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This paper presents an investigation of primary breakup of planar turbulent liquid jets and breakup properties at the surface of turbulent jets in still air at standard conditions. Numerical simulations are carried out for jet exit Reynolds number 23000 and Weber numbers in the range [102–107].
Due to the limitation of direct numerical simulation (DNS) to moderate Reynolds numbers, a stochastic 1D ansatz based on the one-dimensional turbulence (ODT) model is used to simulate a planar liquid jet with a high lateral resolution. ODT permits an affordable high resolution of interface and single-phase property gradients which are key for understanding the local behavior. ODT is a stochastic model simulating turbulent flow evolution along a notional 1D line of sight by applying instantaneous maps to represent the effect of individual turbulent eddies on property profiles. The most relevant mechanisms that influence the primary breakup of liquid jets are found to be represented accurately based on comparisons to experiments and correlations reported in the literature. Building on this finding, future work will focus on the statistics of droplets generated by primary breakup, both to investigate their relationship to breakup mechanisms and to provide input to models of secondary breakup and subsequent spray evolution.
We summarize the group’s progress in applying, analyzing, and improving ODT and ODT-based stochastic turbulence models
like ODTLES. Compared to DNS these models span a wider range of scales while compared to RANS/LES (i) the molecular
effects are retained and (ii) no assumption of scale separation is made. In this regard ODTLES has more properties of DNS than of standard LES.
Although large-eddy simulation (LES) has been shown to produce a reasonable representation of the turbulent circulations within the stratocumulus-topped boundary layer, it has difficulties to accurately predict cloud-top entrainment rates. In this paper, we present a front-tracking algorithm for LES to untangle the numerical and physical contributions to entrainment. Instead of resolving the cloud-top inversion, we treat it as a discontinuity separating the boundary layer from the free atmosphere and use the level set method to track its location. We apply our method to the smoke cloud test case as presented by BRETHERTON et al. (1999) which is simpler than stratocumulus in that it is only driven by radiative cooling avoiding evaporative feedbacks on entrainment. We present three-dimensional LES results with and without use of the level set method varying the grid resolution and the flux limiter. With the level set method, we prescribe
zero entrainment and use this case to evaluate our method’s ability to maintain a non-entraining smoke-cloud
layer. We use an empirically-based entrainment law to estimate numerical errors. With the level set method, the prescribed entrainment rate was maintained with errors about one order of magnitude smaller than the entrainment errors found in the standard LES. At the same time, the dependence of the entrainment errors on the choice of the limiter was reduced by more than a factor of 10.
Turbulent entrainment at the stratocumulus top and its interaction with local processes like radiative or evaporative cooling still remains a source of uncertainty in current atmospheric models. The reason is, at least partly, that the characteristic scales at which those cloud-top processes occur are relatively small, of the order of a few tens of meters, and access to accurate data at those scales has been difficult. In this contribution, we present a simplified model designed to investigate these cloud-top processes in detail and we address some questions regarding the role of buoyancy reversal by evaporative cooling at the cloud top. As a tool, we use direct numerical simulation to remove the uncertainty associated with turbulence models.
Buoyancy reversal refers to the formation of negatively buoyant parcels of fluid within an otherwise stable stratification as a consequence of the local cooling caused by the evaporation of the droplets at the cloud interface. This process leads to convective instability, as heavier parcels of fluid lie on top of lighter ones. This instability promotes turbulence, and hence entrainment and further evaporation of droplets, a feedback process that could eventually lead to a rapid dessication of the cloud -- the so-called cloud-top entrainment instability. Recent work has demonstrated that, in contrast to previous postulates, buoyancy reversal caused by evaporative cooling is not a sufficient condition to break up the cloud: turbulence is indeed enhanced, but very mildly. The reason is that buoyancy reversal alone leads to a meta-stable layer as the mixing rate, or entrainment rate, is diffusively limited, so that the eventual breakup of the cloud by buoyancy reversal alone occurs on time scales that are much too long to be relevant to the stratocumulus-top boundary layer. To become relevant, evaporative cooling requires the interaction with other local mechanisms of turbulence generation, like wind shear or radiative cooling. In this work, we study wind shear effects, without radiative cooling.
There are at least two reasons to study shear effects. First, shear is ubiquitous, as local shear associated with large-scale eddies will also be evident even in the absence of a mean wind. Second, shear alone cannot sustain a continuous deepening of the layer, as shear generated turbulence will locally thicken the entrainment zone, but in the absence of other sources, the turbulence will eventually decay once a critical entrainment-zone thickness is reached. The latter makes it interesting to combine shear with the convective destabilization of the cloud-top layer through buoyancy reversal, as neither process acting alone is efficient in supporting significant mixing at the cloud top. In contrast, by generating convective eddies which locally thin the entrainment zone, buoyancy reversal might help enhance shear, which in turn locally enhances the mixing which sustains the buoyancy reversal, raising the possibility that the processes are self-reinforcing.
Results show that the enhancement by local wind shear can render buoyancy reversal comparable to other forcing mechanisms. However, we also find that (i) the velocity jump across the capping inversion, Δu, needs to be relatively large and typical values of about 1 m s-1 associated with the convective motions inside the boundary layer are generally too small, and (ii) there is no indication of cloud-top entrainment instability. To obtain these results, parametrizations of the mean entrainment velocity and the relevant time scales are derived from the study of the cloud-top vertical structure. Two overlapping layers can be identified: a background shear layer with a thickness (1/3) (Δu)2/(Δb), where Δb is the buoyancy increment across the capping inversion, and a turbulence layer dominated by free convection inside the cloud and by shear production inside the relatively thin overlap region. As turbulence intensifies, the turbulence layer encroaches into the background shear layer and defines thereby the entrainment velocity. Particularized to the first research flight of the Second Dynamics and Chemistry of Marine Stratocumulus (DYCOMS-II) field campaign, the analysis predicts an entrainment velocity of about 3 mm s-1 after 5-10 minutes, a velocity comparable to the measurements and thus indicative of the relevance of mean shear in that case.
Due to its huge complexity, progress in understanding and prediction of turbulent combustion is extremely challenging. In principle, progress is possible without improved understanding through direct numerical solution (DNS) of the exact governing equations, but the wide range of spatial and temporal scales often renders it unaffordable, so coarse-grained 3D numerical simulations with subgrid parameterization of the unresolved scales are often used. This is especially problematic for multi-physics regimes such as reacting flows because much of the complexity is thus relegated to the unresolved small scales. One-Dimensional Turbulence (ODT) is an alternative stochastic model for turbulent flow simulation. It operates on a 1D spatial domain via time advancing individual flow realizations rather than ensemble-averaged quantities. The lack of spatial and temporal filtering on this 1D domain enables a physically sound multiscale treatment which is especially useful for combustion applications where, e.g., sharp interfaces or small chemical time scales have to be resolved. Lignell et al. recently introduced an efficient ODT implementation using an adaptive mesh. As all existing ODT versions it operates in the incompressible regime and thus cannot handle compressibility effects and their interactions with turbulence and chemistry which complicate the physical picture even further. In this paper we make a first step toward an extension of the ODT methodology towards an efficient compressible implementation. The necessary algorithmic changes are highlighted and preliminary results for a standard non-reactive shock tube problem as well as for a turbulent reactive case illustrate the potential of the extended approach.
A numerical experiment is designed to study the interaction at the stratocumulus top between a mean
vertical shear and the buoyancy reversal due to evaporative cooling, without radiative cooling. Direct numerical simulation is used to eliminate the uncertainty introduced by turbulence models. It is found that the
enhancement by shear-induced mixing of the turbulence caused by buoyancy reversal can render buoyancy reversal comparable to other forcing mechanisms. However, it is also found that (i) the velocity jump across the capping inversion Du needs to be relatively large and values of about 1ms21 that are typically associated with the convective motions inside the boundary layer are generally too small and (ii) there is no indication of cloud-top entrainment instability. To obtain these results,parameterizations of the mean entrainment velocity
and the relevant time scales are derived from the study of the cloud-top vertical structure. Two overlapping layers can be identified: a background shear layer with a thickness (1/3)(Du)2/Db, where Db is the buoyancy increment across the capping inversion and a turbulence layer dominated by free convection inside the cloud and by shear production inside the relatively thin overlap region. As turbulence intensifies, the turbulence layer encroaches into the background shear layer and defines thereby the entrainment velocity. Particularized to the first research flight of the Second Dynamics andChemistry of theMarine Stratocumulus (DYCOMS II) field campaign, the analysis predicts an entrainment velocity of about 3mms21 after 5–10 min—a velocity comparable to the measurements and thus indicative of the relevance of mean shear in that case.