Flow Simulations in TwinCaps Dry Powder Inhalerusing OpenFOAM

Nuno Roldao de Aguiar Enesnuno.enes@tecnico.ulisboa.pt

Instituto Superior Tecnico, Lisboa, Portugal

April 2016

Abstract

To date inhalation has been the preferred route for the treatment of lung-associated conditions, forinstance asthma, cystic fibrosis or chronic obstructive pulmonary disease (COPD). Dry powder inhalersare a commonly used vehicle for pulmonary drug delivery, with the majority of the marketed devicesbeing of the passive type. Passive DPIs rely exclusively on the patient’s inspiratory effort to entrain,deaggregate and disperse the resulting active pharmaceutical ingredient (API) particles into the airflowwhich then carries them to the lungs.

Setting a mathematical model able to predict particle behavior within the TwinCaps R© DPI as the endgoal, this thesis work has focused on formulating a model capable of simulating the devices’s internalairflow when suction is applied at its exit.

Because real particle distribution inside TwinCaps R© is hardly ever symmetric, the presented simula-tions were run taking the whole domain into consideration despite of it being symmetric about two planes.Symmetric solutions to this problem would require the meshes, discretization schemes and discretizationerrors to be symmetric, which is impossible to guarantee. To this end, explicit under-relaxation wasadded to OpenFOAM R©. Combining both types of under-relaxation, the model was able to capture theexperimental Q vs. ∆p curve behavior and to predict device outflow with an associated modeling error inthe range [3, 75%; 7, 5%].Keywords: Pulmonary drug delivery, Dry powder inhaler, TwinCaps R©, CFD, OpenFOAM R©

1. Introduction

To date inhalation has been the most com-monly endorsed route for the treatment of lung-associated conditions, for instance asthma, cys-tic fibrosis or chronic obstructive pulmonary dis-ease (COPD). When experiencing symptoms(e.g. COPD or asthma exacerbation), the patientequipped with the prescribed pulmonary drug de-livery device, inhales a pharmaceutical aerosolwhich after traveling the respiratory tract settleson the bronchi-alveolar region, providing on-targettherapeutic effect. Moreover, by being absorbeddirectly into the bloodstream at the alveolar region,the drug bypasses the first-pass metabolism in theliver and intestines, thus requiring smaller doses ofpharmaceutical active ingredient to provide the de-sired therapeutic effect (e.g. bronchodilation) andconsequently diminishing unwanted side effects.

Given the renown problems with patient compli-ance and the consequently low percentage of de-vice label dose that reaches the lungs, cliniciansand patients alike could certainly advocate otheradministration routes besides inhalation. It is in-

deed faster and more convenient to take a pillthan to use an pressurized metered dose inhaler(pMDI), a nebulizer, or a dry powder inhaler (DPI)[12]. However, absorption of the drug via digestivesystem is not as direct as injecting it into the blood-stream or even as inhaling it. The drug’s absorp-tion time is not only variable across patients, dueto the natural duration of the digestive process, butmay also be naturally inactivated (e.g. by the foodingested). Table 1 presents a summary of the mostrelevant benefits and shortcomings of each route.

1.1. Inhaler devicesFour technologies of devices currently coexist ata commercial stage: Nebulizers; pressurized me-tered dose inhaler (pMDI); dry powder inhaler(DPI); and soft mist inhaler (SMI). Each of themhas its particular set of characteristics that makethem more suitable to a given application than theother.

• Nebulizers are the most mature drug deliv-ery device technology marketed today and arewidely used in clinical and home care. This

1

Table 1: Comparative analysis of drug administration routes

Advantages Disadvantages

Oral Convenient Highly variable absorption timeInexpensive Systemic side affects (e.g. First pass metabolism)Portable Drug may be inactivated (e.g. Food ingested)

Injection Bioavailability (100%) Special equipment and trained personnel requiredFastest onset of action Expensive (Transportation and storage costs)

Invasive, can cause injuries and diseasetransmission (e.g. Embolism, Phlebitis)

Inhalation On-target delivery (Lung related diseases) Irritation of the respiratory tract may take placeRapid onset of action Variable dosing (e.g. Faulty inhalation techniqueLow drug dosage Special apparatus is required

type of device uses water-soluble drug formu-lations and a means of dispersing it, to gen-erate inhalable aerosols. It is particularly use-ful for diseases that require large amounts ofemitted dose (ED), i.e. the percentage of labeldrug that exits the inhaler mouthpiece.

• pMDIs are still the most used device to datedue to their compact size, portability, cost-effectiveness, power source independence,and capacity for delivering repeated consistentdrug doses. Despite their undisputed popular-ity, pMDIs have one major drawback: the needof coordination between device actuation andpatient inhalation. Failing to inhale at the righttime might result in severely reduced doses ofdrug reaching the lungs.

• DPIs serve as an alternative to pMDIs andare the preferred device technology for treat-ing a number of increasingly diverse dis-eases [8]. Unlike their counterparts, DPI con-tain a dry powder formulation stored in theform of capsules, blisters or reservoirs (e.g.Turbuhaler R©). Upon patient actuation a la-bel dose of dry powder is entrained and dis-persed in the inspiratory airflow by a variety offluidization and dispersion mechanisms spe-cific to each device.

• Soft mist inhalers (SMI) are the most recentinhaler technology, being Respimat R© SoftMistTM by Boehringer Ingelheim the first ofits kind. In Respimat R© upon actuation, themetered dose of water-based drug solution isforced through a nozzle, producing two finejets of liquid that converge at a predefined an-gle to create a soft mist.

1.2. Types of DPIsUnlike their counterparts, DPIs are breath-actuated devices that rely either solely on the pa-tients respiratory effort (passive) or also on anotherpower source (active).

Active devices are more complex by nature, asthey need the extra parts (e.g springs) to provide

the additional form of deaggregating power. A no-table example is MicroDose R© , patient inhalationtriggers a piezoelectric element that induces vibra-tions which help to deaggregate the formulationpowder [10].

On the other hand, passive devices like Hov-ione’s TwinCaps R© inhaler are made from a smallnumber of parts and are therefore much easier andcheaper [1] to produce. They also eliminate theneed for any hand to breath coordination as thepatient’s inhalation is the only vehicle the powderneeds to reach the target location.

Besides the classification based on dispersionmechanisms, the DPI technology family can alsobe split into three branches based on how theystore their powder doses [11]:

• Single dose devices store only one pre-metered dose at a time, usually in the form ofa gelatin capsule that has to be loaded in be-fore each use. They can either be discardedafter usage as is the case of TwinCaps R© orrefilled an re-used (e.g. Handihaler R©).

• Multiple unit dose devices store multiple pre-metered doses so can be used multiple timesbefore either refilling or disposing. In the caseof the Advair Diskus R©, the inhaler contains acoiled sealed foil strip bearing 60 doses in sep-arate blisters. Upon each actuation a blister isruptured, exposing a single dose.

• Reservoir devices are also of the multiple dosetype, but instead they store the entire amountof pharmaceutical drug in a single container orcannister. Upon actuation a metered amountof powder is harvested from the bulk and ex-posed to the airflow (e.g. Turbuhaler R©).

2. MethodologyThe TwinCaps R© dry powder inhaler consists of twoplastic parts: the inhaler body; and the powder car-tridge, hereby referred to as shuttle (Figure 1). Theshuttle has two inlets to allow atmospheric air totravel into one of two equal powder compartments,disperse the powder, entrain it into the mouthpiece

2

Figure 1: Boundary conditions for the momentum and turbulentquantities variables

and ultimately out into the patient’s mouth [13].Each compartment has a rear inlet in the form ofa slit, small enough to ensure that from the mo-ment the powder is loaded in the compartment un-til patient actuation, no powder flows out of the de-vice under the force of gravity. Moreover, when instorage position (illustrated in 2.3a)), the compart-ment’s inlet and outlet are sealed, preventing pow-der from leaking out protecting it from environmen-tal influences [13]. The body side inlets (Figure 2.2)bring additional air flux to the small amount of airvolume that is able to enter the powder compart-ment through the narrow slit inlet, penetrate andentrain the powder bed and exit at the mouthpieceinlet. These body side inlets guarantee a com-fortable inhalation and enrich the powder-air mixwith air, thus maximizing the entrainment capacityof the flow [13]. Furthermore, with the body sideinlets, the user patient can easily generate a 4kPapressure drop[13], which the pharmacopoeias rec-ognize as suitable from a patient perspective.

2.1. Mathematical modelAssuming first hand an incompressible internal air-flow within TwinCaps R©, the proposed mathemat-ical model encompasses the Reynolds averagedNavier-Stokes (RANS) equations and is closedwith Menter’s k − ω shear stress transport (SST)turbulence mode model.

In order to integrate the governing partial differ-ential equations (PDEs), special treatment is re-quired at the volume bounding surfaces. This treat-ment consists in the prescription of boundary con-ditions.

Figure 2 shows the boundary conditions pre-scribed to: the device’s internal walls (in grey); atthe bottom by the powder cavity inlet (in green); atthe sides by the body side inlets (in blue); and fi-nally at the top by the mouthpiece outlet (in red).

2.2. Spatial and time discretization schemesIn this work two spatial discretization schemes; up-wind; and hybrid and a fully implicit time discretiza-

Figure 2: Boundary conditions for the momentum and turbulentquantities variables

tion scheme were used to proceed with the steady-state and transient simulations accordingly.

2.3. Mesh generationThis work followed a mesh generation procedureincluding the use of the native OpenFOAM v2.4.0mesh generation utilities blockMesh and snappy-HexMesh. These procedure automatically gen-erates three dimensional hex-dominated unstruc-tured meshes from triangulated surface geome-tries, in stereolithography (STL) format.

For this work three unstructured grids, of in-creasing mesh refinement at the wall, were gen-erated. The level of mesh refinement for eachgrid was regulated by a snappyHexMesh parame-ter which defines the overall first cell height relativeto the wall. It was assumed that the first cell centerheight is equal to half the cell height ∆y1 = 2y1.Recalling the definition of the dimensionless dis-tance to the wall y+1 = uτy1/ν and the expressionfor the friction velocity uτ =

√τω/ρ

y+ =uτy

ν=y

ν

√τωρ

(1)

Where τω is the shear stress at the wall, which isdefined as,

τω =1

2ρCfU

2 (2)

Substituting the expression for τω (Equation 1) inEquation 2 yields,

y+ =y

ν

√12ρCfU

2

ρ=

(UD

ν

)︸ ︷︷ ︸ReD

y

D

√Cf2

(3)

Recognizing the under-braced term as the flow’sReynolds number, y can be rewritten as function ofy+, Reynolds number ReD , a flow characteristiclength D and the skin friction coefficient Cf .

y = y+(

D

ReD

)√Cf2

(4)

The flow’s Reynolds number was computed as-suming as reference velocity the device outlet ve-locity, Uout, derived from TwinCaps R©’s experimen-tally measured flow rate at a 4kPa pressure drop,

3

and the mouthpiece median diameter Dm = 8,38×10−3m as reference dimension.

Uout =QoutAout

= 11,42ms−1 (5)

ReD =UoutletDm

ν= 6024,22 (6)

With the Reynolds number calculated, the skinfriction Cf (ReD) could also be assessed

Cf = 0.575Re−1/5D = 0,01 (7)

Substituting these values into Equation 3, theheight of the first cell center to the wall y canbe directly computed for each chosen y+. Ta-ble 2 shows the values of y as well as the threemain mesh quality parameters: maximum aspectratio; maximum skewness; and maximum non-orthogonality for each generated grid.

3. Results & discussionComplementing the existing and ongoing CFD-aided research and development work on the DPI[9] field, this work addresses the TwinCaps R© flowfield problem using an open source CFD tool-box, OpenFOAM R©. In the next subsections thesteady-state and transient TwinCaps R© flow fieldsare characterized respectively. The first subsectionalso includes a mesh dependence study (with ninecases, see Table ??) and a validation exercise ofthe proposed model against experimental data. Fi-nally, in the last subsection section , a comparisonbetween a transient simulation, with massless par-ticle tracking as a post processing task, and highspeed filming of the device operation with a phar-maceutical powder is made.

3.1. Iterative convergenceA good practice when computing CFD simulationsis to start the iterative process with a discretizationmethod that promotes solution stability and finishwith one which provides a higher order of accu-racy. With that in mind, each steady-state simula-tion began with the upwind discretization methodand finished with the hybrid or linear upwind. It isimportant to guarantee that the solution using theupwind scheme is converged before switching spa-tial discretization methods mid-run. Otherwise thenewly appointed scheme may not be stable enoughand consequently may lead to non-realistic resultsor ultimately to solution divergence.

Figure 3 shows the residuals for case 4.3 (seeTable ??) during the first 3000 iterations.

It can be seen that all equation residuals mono-tonically drop bellow the 10−3 threshold value.The lowest residual value belongs to the pres-sure equation, which is already bellow 10−5, due

1e-06

1e-05

0.0001

0.001

0.01

0.1

1

0 500 1000 1500 2000 2500 3000

Residuals

Iteration

pContinuity

UxUyUzk

Figure 3: Equation residuals of case 4.3 run using the upwinddiscretization scheme. In the legend Ux, Uy and Uz are theCartesian components of the velocity vector, k is k, omega is ω,p is pressure and continuity stands for the continuity error

to the fact that the solution is driven by the pres-sure boundary conditions. The equation residualsdropping bellow a this predefined threshold valueis a necessary but not sufficient condition for solu-tion convergence. Thus extra investigations werecarried out in order to check the validity of this as-sumption. In this work, one investigation consistedin defining surfaces, at specific locations of the do-main, to probe the flow rates across them and tocheck if their value stabilized.

Figure 4a, show the progression of the flow ratevalue at the outlet with the successive simulation it-erations. All of the these quantities reach a plateaubefore the last iteration which indicates that, in thiscase in particular 4.3, solution convergence hasbeen achieved.

0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

0 500 1000 1500 2000 2500 3000

Q (

m³/

s )

Iterations

(a) QOUT

0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

0 5000 10000 15000 20000 25000

Q (

m³/

s )

Iterations

(b) QOUT

Figure 4: Probed volumetric flow rates, of the upwind and linearupwind solutions respectively, at the outlet

Now switching discretization schemes to the lin-ear upwind (or hybrid) at the 3000th iteration, andre-plotting the flow rates at the previously specifiedlocations (Figures 4b) it can be seen that these val-ues now fluctuate about a mean value as opposedto the more stable behavior of the upwind solution.This new found instability may be a consequenceof the diminished numerical diffusion effect, i.e.fluctuations of the velocity field (for instance in thefour jet mixing zone) are now less dampened. Inthis solution the body side inlet jets do not balanceeach other out, i.e. the flow rate across each inletis different, rendering the flow field non-symmetric(Figure 5).

In a problem whose geometry and boundaryconditions are symmetric, the solution should also

4

Table 2: Quality parameters of the generated meshes

y+ y Aspect ratio Skewness Non-orthogonality NV OLUMES(m) (◦ )

Ideal mesh - - 1 0 0 -Mesh 1 0, 75 6, 09× 10−5 18, 67 4, 28 64, 69 10, 93×106

Mesh 2 1 8, 12× 10−5 17, 51 6, 06 64, 91 4, 88×106

Mesh 3 1, 5 1, 22× 10−4 16, 08 5, 96 64, 96 1, 33×106

be symmetric. However, to obtain a completelysymmetric solution about the X and Z planes,the mesh, the discretization scheme and the dis-cretization error would also need to be symmetric.Since the unstructured meshes are generated au-tomatically by snappyHexMesh’s algorithm, satis-fying these conditions is impossible.

Figure 5: Asymmetry of the predicted flow field in the case 4.3

In order to maintain solution flow field symmetryits iterative convergence has to be thoroughly con-trolled. A way to control iterative convergence isthrough solution relaxation.

3.2. Solution relaxationIn early calculations, allowing a high variation ofgeneric fluid property, φ may cause instability andconsequently hinder or even prevent convergence.Solution relaxation is a technique applied to the al-gebraic equations, which limits the change in eachvariable between outer iterations.

Solution relaxation is considered to be implicit ifits effect is incorporated into the equation at thebeginning of an inner iteration cycle or explicit if itis applied after the solution of an outer iteration isobtained.

In OpenFOAM R©, only pressure is explicitlyunder-relaxed in the SIMPLE algorithm while othervariables (e.g. U , k, ω) are implicitly under-relaxed.Since these particular cases (see Table ??) re-quired explicit under-relaxation that was not read-ily available on OpenFOAM R©, a few changes weremade to the solver simpleFoam and to the k − ωSST model so as to include this type of relaxationfor the velocity U , turbulent kinetic energy k andspecific turbulent dissipation ratio ω variables.

With the newly added explicit under-relaxationfactors given in Table 3, the simulation wasrestarted from the 3000th iteration resulting in anearly symmetric final solution (depicted in Figure6).

In this solution the side inlets jets balance eachother out and it can be seen that the two lines ofzero velocity component Ux = 0, where the twopairs of jets meet (front and back), are aligned.

(a)

(b)Figure 6: Body side inlets jets mixing site flow field when us-ing: (a) Exclusively implicit under-relaxation for the velocity andturbulent fields; (b) Implicit and explicit under-relaxation for thevelocity and turbulent properties fields

3.3. Experimental methodologyWith the purpose of validating the numerical re-sults with experimental data, tests were run on theTwinCaps R© inhaler using the dosage unit sam-pling apparatus (DUSA) for DPIs. The DUSAis generally used to perform Pharmacopoeia-specified tests, which evaluate device performanceparameters such as the emitted or delivered doseand their uniformity through container life. In thiswork however, this testing apparatus was utilizedexclusively to measure the volumetric flow rate ex-iting a powder-less TwinCaps R© device when sub-jected to constant pressure drops.

Figure 7: Experimental tests equipment set-up, adapted from[5]

An equivalent test-bench to the one representedin Figure 7 was set-up in a laboratory facility atHovione (Loures, Portugal). The set-up comprisesa vacuum pump, which generates the desired pres-sure drop, a critical flow controller, equipped with atwo-way solenoid valve that controls air supply tothe inhaler, and the DUSA. Additionally, the inhaleris connected to one end of the DUSA by a mouth-piece adapter which provides an air tight connec-tion between the inhaler outlet and the samplingapparatus. The measuring procedure consists in

5

Table 3: The new and former relaxation factors configuration

αimp αexp

U p k ω U p k ω

Former relaxation factors 0,1 - 0,1 0,1 - 0,9 - -New relaxation factors 0,1 - 0,1 0,1 0,05 0,9 0,4 0,4

first regulating pressure drop to constant value byvarying the flow rate (with the solenoid valve) andchecking the resulting pressure drop measurementat the device outlet. Once the pressure drop valueis set, the inhaler and mouthpiece adapter are de-tached from the DUSA and in their stead a flowmeter is placed to finally read the volumetric flowrate. Table 4 shows the volumetric flow rate valuesper pressure drop level.

3.4. Inhaler resistanceA DPI’s outlet flow rate is a function of the pres-sure drop level and the device’s specific resistance.In their work, [4] assuming incompressible airflowwithin a device, utilized the following relation,√

∆p =√pamb − poral = RDQ (8)

where the volumetric flow rate is directly propor-tional to the square root of the pressure drop de-veloped across it. This relation is a derived formof the renown Bernoulli equation from which is di-rectly deductible that ∆p ∝ U2.

Here pamb is the ambient pressure, poral is thepressure in the oral cavity,Q is the outlet volumetricflow rate and RD is the device’s specific resistancewhich is the constant of proportionality.

As expected, Figure 8 shows good agreementbetween Equation 8 and the experimental dataobtained earlier for the TwinCaps R© inhaler. Theslope of the linear equation which fits the exper-imental data represents the experimental devicespecific resistance, which in this case was foundto be RD = 0,0533kPa−1/2 L−1 min.

0

1

2

3

4

5

6

7

8

9

10

0 20 40 60 80 100

Sq

ua

re r

oo

t o

f P

ress

ure

Dro

p (

kP

a1

/2)

Flow rate ( L/min )

Rotohaler

Diskhaler

Inhalator

Turbuhaler

TwinCaps

HandiHaler

Figure 8: Relationship between pressure drop and flow rateacross DPI devices adapted from [4]

3.5. ValidationThe exercise of validation attempts to estimate themodeling error associated with the mathematicalmodel used [7]. Validation using experimental re-sults is arguably the most employed method be-cause physical measurements directly show thelevel of model conformity with reality. The Ameri-can Society of Mechanical Engineers (ASME) pro-posed a validation procedure, combining the nu-merical, experimental and parameter uncertainties[7], in which two quantities are compared:

Uval =√U2D + U2

num + U2input (9)

E = S −D (10)

Where Unum, Uinput, UD and Uval are the numer-ical, parameter, experimental and validation uncer-tainties respectively, S is the numerical prediction,D is the experimental value and E is the compari-son error. This procedure aims to estimate the 95%confidence interval (Equation 11) which boundsthe modeling error, δmodel [7].

δmodel ∈ [E − Uval, E + Uval] (11)

To estimate the validation uncertainty Uval, thestandard deviation of the measured flow rates ofthe previously presented TwinCaps R© experimentis taken as the experimental uncertainty and theparameter uncertainty is considered to be negli-gible Uinput ∼ 0. The standard deviation of then = 10 measurements (see Table 4) at a 4kPa con-stant pressure drop, is UD = 0,44Lmin−1. Substi-tuting this result and the numerical uncertainty val-ues estimated before (UnumUDS

= 1,01Lmin−1 andUnumLUDS

= 0,91Lmin−1) in to Equation 9 yields avalidation uncertainty of UvalUDS

= 1,1Lmin−1 forthe upwind scheme and UvalLUDS

= 1,01Lmin−1

for the linear upwind scheme. Knowing from theexperiment that, at a 4kPa pressure drop level, theoutlet flow rate is QOUT = D = 38,89L/min andusing the predicted values S, the comparison errorcan be calculated for each case (Table 5).

Now taking both ELUDS and UvalLUDS, the min-

imum and maximum modeling errors with respectto the experimental value D can be estimated,

δmodelmin=

1, 59

38, 89× 100% = 4, 1% (12)

6

Table 4: Measurements of the flow rate passing through ten powder (n = 10) cavities in five TwinCaps R© devices

N=1 N=2 N=3 N=4 N=5(kPa) (Lmin−1) (Lmin−1) (Lmin−1) (Lmin−1) (Lmin−1)∆p Q1 Q2 Q1 Q2 Q1 Q2 Q1 Q2 Q1 Q2

1 21,8 21,8 21,9 21,7 21,2 20,8 20,6 20,3 20,5 19,92 28,0 28,0 27,6 27,7 28,2 29,8 28,2 27,8 28,9 28,63 34,5 34,1 33,4 33,9 33,9 33,9 33,2 33,2 33,8 33,84 39,4 39,8 38,5 38,8 38,9 38,9 38,1 38,6 38,9 38,95 44,7 44,5 43,4 43,8 43,5 43,8 43,4 43,1 43,3 43,86 48,5 49,8 47,7 48,2 48,6 48,8 47,9 47,8 47,8 48,5

Table 5: Calculation of the comparison error between simulation results and experiment

D SUDS SLUDS EUDS ELUDS

Case (Lmin−1) (Lmin−1) (Lmin−1) (Lmin−1) (Lmin−1)

4.1 41,33 41,48 2,45 2,604.2 38,89 41,51 42,22 2,63 3,344.3 40,50 41,33 1,62 2,45

δmodelmax =3, 61

38, 89× 100% = 9, 3% (13)

Figures 9a and 9b both show the experimentaldata plotted together with the numerical predictionof the outflow, when a 4kPa pressure is appliedacross the device, for cases run with the upwindand the linear upwind schemes respectively.

20

25

30

35

40

45

50

1 2 3 4 5 6

Flo

w R

ate

( L

/min

)

Pressure Drop ( kPa )

Experimental

Mesh 1

(a)

20

25

30

35

40

45

50

1 2 3 4 5 6

Flo

w R

ate

( L

/min

)

Pressure Drop ( kPa )

Experimental

Mesh 1

(b)Figure 9: Comparision of numerical and experimental data.The numerical data originates from the Case 4.1 while usingthe: (a) upwind scheme; (b) linear upwind scheme

There are two potential reasons for the model toover-predict the flow across the device: the turbu-lence model; and the simplifications made to thegeometry. In the present mathematical model, itwas assumed that the k - ω SST model could cap-ture transition from laminar to turbulent flow withinthe inhaler. However, this turbulence model is

known for anticipating transition [6], in which casethe length of the recirculation zones in the mouth-piece might be under-predicted, arguably equatingto a larger numerical outflow prediction, QOUT , forthe same pressure drop level ∆p. Secondly, thegeometry simplifications, however small in numberand change, may have affected the pressure dropat the inlets.

Despite these facts, the proposed mathematicalmodel was able to capture an important physicalproperty of the problem, the slope of the Q vs. ∆pcurve. Figure 10 shows the plot of three operat-ing points 3kPa, 4kPa, 5kPa for the three meshes:Mesh 1; Mesh 2; and Mesh 3 against experimentaldata of the same points. Moreover, the fitted linearequations formulas are presented in the graph andit can be seen that their slope is similar.

y = 0,046x + 0,11

y = 0,045x + 0,091

y = 0,05x - 0,049

y = 0,051x + 0,0260

1

1

2

2

3

0 10 20 30 40 50

Sq

ua

re r

oo

t o

f P

res

su

re D

rop

(k

Pa

)

Flow Rate ( L/min )

Mesh 1

Mesh 2

Mesh 3

Experimental

Figure 10: Comparison between fitted linear curves of experi-mental and computational data

3.6. Transient flowIn order to fully represent the actual patient gen-erated flow, time-dependency characteristic of pa-tient inspiratory effort is i.e. the flow must be takeninto account. The problem of inspiratory flow devel-opment inside TwinCaps R© throughout inhalationtime, is thus transient (time-dependent) in nature.

7

Fortunately, the formulation of this transient prob-lem is similar to that of the steady-state problem,except now both time discretization and time de-pendent boundary conditions need to be taken intoaccount.

DPI devices either rely exclusively (passive) orpartially (active) on patient inspiratory effort to de-liver the label dose to the lungs. Therefore, espe-cially for passive DPI, the device’s inhalation tech-nique and patient compliance are decisive for asuccessful inhaled drug delivery. The total inhaledvolume, the peak inspiratory flow (PIF) and thetime at which it is attained are important inhalationtechnique parameters and are generally deviceand patient dependent. In the case of TwinCaps R©,to the author’s knowledge, there is no availableclinical data that provides a patient inspiratory pro-file specific to the device. For demonstration pur-poses however, a simplified example can be builtbased on the generic inspiratory effort profile intro-duced by [3] and depicted in Figure fig: 3.3b.

On account of TwinCaps R© being a passivereservoir-type DPI, the inhalation technique shouldconsist in a relatively short PIF time, 0,1s ≥ tPIF ≤0,2s coupled with a high PIF to impart sufficientenergy to the flow for particle fluidization, deag-greagation and dispersion. This is the time rangeof interest, from a flow development standpoint,that allows the characterization of the flow patternsidentified as the fluidization and dispersion mech-anisms in the previous steady-state test cases. Inthis work, time-dependency of the airflow acrossthe device is emulated via a simplified ∆p(t) func-tion (Figure 11).

0

1

2

3

4

5

0 0,5 1 1,5 2 2,5

Pre

ss

ure

dro

p (

kP

a )

Time ( s )

Figure 11: Time-dependent pressure boundary condition:pressure drop level rises from 0 to 4kPa in an peak inspiratoryflow rate time of tPIF = 0, 1s and then is kept constant to allowthe flow field solution to reach steady-state

The function is a pressure drop ramp, increasingfrom rest at 0kPa to 4kPa corresponding to the PIFin a time of tPIF = 0, 1s. The pressure drop valueof 4kPa is then maintained to allow the flow to reacha final steady-state.

Just before inhalation, at t = 0s, both the air sur-rounding and within the device is at rest. As thepatient actuates the device, he/she exerts at firsta small pressure drop that drives the internal airvolume towards his/her mouth. When t = 0,001s

1e-05

0.0001

0.001

0.01

0.1

1

10

100

1000

10000

0 500 1000 1500 2000 2500 3000 3500 4000

Iteration

CmaxCmean

t

t

p

Time Step

Figure 12: Evolution of the Courant number and time step val-ues with iteration number

have elapsed the pressure drop is ∆p = 40Pa,a value which generates a ”perfect fluid” like flowfield (Figures 13a and 13e) where the streamlinesat powder compartment’s entrance are able to fol-low its bounding walls. At the second time stept = 0,002s however, the outside air is drawn in at aspeed which does not permit it to follow the com-partment’s walls as before thus flow separation oc-curs and a slit-shaped jet is formed. With the incep-tion of this flow feature, two other arise, two recir-culation zones circumscribing the jet (Figures 13band 13f).

(a) (b) (c) (d) (e) (f) (g) (h)Figure 13: Powder compartment flow streamlines projected inthe Z plane in initial time levels from (a) t = 0,001s to (g) t =0,007s and the final one (h) t = 0,16s

As time progresses so does the pressure droplevel ∆pti+1

= ∆pti + 40Pa and consequently themagnitude of the velocity field and size of the recir-culation zones.

(a) (b) (c) (d) (e) (f) (g) (h)Figure 14: Powder compartment flow streamlines projected inthe X plane in initial time levels from (a) t = 0,001s to (g) t =0,007s and the final one (h) t = 0,16s

The maximum length of the recirculation zone isreached at the t = 0,007s time step. From then onuntil t = 0,1s when ∆p = 4kPa the jet fluctuatesabout its upright centered position (in the x direc-

8

tion) with the recirculation zones varying in widthaccordingly1. This upright position about which thejet fluctuates corresponds to the symmetric steady-state solution.

Until t = 0,1s, the amplitude and frequency of theflow patterns oscillation about their steady-statestates are both a function of the pressure drop gra-dient ∆p/tPIF = 40kPa s−1. The steeper the gra-dient the larger in magnitude and number the fluc-tuations. The real flow generated by the patient’sinspiratory effort, the curve’s gradient is time de-pendent ∆p/t 6= constant and is generally moreaccentuated at the beginning of inhalation gradu-ally tending to zero as PIF is reached (see Figure11). A steeper initial gradient imparts more power,P , to the flow.

P = Q∆p (14)

Where ∆p and Q are the pressure drop and fluidflow rate across the device. This power conju-gated with the above mentioned flow pattern fluc-tuations constitute the driving force behind pow-der fluidization within the TwinCaps R© inhaler. Ul-timately this limits the device’s range of applicabil-ity, i.e. if the patient is unable to generate a highpressure drop gradient (e.g. patients suffering fromsevere COPD) which guarantees the minimum re-quired energy to properly fluidize the powder bed,then device performance may be hindered. It isthen important when conceiving DPI devices, par-ticularly a passive DPI, to aim for a design whichboth promotes a high turbulence intensity level anda low internal device resistance.

3.7. Particle visualizationFor the purpose of tracking particles inside DPIs,researchers have generally utilized one of the fol-lowing methods: Lagrangian particle tracking aspost-processing operation; Euler-fluid/Lagrangian-particle; and CFD + DEM.

Due to the limited time frame of this work, noneof the mentioned methods was pursued. Insteada purely qualitative comparison, between the firstseconds of the real multiphase particle-airflow andits transient simulation, is presented. Figures 15a,15b and 15c show post-processed time framesof a high-speed film featuring a powder loadedTwinCaps R© compartment shot in a laboratory atHovione’s facilities. To enable a comparison withthe real flow, massless spherical particles whereintroduced in a random fashion at several heightsof the powder compartment.

In this case the particles simply follow the flow’sstreamlines (Figures 15d, 15e and 15f2). The only

1if the jet is shifted to the right the left recirculation zone isnecessarily larger than the right one

2The complete set of time steps corresponding to the time

(a) (b) (c)

(d) (e) (f)Figure 15: Powder bed fluidization in the real: a); b) and c) andsimulated flow: d); e) and f)

information that can be extracted from this compar-ison is the visible tendency in both cases of the par-ticles lifting first in center and later shifting to sideof the powder compartment. In the real flow, thiscan be due to an eventual non-symmetric geom-etry of the device used (e.g. surface irregularitiesate slit-shaped powder compartment entrance), toa misalignment between its powder compartmentinlet and its body bottom inlet or even to one sideof the powder bed being more densely packedthan the other. In the flow simulation, this canalso be due to geometric imperfections (e.g. non-symmetric mesh) or to the discretization methodand the numerical diffusion it introduces. However,to gain a better understanding of the real multi-phase flow a test case employing one of the pre-viously mentioned methods would need to be un-dertaken.

4. ConclusionsThis thesis presents the use of OpenFOAM R©, anopen-source CFD toolbox, to determine the com-plex internal airflow within the TwinCaps R©DPI. Be-sides characterizing the main flow patterns, thiswork comprised a mesh dependency study to es-timate the solution’s numerical uncertainty and acomparison of the solution with experimental data.

For an operating pressure drop of 4kPa it wasfound that increasing mesh refinement did not leadto a monotonic convergence of the outflow numer-ical prediction for both linear and linear upwinddiscretization schemes. The discretization uncer-tainty for Mesh 1 is then majored by the maximumdifference between predictions for both methods.The uncertainties associated to the iterative errorwere negligible when compared to the discretiza-tion error, thus the numerical prediction uncertaintyfor the above mentioned pressure drop conditionwas found to be 2, 4% and 2, 2% for the upwind

frames extracted from the video is presented as an annex

9

and linear upwind schemes respectively. The setof results for each mesh showed good agreementwith experimental results, as the corresponding nu-merical flow rate vs. pressure drop curve exhib-ited a similar slope to that of the experimental one.However, the simulations under-predicted the headloss, i.e. the device’s internal resistance, resultingin comparison errors, E, of 6, 7%, 8, 6% and 6, 3%for the 3, 4, and 5kPa pressure drop levels respec-tively. As a result, the modeling error is estimatedto be between 4, 3% and 9%. On this note, shouldfuture work require a lower modeling error, then atransition model should be included in the mathe-matical model as opposed to allowing the SST k-ω turbulence model deal with transition on its ownaccord. On the other hand, should it require amore precise estimate of the modeling error, i.e. anarrower interval [δmodelmin

, δmodelmax], future stud-

ies could include second-order accurate discretiza-tion schemes in space and time. Additionally, in-vesting in a multi-block structured mesh generator(e.g. GridPro) could sharply increase mesh qualityand consequently the accuracy of numerical pre-dictions.

These simulations also uncovered the flow pat-terns behind the fluidization, powder deaggrega-tion and dispersion mechanisms. Two nearly in-dependent sub-flows were identified, one consist-ing of a jet inside the powder compartment whichprovides fluidizing power and a second comprisinga high turbulent mixing zone formed by the frontalcollision of two pairs of jets that deaggregate anddisperse the powder.

Considering the information acquired from thesteady-state stage, and by applying a time-dependent pressure boundary condition, a tran-sient case representative of patient inspiratory ef-fort, was simulated. Further insight on the actualdevelopment of the flow patterns could be gainedby applying a pressure boundary condition derivedfrom a real patient inspiratory effort profile such asthe ones presented in the work of [2].

Finally, a purely qualitative comparison is madebetween time frames of a high speed film featur-ing a drug filled TwinCaps R© powder compartmentand the transient simulation with massless spheri-cal particles placed as a post-processing task. Asthe real flow inside the powder compartment is adense particle flow, no conclusions can be drawnfrom this comparison besides the tendency of theparticles to be lifted towards one of the sides of thecompartment observed in both real and simulatedflows.

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