Analysis of the Droplet Size Reduction in a pMDI Due

to the Addition of a Turbulence Generating

Nozzleby

Michael P. MedlarDr. Risa Robinson

Objective

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

Abstract

Modeling

Flow Equations• Governing equations

• Standard k- turbulence model

0

i

i

x

u

j

tij

j

ij

ii

i

xxx

Pg

Dt

uD

l

iii

llk

l x

uuu

x

k

x

kkC

xDt

Dk ''2

kC

x

uuu

kC

x

kC

xDt

D

l

ili

ll

2

2''

1

2

''ji

tij uu

Continuity:

Navier-Stokes:

Transport of k:

Transport of

where,

Huh Atomization Model• Considers turbulence as a primary part in

the atomization process

• Calculates PDF for secondary drop sizes, p(x)

where,(x) is the turbulence energy spectrum and A(x) is the atomization time scale

)(

)()(

x

xCxp

A

611914.0

086.2222

914.0

3535086.22 0828.078.1

0828.078.1)(

t

CkkCxt

CkxkCCx avgavgavgavgavgavgavgavg

212121

2285.05215.0212715.0 0828.009936.02.1

avgg

avgavgavgf

avg

avgA U

tkCkCt

kC

The turbulence energy spectrum is given as,

The atomization time scale is given as,

kavg, avg, U, t, f, and g are input to find p(x)

Huh Atomization Model AnalysisThis analysis was needed to determine the exit turbulence parameters

that lead to a reduction in the median secondary drop size-low kavg/avg at low kavg leads to a reduction in the median

0

200

400

600

800

1000

1200

1400

0.00E+00 5.00E-05 1.00E-04 1.50E-04 2.00E-04 2.50E-04 3.00E-04 3.50E-04 4.00E-04

kav g/av g

Med

ian

,

m

kavg=10

kavg=20

Pressurized Metered-Dose Inhaler

Canister

Actuator

Mouthpiece

Actuator Orifice

Inhaler Internal Flow PassageInlet B.C.’sV=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

Outlet B.C.’sOutflow condition assumes zero normal gradient for all flow properties except pressure (used when outlet conditions aren’t known and want to be determined)

Fluid Propertiesf = 1000 kg/m3 = 0.001 Pa-s

Flow equation solved in CFD software package

Add-on NozzleInlet B.C.’s for add-on nozzleCorrespond to exit conditions of inhaler baseline modelQ=5.0e-06 m3/sk=5.8 m2/s2

=7.0e+04 m2/s3

Outlet B.C.’s for add-on nozzleOutflow 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

Results

Inhaler Internal Flow PassageTurbulent Kinetic Energy, k Turbulent Kinetic Energy Dissipation Rate,

kavg=5.8 m2/s2

avg=7.0e+04 m2/s3

kavg/avg=8.29e-05

Predicted Median Droplet Size-290 m

Optimization of Add-on Nozzle

Separation Point

Inlet

Outlet-fixed to keep outlet velocity same as baseline

h

500 m

s

53o etch angle

Line of symmetrymm

Based on h and s dimensions

Optimization Results

0

20

40

60

80

100

120

140

160

180

0 50 100 150 200 250 300 350 400 450 500

s, m

Pro

ject

ed m

edia

n,

m

h=100

h=150

h=50

Optimum dimensions are h=100 m, s=350 m

Add-on NozzleTurbulent Kinetic Energy, k Turbulent Kinetic Energy Dissipation Rate,

kavg=60.8 m2/s2

avg=8.13e+06 m2/s3

kavg/avg=7.48e-06

Predicted Median Droplet Size-245 m

Summary

• Current inhaler design-290 m

• Current inhaler with add-on nozzle-245 m

• Relative reduction of 15.5% in the median secondary drop size as predicted from the Huh Atomization Model based on turbulence effects alone

Conclusions

• 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