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Analysis of the Droplet Size Reduction in a pMDI Due to the Addition of a Turbulence Generating Nozzle by Michael P. Medlar Dr. Risa Robinson

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Objective

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To improve Medical Inhalation Therapy by reducing the median droplet size resulting from the pMDI through the addition of a turbulence generating nozzle

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Abstract

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Modeling

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**Flow Equations Governing equations Standard k-e turbulence model**

Continuity: where, Navier-Stokes: Transport of k: Transport of e:

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Huh Atomization Model Considers turbulence as a primary part in the atomization process Calculates PDF for secondary drop sizes, p(x) where, f(x) is the turbulence energy spectrum and tA(x) is the atomization time scale

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**The turbulence energy spectrum is given as,**

The atomization time scale is given as, kavg, eavg, U, t, rf, and rg are input to find p(x)

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**Huh Atomization Model Analysis**

This analysis was needed to determine the exit turbulence parameters that lead to a reduction in the median secondary drop size-low kavg/eavg at low kavg leads to a reduction in the median

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**Pressurized Metered-Dose Inhaler**

Canister Actuator Actuator Orifice Mouthpiece

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**Inhaler Internal Flow Passage**

Inlet B.C.’s V=2.34 m/s (normal to boundary) I=5.7 % (turbulent intensity) I=0.16(Re)-1/8 L=1.155e-04 m (turbulent length scale) L=0.07l Fluid Properties rf = 1000 kg/m3 m = Pa-s Outlet B.C.’s Outflow condition assumes zero normal gradient for all flow properties except pressure (used when outlet conditions aren’t known and want to be determined) Flow equation solved in CFD software package

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**Add-on Nozzle Flow equation solved in CFD software package**

Inlet B.C.’s for add-on nozzle Correspond to exit conditions of inhaler baseline model Q=5.0e-06 m3/s k=5.8 m2/s2 e=7.0e+04 m2/s3 Outlet B.C.’s for add-on nozzle Outflow condition assumes zero normal gradient for all flow properties except pressure (used when outlet conditions aren’t known and want to be solved for) Flow equation solved in CFD software package

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Results

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**Inhaler Internal Flow Passage**

Turbulent Kinetic Energy, k Turbulent Kinetic Energy Dissipation Rate, e kavg=5.8 m2/s2 eavg=7.0e+04 m2/s3 kavg/eavg=8.29e-05 Predicted Median Droplet Size-290 mm

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**Optimization of Add-on Nozzle**

Based on h and s dimensions Separation Point Inlet Outlet-fixed to keep outlet velocity same as baseline h 500 mm s 53o etch angle Line of symmetry 1 mm

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Optimization Results Optimum dimensions are h=100 mm, s=350 mm

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**Add-on Nozzle Predicted Median Droplet Size-245 mm**

Turbulent Kinetic Energy, k Turbulent Kinetic Energy Dissipation Rate, e kavg=60.8 m2/s2 eavg=8.13e+06 m2/s3 kavg/eavg=7.48e-06 Predicted Median Droplet Size-245 mm

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**Summary Current inhaler design-290 mm**

Current inhaler with add-on nozzle-245 mm Relative reduction of 15.5% in the median secondary drop size as predicted from the Huh Atomization Model based on turbulence effects alone

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Conclusions

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Fluent/Huh Atomization Model combination can be used to evaluate the significance of an add-on turbulence generating nozzle in reducing droplet size Add-on turbulence generating nozzle can reduce the droplet sizes produced from the pMDI

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