Characterising entrainment in fountains and negatively buoyant jets

Turbulent fountain flow consists of two distinct stages, the initial ‘negatively buoyant jet’ (NBJ) stage, and the fully developed ‘fountain’ stage. The present study investigates both stages of the flow using particle image velocimetry and planar laser-induced fluorescence, over a range of source Froude numbers, 10≲Fro≲30 , and Reynolds numbers, 5500≲Reo≲7700 . While the velocity and buoyancy profiles in NBJs take similar Gaussian shapes over a wide range of axial locations, this was not observed in fountains. The changing profile shape is most evident in the outer flow (OF) region, while there is a degree of similarity in the inner flow (IF). Entrainment between IF and OF is shown to depend on the local Richardson number, Ri . The fountains are found to have a negative entrainment coefficient, α<0 , for the majority of their height, implying a net radial outflow of fluid from the IF to the OF. An alternative description of entrainment is considered, the ‘decomposed top-hat’ model, where the radial flow is separated into inflow and outflow components that are then estimated using the present experimental data. The inflow component was found to be proportional to the axial IF velocity, which is similar to the classical description of entrainment in pure jets/plumes, while the outflow depends on the local Ri . Entrainment in NBJs may also be described by this framework, which, despite not having an OF, is still subject to an Ri -dependent radial outflow

Understanding the effects of inhaler resistance on particle deposition behaviour – A computational modelling study

Background and objective: Understanding the impact of inhaler resistance on particle transport and deposition in the human upper airway is essential for optimizing inhaler designs, thereby contributing to the enhancement of the therapeutic efficacy of inhaled drug delivery. This study demonstrates the potential effects of inhaler resistance on particle deposition characteristics in an anatomically realistic human oropharynx and the United States Pharmacopeia (USP) throat using computational fluid dynamics (CFD). Method: Magnetic resonance (MR) imaging was performed on a healthy volunteer biting on a small mockup inhaler mouthpiece. Three-dimensional geometry of the oropharynx and mouthpiece were reconstructed from the MR images. CFD simulations coupled with discrete phase modelling were conducted. Inhaled polydisperse particles under two different transient flow profiles with peak inspiratory flow rates (PIFR) of 30 L/min and 60 L/min were investigated. The effect of inhaler mouthpiece resistance was modelled as a porous medium by varying the initial resistance (Ri) and viscous resistance (Rv). Three resistance values, 0.02 kPa0.5minL−1, 0.035 kPa0.5minL−1 and 0.05 kPa0.5 minL−1, were simulated. The inhaler outlet velocity was set to be consistent across all models for both flow rate conditions to enable a meaningful comparison of models with different inhaler resistances. Result: The results from this study demonstrate that investigating the effect of inhaler resistance by solely relying on the USP throat model may yield misleading results. For the geometrically realistic oropharyngeal model, both the pressure and kinetic energy profiles at the mid-sagittal plane of the airway change dramatically when connected to a higher-resistance inhaler. In addition, the geometrically realistic oropharyngeal model appears to have a resistance threshold. When this threshold is surpassed, significant changes in flow dynamics become evident, which is not observed in the USP throat model. Furthermore, this study also reveals that the impact of inhaler resistance in a geometrically realistic throat model extends beyond the oral cavity and affects particle deposition downstream of the oral cavity, including the oropharynx region. Conclusion: Results from this study suggest that key mechanisms underpinning the working principles of inhaler resistance are intricately connected to their complex interaction with the pharynx geometry, which affects the local pressure, local variation in velocity and kinetic energy profile in the airway

Numerical analysis of airflow and particle deposition in multi-fidelity designs of nasal replicas following nasal administration

Background and Objective: An improved understanding of flow behaviour and particle deposition in the human nasal airway is useful for optimising drug delivery and assessing the implications of pollutants and toxin inhalation. The geometry of the human nasal cavity is inherently complex and presents challenges and manufacturing constraints in creating a geometrically realistic replica. Understanding how anatomical structures of the nasal airway affect flow will shed light on the mechanics underpinning flow regulation in the nasal pharynx and provide a means to interpret flow and particle deposition data conducted in a nasal replica or model that has reduced complexity in terms of their geometries. This study aims to elucidate the effects of sinus and reduced turbinate length on nasal flow and particle deposition efficiencies. Methods: A complete nasal airway with maxillary sinus was first reconstructed using magnetic resonance imaging (MRI) scans obtained from a healthy human volunteer. The basic model was then modified to produce a model without the sinus, and another with reduced turbinate length. Computational fluid dynamics (CFD) was used to simulate flow in the nasal cavity using transient flow profiles with peak flow rates of 15 L/min, 35 L/min and 55 L/min. Particle deposition was investigated using discrete phase modelling (DPM). Results: Results from this study show that simplifying the nasal cavity by removing the maxillary sinus and curved sections of the meatus only has a minor effect on airflow. By mapping the spatial distribution of monodisperse particles (10 μm) in the three models using a grid map that consists of 30 grids, this work highlights the specific nasal airway locations where deposition efficiencies are highest, as observed within a single grid. It also shows that lower peak flow rates result in higher deposition differences in terms of location and deposition quantity, among the models. The highest difference in particle deposition among the three nasal models is ∼10%, and this is observed at the beginning of the middle meatus and the end of the pharynx, but is only limited to the 15 L/min peak flow rate case. Further work demonstrating how the outcome may be affected by a wider range of particle sizes, less specific to the pharmaceutical industries, is warranted. Conclusion: A physical replica manufactured without sections of the middle meatus could still be adequate in producing useful data on the deposition efficiencies associated with an intranasal drug formulation and its delivery device

Entrainment and mixing in turbulent negatively buoyant jets and fountains

Turbulent negatively buoyant jets occur when the buoyancy of a jet directly opposes its momentum, and will decelerate until its mean momentum is reduced to zero. Here the flow reverses direction and returns annularly towards the source, mixing with the opposing fluid and forming a fountain. The initial stage, before the return flow forms, is referred to as the `negatively buoyant jet' (NBJ) stage. Once the return flow has established, it is referred to as the fully developed `fountain' (F) stage. This study investigates both stages of this flow experimentally, using 2D particle image velocimetry and laser induced fluorescence. Analysing the mean statistics of the NBJ stage reveals several important differences with neutral jets. Although the mean velocity and scalar profiles are found to take similar Gaussian shapes at a wide range of axial locations, the widths of these profiles do not grow at the same rate. The turbulence intensity and Reynolds stress do not decrease at the same rate as the mean flow in NBJs, and a new turbulence scale is defined that can collapse these profiles onto approximately a single curve. The entrainment coefficient is estimated for NBJs, where it is found to decrease with axial distance or increasingly negative local Richardson number. Fully developed fountains are explored alongside NBJs, allowing the effect of the return flow to be investigated. The mean and turbulence profiles in fountains are generally not self-similar. This is most evident in the outer region of the mean profiles, and across the full width of the turbulence profiles. Entrainment between the inner and outer flow is investigated using two alternative approaches, both finding that radial flow is predominantly from the inner to the outer flow for the majority of the height

Experimental investigation into turbulent negatively buoyant jets using combined PIV and PLIF measurements

Turbulent negatively buoyant jets occur when the buoyancy of a jet opposes its source momentum. In these flows, the fluid will rise until it reaches a stagnation point and a return flow is established, forming a fountain (Hunt and Burridge, 2015). This study looks at both the initial negatively buoyant jet stage of this flow, before the return flow has established, and the fully developed fountain stage. Two-dimensional particle image velocimetry (PIV) and planar laser in- duced fluorescence (PLIF) are used to simultaneously measure the velocity and scalar concentration fields. An experimental and image processing procedure for the PLIF is introduced that accounts for pulse-to-pulse variations in laser power and beam profile for an Nd:YAG laser, which has been demonstrated to reduce the error in scalar concentration measurements. The flow is investigated experimentally using a 1m3 tank of salt-water ambient with freshwater+ethanol negatively buoyant jets, allowing for measurements to be taken at F ro = 30 and Reo = 5900. The entrainment coefficient for a negatively buoyant jet has been estimated as α ∼= 0.054, lower than a neutral jet at α ∼= 0.058. A finding con- sistent with existing literature (Bloomfield and Kerr, 2000; McDougall, 1981)

Entrainment and structure of negatively buoyant jets

Turbulent negatively buoyant jets occur when the buoyancy of a jet directly opposes its momentum, and will decelerate until its mean momentum is reduced to zero. Here the flow reverses direction and, for an axisymmetric flow originating from a round inlet, returns annularly towards the source, mixing with the opposing fluid and forming a fountain. This investigation focuses on the initial stage of the flow, before the return flow is established. Data is obtained experimentally using two-dimensional particle image velocimetry (PIV) and planar laser induced fluorescence (PLIF) for saline/freshwater negatively buoyant jets with source Froude number F ro = 30 and Reynolds numbers 5500 Reo 5900 at axial locations 18 z/D 30, and compared to a neutral jet. The development of the mean and turbulence profiles with local Fr are investigated, and it is found that, unlike neutral jets and plumes, the turbulence intensity in negatively buoyant jets does not scale with the mean flow. Additionally, the ratio of widths of the buoyancy and velocity profiles, λ, increases along the jet. The entrainment coefficient, α, was estimated for a negatively buoyant jet, and was found to decrease with local Fr, eventually becoming negative, indicating fluid is being ejected from the jet. These observations differ to neutral or buoyant jets and plumes, which approach a constant λ and α in the far field. This different behaviour in negatively buoyant jets is a natural consequence of the strongly decelerating mean flow as a result of opposing buoyancy, which is demonstrated in the context of the integral model framework developed by Morton et al. (1956)

Turbulence structure of neutral and negatively buoyant jets

High-fidelity measurements of velocity and concentration are carried out in a neutral jet (NJ) and a negatively buoyant jet (NBJ) by injecting a jet of fresh water vertically downwards into ambient fresh and saline water, respectively. The Reynolds number (Re)based on the pipe inlet diameter (d) and the source velocity (Wo) is approximately 5900 in all the experiments, while the source Froude number based on density difference is approximately 30 in the NBJ experiments. Velocity and concentration measurements are obtained in the region 17 ≤ z/d ≤ 40 (z being the axial coordinate) using particle image velocimetry and planar laser induced fluorescence techniques, respectively. Consistent with the literature on jets, the centreline velocity (Wc) decays as z−1 in the NJ, but in the NBJ, Wc decays faster along z due to the action of negative buoyancy. Nonetheless, the mean velocity (W) and concentration (C) profiles in both the flows exhibit self-similar Gaussian form, when scaled by the local centreline parameters (Wc,Cc) and the jet half-widths (rW , rC ). On the other hand, the turbulence statistics and Reynolds stress in the NBJ do not scale with Wc. The results of autocorrelation functions, integral length scales and two-dimensional correlation maps show the similarity of turbulence structure in the NJ and the NBJ when the axial and radial distances are normalised by the local jet half-width. Further, the spectra and probability density functions are similar on the axis and only minor differences are seen near the jet interface. The above findings are fundamentally consistent with our recent analysis (Milton-McGurk et al., J. Fluid Mech., 2020b), where we observed that the mean and turbulence statistics in the NBJ have different development characteristics. Overall, we find that the turbulence structure of the NBJ (when scaled by local velocity and length scales) is very similar to the momentum-driven NJ, and the differences (e.g. spreading rate, scaling of turbulence intensities, etc.) between the NJ and the NBJ seem to be of secondary importance