeling effort seeks to improve the interlaminate bond strength of thermoplastic carbon composites produced by the in-situ automated tape placement (ATP) process. An existing high productivity model is extended to lower values of the Peclet number that correspond to the present operating conditions of the Langley ATP robot. (The Peclet number is the dimensionless ratio of inertial to diffusive heat transfer.) In sensitivity studies, all of the process and material parameters are individually varied. The model yields the corresponding variations in the effective bonding time (EBT) referred to the glass transition temperature. According to reptation theory, the interlaminate bond strength after wetting occurs is proportional to the one-fourth power of EBT. The model also computes the corresponding variations in the thermal input power (TIP) and the mass and volumetric process rates. Process studies show that a 10 percent increase in the consolidation length results in a 20 percent increase in EBT and a 5 percent increase in TIP. A surprising result is that a 10 K decrease in the tooling temperature results in a 25 percent increase in EBT and an 8 percent increase in TIP. Material studies show that a 10 K decrease in glass transition temperature results in an 8 percent increase in EBT and a 8 percent decrease in TIP. A 20 K increase in polymer degradation temperature results in a 23 percent increase in EBT with no change in TIP.

Costen, Robert C.↗

NASA NTRS1992

Experimental verification of scaling parameters for thermal stratification

A study to determine important dimensionless parameters associated with thermal stratification of a heated container of liquid, and the pressure history of its vapor, was performed. Analysis of the governing equations identified the modified Grashoff number, the modified Fourier number, and the interface number as the dominant dimensionless parameters associated with this process. A test program designed to verify the validity of these scaling parameters was executed. The quality of scaling was checked by comparing the dimensionless pressures and temperatures for scaled pairs of tests. Results indicate that the bulk liquid temperature, the surface temperature of the liquid, and the tank pressure can be scaled with the three dimensionless parameters. Some deviations were found in the detailed temperature profiles between the scaled pairs of tests.

Ji, H.-C.↗

DOE OSTI2021

Methods—Design Guidelines for Tubular Flow-through Electrodes for Use in Electroanalytical Studies of Redox Reaction Kinetics

The tubular flow-through electrode (FTE) is a facile electroanalytical tool for investigating electrochemical reaction kinetics; however, its suitability for this purpose requires careful design and operation under conditions that guarantee uniform current distribution. In this perspective article, we provide a scaling analysis of the transport and reaction processes within a tubular FTE leading to quantitative guidelines for the FTE design and operation. Two dimensionless parameters (classical Wagner number Wa I and modified Wagner number incorporating the effect of mass transport Wa II ) are utilized to compare the magnitudes of the ohmic, activation and transport resistances of the tubular FTE, and to quantify its current distribution uniformity. With the aid of analytical modeling of the current distribution, optimal ranges for these two dimensionless parameters are defined so as to ascertain uniform current distribution. Application of these guidelines to a graphite tubular FTE is shown to enable the precise determination of the charge-transfer kinetics of the ferri/ferrocyanide redox reaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2023

Hydrodynamics of bubble flow through a porous medium with applications to packed bed reactors

Gas-liquid flows through packed bed reactors (PBRs) are challenging to predict due to the tortuous flow paths that fluid interfaces must traverse. Experiments at the International Space Station showed that bubble and pulse flows are predominately observed under microgravity conditions, while the trickle and spray flows observed under terrestrial conditions are not present in microgravity. To understand the physics behind the former experiments, we simulate bubble flow through a PBR for different packing-particle-diameter-based Weber numbers and under different gravity conditions. We demonstrate different pore-scale mechanisms, such as capillary entrapment, buoyancy entrapment, and inertia-induced bubble displacement. Then, we perform a quantitative analysis by introducing new dynamic scales, dependent upon the evolving gas-liquid interfacial area, to understand the dynamic trade-offs between the inertia, capillary, and buoyancy forces on a bubble passing through a PBR. This analysis leads us to define new dimensionless Weber-like numbers that delineate bubble entrapment from bubble displacement.

Pranay P Nagrani↗

DOE OSTI2026

Pore-Scale Transport Effects in Electrochemical CO 2 Reduction on Gold via Coupled Microkinetic-Transport Modeling

A pore-resolved modeling framework is developed to quantify how pore-scale transport affects the intrinsic microkinetics of CO 2 -to-CO on Au. A DFT-informed microkinetic model is coupled self-consistently to a Generalized-Modified Poisson–Nernst–Planck (GMPNP) transport description in a single, electrolyte-filled cylindrical pore, allowing local concentrations and potential to feed back into site-specific reaction rates. FIB-SEM is used to determine pore sizes within realistic electrode materials. Across pore diameters, d p = 10–6000 nm, the surface-averaged CO 2 reduction rate is systematically reduced relative to the ideal microkinetic baseline where mass transport is not accounted for; the effectiveness factor 𝜂 𝑠,CO 2 , which quantifies this ratio, decreases rapidly at more negative potentials and is about 1% near −1.0 V vs SHE due to reactant depletion. Spatial maps reveal pore-bulk alkalization that emerges at higher cathodic bias, with a small, near-wall pH dip due to electrostatic repulsion of hydroxide at the cathode interface. For a fixed aspect ratio L p /d p , narrower pores exhibit larger 𝜂 𝑠,CO 2 by shortening diffusion paths, whereas variations in the aspect ratio L p /d p play a secondary role. A dimensionless analysis (surface/bulk Damköhler numbers) delineates operating regimes. In conclusion, this work offers a concept for incorporating microkinetic models into homogenized porous-electrode models through effectiveness factors and pore-size distribution.

Au-catalyst↗

NASA NTRS1975

Non-equilibrium one-dimensional two-phase flow in variable area channels

A one-dimensional nonequilibrium flow analysis has been formulated for a one component two phase flow. The flow is considered homogeneous and essentially isothermal. Phase change is assumed to occur at heterogeneous nucleation sites and the growth of the vapor bubbles is governed by heat conduction from the liquid to the bubble. The analysis adjusted for friction is applied to liquid nitrogen flow in a venturi and comparison is made with the NASA experimental results of Simoneau. Good agreement with the experiments is obtained when one assumes the effective activation energy for nucleus formation to be small but nonzero. The computed pressure distributions deviate from the experimental results in the throat region of the venturi in a manner consistent with centrifugal effects not accounted for in the one-dimensional theory. The results are shown to depend not only on cavitation number but on additional dimensionless parameters governing the nonequilibrium production and subsequent growth of nuclei.

Rohatgi, U. S.↗

NASA NTRS1981

Beam stresses induced by a turbulent boundary layer and simulated with a reverberant acoustic field

Unsteady pressure fluctuations are a feature of the flow field of an airplane or a space vehicle in atmospheric flight. Undesirable effects of these fluctuations range from internal (cabin) noise to structural fatigue and damage of avionic and ordnance systems. The integrity to withstand these fluctuating loads is established through reverberant room acoustical qualification testing. The purpose of this paper is to develop a methodology of simulating turbulent boundary layer fluctuating pressure loading for a simply supported beam with a reverberant acoustic field. This goal was accomplished using normal mode vibration analysis. The main results were developed in terms of dimensionless quantities such as turbulent boundary layer spectrums, reverberant acoustical field simulation spectrums, and stress response spectrums with parameters: dimensionless fundamental frequency, Mach number, and relative boundary layer displacement thickness.

Schutzenhofer, L. A.↗

NASA NTRS1982

Asymptotic Expansions and Estimates for the Capillary Problem

The asymptotic properties for the small Bond number B of the equilibrium capillary interface interior to a circular cylindrical tube vertically dipped in an infinite reservoir of liquid are discussed. (The Bond number B is a dimensionless parameter which is the ratio of gravitational to capillary forces.) The formal expansion in powers of B of the solution to the differential equation describing the equilibrium surface (as can be obtained by standard perturbation methods) is proved to be truly asymptotic -- to all orders and uniformly in the variable and parameter gamma, the contact angle. Sequences of general estimates, in closed form, from above and from below, are also given for the solution and related functions. The M-th term in these sequences are asymptotically exact to order m. An idiosyncrasy of the problem, crucial in obtaining these estimates, is the absolute monotonicity of the structural function of the system in integral form.

Brulois, F. P.↗

NASA NTRS1983

Optimum parallel step-sector bearing lubricated with an incompressible fluid

The dimensionless parameters normally associated with a step sector thrust bearing are the film thickness ratio, the dimensionless step location, the number of sectors, the radius ratio, and the angular extent of the lubrication feed groove. The optimum number of sectors and the parallel step configuration for a step sector thrust bearing while considering load capacity or stiffness and assuming an incompressible fluid are presented.

Hamrock, B. J.↗

NASA NTRS1985

Liquid fuel spray processes in high-pressure gas flow

Atomization of single liquid jets injected downstream in high pressure and high velocity airflow was investigated to determine the effect of airstream pressure on mean drop size as measured with a scanning radiometer. For aerodynamic - wave breakup of liquid jets, the ratio of orifice diameter D sub o to measured mean drop diameter D sub m which is assumed equal to D sub 32 or Sauter mean diameter, was correlated with the product of the Weber and Reynolds numbers WeRe and the dimensionless group G1/square root of c, where G is the gravitational acceleration, 1 the mean free molecular path, and square root of C the root mean square velocity, as follows; D sub o/D sub 32 = 1.2 (WeRe) to the 0.4 (G1/square root of c) to the 0.15 for values of WeRe 1 million and an airstream pressure range of 0.10 to 2.10 MPa.

Ingebo, R. D.↗

NASA NTRS1986

Liquid fuel spray processes in high-pressure gas flow

Ingebo, R. D.↗