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All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

Effects of Fuel Preheat on Soot Formation in Microgravity Laminar Diffusion Flames

Nonbuoyant flames offer themselves as an attractive and promising platform to gain a better understanding of soot mechanisms. The effects of buoyancy can be eliminated temporarily in drop towers which sustain brief intervals of reduced gravity-typically lower than 10(exp -3)g- extending up to several seconds at a time. Microgravity facilities have been employed to show that nonbuoyant flames are longer, wider and sootier than their normal-gravity counterparts. Sunderland et al. recently verified the existence of smoke point in laminar nonbuoyant flames. As reported, microgravity flames operating above their smoke point displayed a blunt tip and much broader soot-containing regimes in comparison to their buoyant counterparts. Mortazavi et al. established that residence times in microgravity laminar jet diffusion flames with Re=0(100) tend to be proportional to burner diameter and inversely proportional to burner exit velocity. This offers the capability to alter residence times in nonbuoyant laminar jet diffusion flames when varying the burner exit diameters and velocities. Megaridis et al. presented a quantitative definition of the soot-field structure within laminar microgravity jet diffusion flames which operated well above their smoke point. The experimental methodology involved a full-field laser-light extinction technique and jet diffusion flames of nitrogen-diluted (50% vol.) acetylene fuel burning in quiescent air at atmospheric pressure. The work was conducted at the 2.2s drop tower of the NASA Lewis Research Center (NASA-LeRC). Parallel work on 1-g flames was also presented in (6) to facilitate comparisons on the effect of gravity on the soot fields. As reported, the soot spatial distributions in 0-g flames did not change in a detectable manner after 1s within a typical 2.2s experiment. During that period, the soot field was shown to sustain a pronounced annular structure throughout the luminous nonbuoyant-flame zone. The maximum soot volume fraction measured at 0-g was nearly a factor of two higher than that at 1-g, thus confirming the enhanced sooting tendency of nonbuoyant flames. Greenberg and Ku presented a similar study and reported trends that matched those of for the 50% (vol.) nitrogen-diluted acetylene fuel. Furthermore, they examined pure acetylene flames and reported similar trends with respect to the influence of gravity on maximum soot volume fractions and flame cross-section-averaged soot loadings. Both studies clearly demonstrated the improved spatial resolution of microgravity flames compared to their normal-gravity counterparts. The current study evaluates the influence of moderate fuel preheat on soot formation within 0-g laminar gas jet diffusion flames. While fuel temperature variations have little influence on residence times in 1-g, they have a much more significant effect in 0-g. The primary objective of this program is to quantify this effect and its consequences on sooting by comparing soot volume fraction distributions under preheated and unpreheated-fuel conditions. Furthermore, the current work aims at expanding the limited soot database available for nonbuoyant flames. Soot fields in such flames can be used to perform additional tests of recently developed soot sub-models which have the potential to become powerful predicting tools in combustion design.

Konsur, Bogdan↗
NASA NTRS1999

Laminar Dust Flames: A Program of Microgravity and Ground Based Studies at McGill

Fundamental knowledge of heterogeneous combustion mechanisms is required to improve utilization of solid fuels (e.g. coal), safe handling of combustible dusts in industry, and solid propulsion systems. The objective of the McGill University research program on dust combustion is to obtain a reliable set of data on basic combustion parameters for dust suspensions (i.e. laminar burning velocity, flame structure, quenching distance, flammability limits, etc.) over a range of particle sizes, dust concentrations, and types of fuel. This set of data then permits theoretical models to be validated and, when necessary, new models to be developed to describe the detailed reaction mechanisms and transport processes. Microgravity is essential to the generation of a uniform dust suspension of arbitrary particle size and concentration. When particles with a characteristic size on the order of tens of microns are suspended, they rapidly settle in a gravitational field. To maintain a particulate in suspension for time duration adequate to carry out combustion experiments invariably requires continuous convective flow in excess of the gravitational settling velocity (which is comparable with and can even exceed the dust laminar burning velocity). This makes the experiments turbulent in nature and thus renders it impossible to study laminar dust flames. Even for small particle sizes on the order of microns, a stable laminar dust flow can be maintained only for relatively low dust concentrations at normal gravity conditions. High dust loading leads to gravitational instability of the dust cloud and to the formation of recirculation cells in the dust suspension in a confined volume, or to the rapid sedimentation of the dense dust cloud, as a whole, in an unconfined volume. Many important solid fuels such as carbon and boron also have low laminar flame speeds (of the order of several centimeters per second). Convection that occurs in combustion products due to buoyancy disrupts the low speed dust flames and makes observation of such flames at normal gravity difficult.

Goroshin, Sam↗
NASA NTRS1999

A History of Suction-Type Laminar Flow Control with Emphasis on Flight Research

Laminar-flow control is an area of aeronautical research that has a long history at NASA's Langley Research Center, Dryden Flight Research Center, their predecessor organizations, and elsewhere. In this monograph, the author, who spent much of his career at Langley working with this research, presents a history of that portion of laminar-flow technology known as active laminar-flow control, which employs suction of a small quantity of air through airplane surfaces. This important technique offers the potential for significant reduction in drag and, thereby, for large increases in range or reductions in fuel usage for aircraft. For transport aircraft, the reductions in fuel consumed as a result of laminar-flow control may equal 30 percent of present consumption. Given such potential, it is obvious that active laminar-flow control with suction is an important technology. In this study, the author covers the early history of the subject and brings the story all the way to the mid-1990s with an emphasis on flight research, much of which has occurred at Dryden. This is an important monograph that not only encapsulates a lot of history in a brief compass but also does so in language that is accessible to non-technical readers. NASA is publishing it in a format that will enable it to reach the wide audience the subject deserves.

Braslow, Albert L.↗
NASA NTRS1999

Boundary-Layer Transition Results from the F-16XL-2 Supersonic Laminar Flow Control Experiment

A variable-porosity suction glove has been flown on the F-16XL-2 aircraft to demonstrate the feasibility of this technology for the proposed High-Speed Civil Transport (HSCT). Boundary-layer transition data have been obtained on the titanium glove primarily at Mach 2.0 and altitudes of 53,000-55,000 ft. The objectives of this supersonic laminar flow control flight experiment have been to achieve 50- to 60-percent-chord laminar flow on a highly swept wing at supersonic speeds and to provide data to validate codes and suction design. The most successful laminar flow results have not been obtained at the glove design point (Mach 1.9 at an altitude of 50,000 ft). At Mach 2.0 and an altitude of 53,000 ft, which corresponds to a Reynolds number of 22.7 X 10(exp 6), optimum suction levels have allowed long runs of a minimum of 46-percent-chord laminar flow to be achieved. This paper discusses research variables that directly impact the ability to obtain laminar flow and techniques to correct for these variables.

Marshall, Laurie A.↗
NASA NTRS2000

Summary of Transition Results From the F-16XL-2 Supersonic Laminar Flow Control Experiment

A variable-porosity suction glove has been flown on the F-16XL-2 aircraft to demonstrate the feasibility of this technology for the proposed High-Speed Civil Transport. Boundary-layer transition data on the titanium glove primarily have been obtained at speeds of Mach 2.0 and altitudes of 15,240-16,764 m (50,000-55,000 ft). The objectives of this flight experiment have been to achieve 0.50-0.60 chord laminar flow on a highly swept wing at supersonic speeds and to provide data to validate codes and suction design. The most successful laminar flow results have not been obtained at the glove design point, a speed of Mach 1.9 at an altitude of 15,240 m (50,000 ft); but rather at a speed of Mach 2.0 and an altitude of 16,154 m (53,000 ft). Laminar flow has been obtained to more than 0.46 wing chord at a Reynolds number of 22.7 x 10(exp 6). A turbulence diverter has been used to initially obtain a laminar boundary layer at the attachment line. A lower-surface shock fence was required to block an inlet shock from the wing leading edge. This paper discusses research variables that directly impact the ability to obtain laminar flow and techniques to correct for these variables.

Marshall, Laurie A.↗
NASA NTRS2001

Laminarization of Turbulent Boundary Layer on Flexible and Rigid Surfaces

An investigation of the control of turbulent boundary layer flow over flexible and rigid surfaces downstream of a concave-convex geometry has been made. The concave-convex curvature induces centrifugal forces and a pressure gradient on the growth of the turbulent boundary layer. The favorable gradient is not sufficient to overcome the unfavorable; thus, the net effect is a destabilizing, of the flow into Gortler instabilities. This study shows that control of the turbulent boundary layer and structural loading can be successfully achieved by using localized surface heating because the subsequent cooling and geometrical shaping downstream over a favorable pressure gradient is effective in laminarization of the turbulence. Wires embedded in a thermally insulated substrate provide surface heating. The laminarized velocity profile adjusts to a lower Reynolds number, and the structure responds to a lower loading. In the laminarization, the turbulent energy is dissipated by molecular transport by both viscous and conductivity mechanisms. Laminarization reduces spanwise vorticity because of the longitudinal cooling gradient of the sublayer profile. The results demonstrate that the curvature-induced mean pressure gradient enhances the receptivity of the flow to localized surface heating, a potentially viable mechanism to laminarize turbulent boundary layer flow; thus, the flow reduces the response of the flexible structure and the resultant sound radiation.

Maestrello, Lucio↗
NASA NTRS2000

Laminar Premixed and Diffusion Flames (Ground-Based Study)

Ground-based studies of soot processes in laminar flames proceeded in two phases, considering laminar premixed flames and laminar diffusion flames, in turn. The test arrangement for laminar premixed flames involved round flat flame burners directed vertically upward at atmospheric pressure. The test arrangement for laminar jet diffusion flames involved a round fuel port directed vertically upward with various hydrocarbon fuels burning at atmospheric pressure in air. In both cases, coflow was used to prevent flame oscillations and measurements were limited to the flame axes. The measurements were sufficient to resolve soot nucleation, growth and oxidation rates, as well as the properties of the environment needed to evaluate mechanisms of these processes. The experimental methods used were also designed to maintain capabilities for experimental methods used in corresponding space-based experiments. This section of the report will be limited to consideration of flame structure for both premixed and diffusion flames.

Dai, Z.↗
NASA NTRS2002

Laminar Soot Processes (LSP)

This is the final report of a research program considering the structure and the soot surface reaction properties of laminar nonpremixed (diffusion) flames. The study was limited to ground-based measurements of buoyant laminar jet diffusion flames at pressures of 0.1-1.0 atm. The motivation for the research is that soot formation in flames is a major unresolved problem of combustion science that influences the pollutant emissions, durability and performance of power and propulsion systems, as well as the potential for developing computational combustion. The investigation was divided into two phases considering the structure of laminar soot-containing diffusion flames and the soot surface reaction properties (soot surface growth and oxidation) of these flames, in turn. The first phase of the research addressed flame and soot structure properties of buoyant laminar jet diffusion flames at various pressures. The measurements showed that H, OH and O radical concentrations were generally in superequilibrium concentrations at atmospheric pressure but tended toward subequilibrium concentrations as pressures decreased. The measurements indicated that the original fuel decomposed into more robust compounds at elevated temperatures, such as acetylene (unless the original fuel was acetylene) and H, which are the major reactants for soot surface growth, and that the main effect of the parent fuel on soot surface growth involved its yield of acetylene and H for present test conditions. The second phase of the research addressed soot surface reaction properties, e.g., soot surface growth and surface oxidation. It was found that soot surface growth rates in both laminar premixed and diffusion flames were in good agreement, that these rates were relatively independent of fuel type, and that these rates could be correlated by the Hydrogen-Abstraction/Carbon-Addition (HACA) mechanisms of Colket and Hall (1994), Frenklach et al. (1990,1994), and Kazakov et al. (1995). It was also found that soot surface oxidation rates were relatively independent of fuel type, were not correlated with O2, CO2, H2O and O collision rates but were correlated with the collision rates of OH with a collision efficiency of 0.14, in agreement with the early measurements in premixed flames of Neoh et al. (1980), after allowing for oxidation by O2 via the classical rate expression of Nagle and Strickland-Constable (1962).

Dai, Z.↗
NASA NTRS2003

Laminar Soot Processes (LSP) Experiment: Findings From Space Flight Measurements

The present experimental study of soot processes in hydrocarbon-fueled laminar nonbuoyant and nonpremixed (diffusion) flames at microgravity within a spacecraft was motivated by the relevance of soot to the performance of power and propulsion systems, to the hazards of unwanted fires, and to the emission of combustion-generated pollutants. Soot processes in turbulent flames are of greatest practical interest, however, direct study of turbulent flames is not tractable because the unsteadiness and distortion of turbulent flames limit available residence times and spatial resolution within regions where soot processes are important. Thus, laminar diffusion flames are generally used to provide more tractable model flame systems to study processes relevant to turbulent diffusion flames, justified by the known similarities of gas-phase processes in laminar and turbulent diffusion flames, based on the widely-accepted laminar flamelet concept of turbulent flames. Unfortunately, laminar diffusion flames at normal gravity are affected by buoyancy due to their relatively small flow velocities and, as discussed next, they do not have the same utility for simulating the soot processes as they do for simulating the gas phase processes of turbulent flames.

Sunderland, P. B.↗
NASA NTRS2004

Assessment of LAURA for Laminar Supersonic Shallow Cavities

The ability of the Laura flow solver to predict local heating augmentation factors for shallow cavities is assessed. This assessment is part of a larger e ort within the Space Shuttle return-to-flight program to develop technologies to support on-orbit tile repair decisions. The comparison is made against global phosphor thermography images taken in the Langley Aerothermodynamic Laboratory 20-Inch Mach 6 Air Tunnel. The cavities are rectangular in shape, with lengths L/H of 14 20 and depths H/ of 1.1 5.2. The fully laminar results, for Re = 300, show good agreement between the data sets. For Re = 503, the wind tunnel data indicates boundary layer transition with turbulent flow both within and downstream of the cavity. The turbulent flow structures are significantly di erent from the laminar predictions, with order of magnitude increases in the heating augmentations. Because of the di erent flow structures, no simple bump factor can be used to correct the laminar calculations to account for the turbulent heating levels. A fine gradation in wind tunnel cases will be required to clearly delineate the laminar-to-turbulent transition point, and hence the limits of applicability of the laminar numerical approach.

Wood, William A.↗
NASA NTRS1949

An Approximate Method for Calculation of the Laminar Boundary Layer with Suction for Bodies of Arbitrary Shape

Various ways were tried recently to decrease the friction drag of a body in a flow; they all employ influencing the boundary layer. One of them consists in keeping the boundary layer Laminar by suction; promising tests have been carried out. Since for large Reynolds numbers the friction drag of the laminar boundary layer is much lower than that of the turbulent boundary layer, a considerable saving in drag results from keeping the boundary layer laminar, even with the blower power required for suction taken into account. The boundary layer is kept laminar by suction in two ways: first, by reduction of the thickness of the boundary layer and second, by the fact that the suction changes the form of the velocity distribution so that it becomes more stable, in a manner similar to the change by a pressure drop. There by the critical Reynolds number of the boundary layer (USigma*/V) (sub crit) becomes considerably higher than for the case without suction. This latter circumstance takes full effect only if continuous suction is applied which one might visualize realized through a porous wall. Thus the suction quantities required for keeping the boundary layer laminar become so small that the suction must be regarded as a very promising auxiliary means for drag reduction.

Schlichting, H.↗
NASA NTRS2005

Soot Formation in Purely-Curved Premixed Flames and Laminar Flame Speeds of Soot-Forming Flames

The research addressed here is a collaborative project between University of Delaware and Case Western Reserve University. There are two basic and related scientific objectives. First, we wish to demonstrate the suitability of spherical/cylindrical, laminar, premixed flames in the fundamental study of the chemical and physical processes of soot formation. Our reasoning is that the flame standoff distance in spherical/cylindrical flames under microgravity can be substantially larger than that in a flat burner-stabilized flame. Therefore the spherical/cylindrical flame is expected to give better spatial resolution to probe the soot inception and growth chemistry than flat flames. Second, we wish to examine the feasibility of determining the laminar flame speed of soot forming flames. Our basic assumption is that under the adiabatic condition (in the absence of conductive heat loss), the amount and dynamics of soot formed in the flame is unique for a given fuel/air mixture. The laminar flame speed can be rigorously defined as long as the radiative heat loss can be determined. This laminar flame speed characterizes the flame soot formation and dynamics in addition to the heat release rate. The research involves two integral parts: experiments of spherical and cylindrical sooting flames in microgravity (CWRU), and the computational counterpart (UD) that aims to simulate sooting laminar flames, and the sooting limits of near adiabatic flames. The computations work is described in this report, followed by a summary of the accomplishments achieved to date. Details of the microgra+ experiments will be discussed in a separate, final report prepared by the co-PI, Professor C-J. Sung of CWRU. Here only a brief discussion of these experiments will be given.

Buchanan, Thomas↗
NASA NTRS2011

Computational Analysis of the G-III Laminar Flow Glove

Under NASA's Environmentally Responsible Aviation Project, flight experiments are planned with the primary objective of demonstrating the Discrete Roughness Elements (DRE) technology for passive laminar flow control at chord Reynolds numbers relevant to transport aircraft. In this paper, we present a preliminary computational assessment of the Gulfstream-III (G-III) aircraft wing-glove designed to attain natural laminar flow for the leading-edge sweep angle of 34.6deg. Analysis for a flight Mach number of 0.75 shows that it should be possible to achieve natural laminar flow for twice the transition Reynolds number ever achieved at this sweep angle. However, the wing-glove needs to be redesigned to effectively demonstrate passive laminar flow control using DREs. As a by-product of the computational assessment, effect of surface curvature on stationary crossflow disturbances is found to be strongly stabilizing for the current design, and it is suggested that convex surface curvature could be used as a control parameter for natural laminar flow design, provided transition occurs via stationary crossflow disturbances.

Malik, Mujeeb R.↗
NASA NTRS2021

ARTEMIS Observations of Plasma Waves in Laminar and Perturbed Interplanetary Shocks

The ‘Acceleration, Reconnection, Turbulence and Electrodynamics of the Moon's Interaction with the Sun’ (ARTEMIS) mission provides a unique opportunity to study the structure of interplanetary shocks and the associated generation of plasma waves with frequencies between ~50-8000 Hz due to its long duration electric and magnetic field burst waveform captures. We compare wave properties and occurrence rates at 11 quasi-perpendicular interplanetary shocks with burst data within 10 minutes (~3200 proton gyroradii upstream, ~1900 downstream) of the shock ramp. A perturbed shock is defined as possessing a large amplitude whistler precursor in the quasi-static magnetic field with an amplitude greater than ⅓ the difference between the upstream and downstream average magnetic field magnitudes; laminar shocks lack these large precursors and have a smooth, step function-like transition. In addition to wave modes previously observed, including ion acoustic, whistler, and electrostatic solitary waves, waves in the ion acoustic frequency range that show rapid temporal frequency change are common. Three shocks had burst captures in the ramp; of these, the two laminar shocks with burst data in the ramp contained a wide range of large amplitude wave modes in the ramp whereas the one perturbed shock contained no such waves. Thus, energy dissipation through wave-particle interactions is more prominent in these two laminar shocks than in the perturbed shock. Based on observations from all 11 shocks, the The wave occurrence rates for laminar shocks are higher in the transition region, especially the ramp, than downstream. In contrast, perturbed shocks have approximately 2-3 times the wave occurrence rate downstream than laminar shocks.

L. A. Davis↗
DOE OSTI2020

Laminar-to-turbulent flame transition and cycle-to-cycle variations in large eddy simulation of spark-ignition engines

This paper investigates the effect of laminar-to-turbulent flame transition modeling on the prediction of cycle-to-cycle variations (CCVs) in large eddy simulation (LES) of spark-ignition (SI) engines. A laminar-to-turbulent flame transition model that describes the non-equilibrium sub-filter flame speed evolution during an early stage of flame kernel growth is developed. In the present model, the flame transition is characterized by the flame kernel size at which the flame transition ends, defined here as the flame transition scale. The proposed model captures the effects that variations in a turbulent flow field have on the evolution of early-stage burning rates, through variations in the flame transition scale. The proposed flame transition model is combined with the front propagation formulation (FPF) method and a spark-ignition model to predict CCVs in a gasoline direct injection SI engine. It is found that multi-cycle LES with the proposed flame transition model reproduces experimentally-observed CCVs satisfactorily. When the transition model is not considered or when variations in the transition process are neglected, CCVs are significantly under-predicted for the case considered here. These results indicate the importance of modeling the laminar-to-turbulent flame transition and the effect of turbulence on the transition process, when predicting CCVs, under certain engine conditions. The LES results are also used to analyze sources for variations in the flame transition. It is found, for the present engine case, that the most important source is the cycle-to-cycle variation in the turbulence dissipation rate, which is used to measure the strength of turbulence in the proposed model, near a spark plug. The large-scale velocity field and the variations of the laminar flame speed due to the mixture composition and thermal stratification are also found to be important factors to contribute to the variations in the flame transition.

42 ENGINEERING↗
NASA NTRS2015

Flight Tests of a Supersonic Natural Laminar Flow Airfoil

A flight-test campaign of a supersonic natural laminar flow airfoil has been recently completed. The test surface was an 80-inch (203 cm) chord and 40-inch (102 cm) span article mounted on the centerline store location of an F-15B airplane (McDonnell Douglas Corporation, now The Boeing Company, Chicago, Illinois). The test article was designed with a leading edge sweep of effectively 0 deg to minimize boundary layer crossflow. The test article surface was coated with an insulating material to avoid significant heat transfer to and from the test article structure to maintain a quasi-adiabatic wall. An aircraft-mounted infrared camera system was used to determine boundary layer transition and the extent of laminar flow. The tests were flown up to Mach 2.0 and chord Reynolds numbers in excess of 30 million. The objectives of the tests were to determine the extent of laminar flow at high Reynolds numbers and to determine the sensitivity of the flow to disturbances. Both discrete (trip dots) and 2-D disturbances (forward-facing steps) were tested. A series of oblique shocks, of yet unknown origin, appeared on the surface, which generated sufficient crossflow to affect transition. Despite the unwanted crossflow, the airfoil performed well. The results indicate the sensitivity of the flow to the disturbances, which can translate into manufacturing tolerances, were similar to that of subsonic natural laminar flow wings.

supersonic boundary layer↗
DOE OSTI2023

Improved representation of laminar and turbulent sheet flow in subglacial drainage models

Subglacial hydrology models struggle to reproduce seasonal drainage patterns that are consistent with observed subglacial water pressures and surface velocities. We modify the standard sheet-flow parameterization within a coupled sheet–channel subglacial drainage model to smoothly transition between laminar and turbulent flow based on the locally computed Reynolds number in a physically consistent way (the ‘transition’ model). We compare the transition model to standard laminar and turbulent models to assess the role of the sheet-flow parameterization in reconciling observed and modelled water pressures under idealized and realistic forcing. Relative to the turbulent model, the laminar and transition models improve seasonal simulations by increasing winter water pressure and producing a more prominent late-summer water pressure minimum. In contrast to the laminar model, the transition model remains consistent with its own internal assumptions across all flow regimes. Based on the internal consistency of the transition model and its improved performance relative to the standard turbulent model, we recommend its use for transient simulations of subglacial drainage.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Critical Shear Stress for Erosion Under Laminar Jet Flow

Particle erosion is an important process in both natural and manmade environments. For example, in natural environments particle or sediment erosion rates determine the course of rivers, depth of streams, and fate of deltas. The interplay between erosion rates and flow patterns can have dramatic impact on shorelines. Where hydrodynamic jet flows or rip currents change direction, sediments may accumulate or disperse altering the shape of coastlines and the ecosystems and economies that rely on them. In man-made systems, jet flows may be used to mobilize particles from surfaces or within industrial scale mixing tanks. For example, in the nuclear industry, impinging jet mixers may be used to mobilize and suspend sludges at the bottom of waste tanks. In each of these examples, the Shields diagram is useful to determine the conditions under which erosion occurs. This diagram plots the scaled critical shear stress for erosion as a function of the particle size as embedded in particle Reynolds numbers, Archimedes numbers, or their equivalents. Although the data, that carries a large spread, is largely in agreement with mathematical models, for the smallest particles, model predictions diverge from each other and from experimental data. Indeed, there is substantial uncertainty about the Shields diagrams at relatively small particle sizes and flow rates. Here we evaluate critical shear stresses for erosion under laminar jet flow. To date critical shear stresses for erosion, as embodied in Shields diagrams, have largely been developed for turbulent flow both experimental and mathematically. However, curves on the Shields diagrams diverge among various models at lower particle Reynolds numbers. Indeed, how critical shear stresses for erosion develop under fully laminar jet flow conditions (not simply laminar boundary layers under turbulent flow) remains unclear. Here we address this gap, which is particularly important for mobilization of the smallest particles. We find the Shields parameter to be inversely proportional to the particle Reynolds numbers under laminar jet flow conditions similar to turbulent conditions.

critical shear stresses, erosion rates, effective ↗