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NASA NTRS1979

Large-scale turbulent structures in jets and in flows over cavities and their relationship to entrainment and mixing

Large scale structures in jets and in flows over cavities were investigated experimentally to determine their role in entrainment, mixing, and noise production. The presence of these structures resulted in growth of the shear layer and entrainment. Merging of adjacent large scale structures caused the near field pressure signal in excited flows. It is believed that both the entrained fluid as well as its eventual mixing with the jet flow can be controlled by introducing pulsation in the jet flow at a frequency for which the flow is most unstable.

Sarohia, V.↗

NASA NTRS1980

Entrainment into a stratocumulus layer with distributed radiative cooling

It is shown that the radiative cooling of a cloud layer strongly influences the turbulent flux profiles and the entrainment rate, and that the radiative cooling should be modeled as acting inside the turbulent layer. Numerical experiments demonstrate that a cloud-topped mixed-layer model, similar to that of Lilly (1968), is quite sensitive to delta (p) sub R, the depth of the radiatively cooled layer near cloud top. As delta (p) sub R increases, the model's sensitivity to the entrainment assumption is markedly heightened; for large delta (p) sub R the cloud top and cloud base rise as the entrainment parameter k is increased, while for small delta (p) sub R an increase in k has almost no effect. The model is most sensitive to delta (p) sub R for the cold-water, strong-divergence regime of greatest interest.

Randall, D. A.↗

NASA NTRS1982

Resonant entrainment of a confined pulsed jet

This paper reports the discovery of a new resonant entrainment phenomenon associated with a confined, pulsed jet flow. It was found that a confined jet, when pulsed at an organ-pipe resonant frequency of the confinement tube, experiences greatly enhanced entrainment and mixing near the exit end of the confinement tube compared to a steady confined jet. The mixing and entrainment rates for the resonantly pulsed confined jet approach, and in some cases slightly exceed, those for an unconfined pulsed jet. Both visual and quantitative evidence of this phenomenon is presented. The new effect should be of considerable interest in ejector and combustor design, both of which benefit from any enhancement in mixing between a primary and a secondary flow

Parikh, P. G.↗

NASA NTRS1984

Lidar observations of mixed layer dynamics - Tests of parameterized entrainment models of mixed layer growth rate

Ground based lidar measurements of the atmospheric mixed layer depth, the entrainment zone depth and the wind speed and wind direction were used to test various parameterized entrainment models of mixed layer growth rate. Six case studies under clear air convective conditions over flat terrain in central Illinois are presented. It is shown that surface heating alone accounts for a major portion of the rise of the mixed layer on all days. A new set of entrainment model constants was determined which optimized height predictions for the dataset. Under convective conditions, the shape of the mixed layer height prediction curves closely resembled the observed shapes. Under conditions when significant wind shear was present, the shape of the height prediction curve departed from the data suggesting deficiencies in the parameterization of shear production. Development of small cumulus clouds on top of the layer is shown to affect mixed layer depths in the afternoon growth phase.

Boers, R.↗

NASA NTRS1988

The role of entrainment by falling raindrops in microbursts

The numerical model of Krueger et al. (1986) for dry microburst simulations is used to study the role of entrainment by falling raindrops. Two series of numerical simulations were conducted: a control series, and a series with the raindrop fall speed set to zero so that the rain moved with the air instead of falling through it. The results show that entrainment due to falling raindrops helps microbursts with large raindrop mixing ratios to form in stable stratifications. It is found that entrainment appears to contribute to the small spatial and temporal scales that characterize microburst outflows.

Krueger, Steven K.↗

NASA NTRS1989

An observational study of stratocumulus entrainment and thermodynamics

The stratocumulus (SC) entrainment and thermodynamics are studied using data from the Dynamics and Chemistry of Marine Stratocumulus (DYCOMS) experiment. The rate of entrainment of air from the free troposphere into the cloud-topped PBL is estimated using a technique based on the measurement of ozone flux and mean distribution. The average measured value of entrainment rate was found to be 3.0 mm/s with a range of 1.0 to 5.0 mm/s for cloudy cases. Thermodynamic budgets are constructed for eight DYCOMS cases. It was found that the divergence of the solar radiative flux is an important component of the boundary-layer energetics during midday, the factor which must be accounted for in mixed-layer models. The net longwave radiative flux profiles show good agreement with theoretical models, but an unambiguous partitioning of the flux divergence between inversion and mixed layers could not be established.

Kawa, S. R.↗

NASA NTRS1991

Saturation point representation of cloud-top entrainment instability

Cloud-top entrainment instability was investigated using a mixing line analysis. Mixing time scales are closely related to the actual size of the parcel, so that local instabilities are largely dependent on the scales of mixing near the cloud top. Given a fixed transport velocity, variation over a small range of parcel length scales (parcel mixing velocities) turns an energy-producing mixing process into an energy-consuming mixing process. It is suggested that a single criterion for cloud-top entrainment instability will not be found due to the role of at least three factors operating more or less independently; the stability of the mixing line, the entrainment speed, and the strength of the internal boundary-layer circulation.

Boers, Reinout↗

DOE OSTI2026

Examination of entrainment, combustibility, and heat transfer due to cell venting inside simplified battery energy storage enclosures

Battery energy storage systems (ESS) assembled of modules containing lithium-ion batteries can pose fire and explosion hazards during thermal runaway because vented gases may accumulate, combust, or escape enclosures. Here, we propose a prototypical configuration composed of the main components of an ESS rack, where modules are represented as rectangles within an enclosure and vent gas is injected steadily through the top of a module. This idealized geometry allows for exploration of how rack-level characteristics can influence smaller single-cell or module-level scales. Through this geometry, we conduct numerical simulations to understand how variations in the vent velocity, temperature, and vertical location affect entrainment rates, fraction of uncombusted fuel, rich-gas coverage, and heat flux to other modules. At lower vent velocities and vertical positions, buoyancy drives enough entrainment and mixing to react with most of the vent gases on the converging plenum. As jet momentum increases and/or buoyancy decreases via higher vent position in the rack, vent gases can propagate into and burn in the divergence plenum. Heat flux to the impinged module scales strongly with vent momentum and temperature, while heat transfer to upper modules peaks when flames in the diverging plenum reach the surface and declines when combustion is suppressed.

Computational fluid dynamics↗

DOE OSTI2026

Drop clustering and drop size correlations from holographic imagery suggest cloud droplet spectral broadening via entrainment-mixing

The question of how droplets rapidly grow large enough to initiate collision-coalescence has persisted for decades. Many theories explaining the production of sufficiently large drops (i.e., those in the “bottleneck” size range; ∼ 25–50 µm diameters) involve drop clustering on millimeter scales. A novel method is introduced to evaluate drop clustering trends particle-by-particle (i.e., the number/proximity of neighboring drops for given droplets; defined as drop clustering fields) which are diagnosed relative to drops within their shared drop environments – in contrast to previous studies which diagnose drop clustering of defined sample volumes, or in terms of absolute length scales. Specifically, this study evaluates the statistical likelihood that drops of a given size are associated with either a significant number of neighboring drops, or are significantly isolated from neighboring drops. Observations are acquired from the HOLODEC during the Cloud System Evolution in the Trades campaign, which sampled subtropical marine clouds. The HOLODEC measures drop size distributions and the 3D spatial coordinates of droplets. Results show drops within the bottleneck size range (diameters of ∼ 25–50 µm) are most likely to be significantly isolated from neighboring drops. This “isolated large drop trend” is primarily observed at subsaturated conditions, suggesting entrainment is the contributing factor. Holograms associated with this trend are more likely to have broader drop size distributions, larger maximum drop sizes and overly regions where precipitation reaches the lowest altitudes from the sampled cloud, suggesting entrainment-mixing drop size distribution broadening is a relevant precipitation-initiation mechanism.

D'Alessandro, John J. [Univ. of Washington, Seattl↗

DOE OSTI2026

Aircraft-derived particle fluxes distinguish entrainment zone and decoupled layer nucleation in marine boundary layers

The vertical distribution of freshly nucleated aerosol particles in the marine boundary layer remains poorly constrained, limiting our ability to represent new particle formation in climate models. Here we characterize 3–10 nm particle events, termed small particle events (SPEs), by deriving their vertical turbulent fluxes from aircraft measurements during the Aerosol and Cloud Experiments in the Eastern North Atlantic (ACE-ENA) campaign. To overcome stationarity limitations of traditional eddy covariance methods, we applied continuous wavelet transform analysis to data collected during June–July 2017 and January–February 2018 flights over the Azores. Our flux-based analysis revealed two distinct SPE scenarios with different vertical structures and spatial extents. The first featured nucleation in the entrainment zone, where free tropospheric air entrains into the boundary layer. The second showed nucleation in the decoupled layer, a stratified region between the well-mixed surface layer and cloud-topped upper boundary layer. In both cases, convergence of air masses from different layers diluted preexisting aerosol surface area to very low levels, creating conditions favorable for nucleation and generating strong downward particle fluxes. SPEs occurred in 15 % of flights, challenging prevailing theoretical expectations that new particle formation should rarely occur in marine boundary layers due to high condensation and coagulation sink capacity of sea spray aerosols. Aircraft-derived particle fluxes provide first observational constraints on the vertical location and source strength of likely nucleation regions in the remote marine boundary layer, improving aerosol source representations in climate models and reducing uncertainties in aerosol-cloud interactions.

Rasheeda Satheesh, Ajmal [North Carolina State Uni↗

NASA NTRS1972

Analysis of an entrainment model of the jet in a crossflow

A theoretical model has been proposed for the problem of a round jet in an incompressible cross-flow. The method of matched asymptotic expansions has been applied to this problem. For the solution to the flow problem in the inner region, the re-entrant wake flow model was used with the re-entrant flow representing the fluid entrained by the jet. Higher order corrections are obtained in terms of this basic solution. The perturbation terms in the outer region was found to be a line distribution of doublets and sources. The line distribution of sources represents the combined effect of the entrainment and the displacement.

Chang, H. S.↗

NASA NTRS1978

Prediction of nearfield jet entrainment by an interactive mixing/afterburning model

The development of a computational model (BOAT) for calculating nearfield jet entrainment, and its application to the prediction of nozzle boattail pressures, is discussed. BOAT accounts for the detailed turbulence and thermochemical processes occurring in the nearfield shear layers of jet engine (and rocket) exhaust plumes while interfacing with the inviscid exhaust and external flowfield regions in an overlaid, interactive manner. The ability of the model to analyze simple free shear flows is assessed by detailed comparisons with fundamental laboratory data. The overlaid methodology and the entrainment correction employed to yield the effective plume boundary conditions are assessed via application of BOAT in conjunction with the codes comprising the NASA/LRC patched viscous/inviscid model for determining nozzle boattail drag for subsonic/transonic external flows. Comparisons between the predictions and data on underexpanded laboratory cold air jets are presented.

Dash, S. M.↗

NASA NTRS1978

A computational model for the prediction of jet entrainment in the vicinity of nozzle boattails (the BOAT code)

The development of a computational model (BOAT) for calculating nearfield jet entrainment, and its incorporation in an existing methodology for the prediction of nozzle boattail pressures, is discussed. The model accounts for the detailed turbulence and thermochemical processes occurring in the mixing layer formed between a jet exhaust and surrounding external stream while interfacing with the inviscid exhaust and external flowfield regions in an overlaid, interactive manner. The ability of the BOAT model to analyze simple free shear flows is assessed by comparisons with fundamental laboratory data. The overlaid procedure for incorporating variable pressures into BOAT and the entrainment correction employed to yield an effective plume boundary for the inviscid external flow are demonstrated. This is accomplished via application of BOAT in conjunction with the codes comprising the NASA/LRC patched viscous/inviscid methodology for determining nozzle boattail drag for subsonic/transonic external flows.

Dash, S. M.↗

NASA NTRS1981

Entrainment and thrust augmentation in pulsatile ejector flows

This study comprised direct thrust measurements, flow visualization by use of a spark shadowgraph technique, and mean and fluctuating velocity measurements with a pitot tube and linearized constant temperature hot-wire anemometry respectively. A gain in thrust of as much as 10 to 15% was observed for the pulsatile ejector flow as compared to the steady flow configuration. From the velocity profile measurements, it is concluded that this enhanced augmentation for pulsatile flow as compared to a nonpulsatile one was accomplished by a corresponding increased entrainment by the primary jet flow. It is also concluded that the augmentation and total entrainment by a constant area ejector critically depends upon the inlet geometry of the ejector. Experiments were performed to evaluate the influence of primary jet to ejector area ratio, ejector length, and presence of a diffuser on pulsatile ejector performance.

Sarohia, V.↗

NASA NTRS1984

Problems with the process partitioning theory of stratocumulus entrainment

Three different approaches to partitioning were proposed. Ball (1960), Lilly (1968), and Deardorff et al. (1969, 1974) considered the sign of the net buoyancy flux at each level. If the net flux is positive, it is counted as TKE producing; otherwise, it is counted as TKE consuming. This approach can be called Eulerian partitioning. The second approach can be called process partitioning. It is assumed that the various processes acting in concert each produce and consume the same energy as if they acted independently (Manins and Turner, 1978). The total rates of TKE production and consumption are obtained by summing the effects of all the forcing processes. The third approach is Lagrangian partitioning. Each air parcel is considered as either producing or consuming TKE, according to the sign of the product of its density and vertical velocity anomalies. Stage and Businger (1981a,b) have applied process partitioning to the cloud topped mixed layer. One of the most important processes influencing entrainment into such a layer is cloud top radiative cooling. The production and consumption due to entrainment and radiative cooling are thus closely related. Model results are sensitive to the choice of formulation.

Randall, D. A.↗

NASA NTRS1985

Entrainment region phenomena for a large plane shear layer

The subatmospheric test section of the present free shear layer facility allows the entrainment air to be introduced with a negligible disturbance level. The very low frequency oscillations, which are prominently observed in the entrainment stream and which are present throughout the shear layer, are attributed to an inherent instability in the transition from a boundary layer to a free shear layer state. The basic features of the disturbance field are documented herein.

Ali, S. K.↗

NASA NTRS1989

A parameterization of the depth of the entrainment zone

A theory of the parameterization of the entrainment zone depth has been developed based on conservation of energy. This theory suggests that the normalized entrainment zone depth is proportional to the inverse square root of the Richardson number. A comparison of this theory with atmospheric observations indicates excellent agreement. It does not adequately predict the laboratory data, although it improves on parcel theory, which is based on a momentum balance.

Boers, Reinout↗

NASA NTRS1989

Ozone conservation and entrainment in cumulus congestus

This study demonstrates that ozone mixing ratio is conserved during moist convection and can be used as a tracer for cloud entrainment studies. The approach is to apply mixing line analysis to pairs of liquid water potential temperature, total water mixing ratio, O3 and pseudo-equivalent potential temperature derived from aircraft penetrations of growing cumulus congestus. Conclusions about entrainment from the mixing diagrams employing O3 agree with those using thermodynamic quantities. Any disagreement uncovered deficiencies in the water substance measurement technique.

Pearson, R., Jr.↗