Flow, heat and mass transfer through CBRN protective clothing

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through

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through

CBRN protective clothing

Proefschrift

ter verkrijging van de graad van doctor aan de Technische Universtiteit Delft,

op gezag van de Rector Magnificus Prof. ir. K.C.A.M. Luyben, voorzitter van het College voor Promoties,

in het openbaar te verdedigen op dinsdag 7 mei 2013 om 15:00 uur

door

Davide AMBESI

Ingegnere Aerospaziale, Politecnico di Torino, Italië

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Samenstelling promotiecommissie: Rector Magnificus,

Prof. dr. ir. C.R. Kleijn,

Prof. dr. ir. H.E.A. van den Akker, Prof. dr. ir. M.T. Kreutzer,

Prof. dr. A.I. Stankiewicz, Prof. dr. D.J.E.M. Roekaerts, Dr. P.W. Gibson,

Dr. E.A. den Hartog, Prof. dr. R.F. Mudde,

voorzitter

Technische Universiteit Delft, promotor Technische Universiteit Delft

Technische Universiteit Delft Technische Universiteit Delft Technische Universiteit Delft

US Army Natick Soldier R, D & E Center TNO

Technische Universiteit Delft, reservelid

Financial support

This research was sponsored by the Netherlands Ministry of Defence and supported by the TNO (The Netherlands Organization for Applied Scientific Research). The statements in this thesis do not necessarily reflect their opinions.

ISBN 12345678

Copyrights c 2013 by Davide Ambesi

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Summary

The need of performing work operations in areas contaminated by hazardous gases for soldiers and law enforcement has led to the development of special pro-tective garments. CBRN (Chemical, Biological, Radiological, Nuclear) propro-tective garments are a type of personal protective equipment designed to provide pro-tection against direct contact with, and contamination by, radioactive, biological, nuclear or chemical substances in the form of gases or vapors. These garments are generally designed to be worn for extended periods, to allow the wearer to function while under threat of nuclear, biological, or chemical exposure. Nowadays CBRN protective garments consist of a single layer of active carbon material (e.g. carbon spheres or fibers of∼ 500µm diameter), embedded between two textile layers. When exposed to contaminated air flows, the hazardous gases transported in the incoming air are adsorbed onto the active carbon material. The resulting cleaned air is free to stream through the protective clothing, assuring ventilation and thermal comfort to the wearer. In the first hours of exposure (i.e. when the carbon material is not yet saturated and still fully active), still little amounts of hazardous gases can pass the active carbon layer without getting adsorbed. This phenomenon is known as initial breakthrough and is mainly due to the the fact that the filter layer is thin and has a high porosity. Initial breakthrough is also caused by "leakages" that occur at the garment extremities, e.g. neck, wrists and ankles, and seams, where good isolation from the surrounding environment is difficult to achieve. After this initial stage the active carbon filter becomes saturated and the adsorbing capabilities of the carbon material drastically reduce in time. Eventually this results in a total loss of the filtering capabilities. Other than the requirement that this should happen as late as possible, this stage is of little relevance since the protective garment should not be worn anymore. In addition to reducing leakages, increasing the packing density of the carbon filter material, and embedding this filter material in low permeability textile layers can reduce the amount of gas initial breakthrough. However, this results in a lower air permeability of the protective

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clothing, leading to undesired higher heat stresses on the wearer. Such contradict-ory requirements make the right balance between high protection and acceptable ventilation difficult to achieve. Consequently, design and development of CBRN protective clothing result in a very complex optimization problem.

Whereas experimental studies of CBRN protective clothing are time consuming, and require expensive experimental setups, Computational Fluid Dynamics (CFD) simulations can be a powerful alternative tool of investigation. This thesis deals with the CFD modeling and optimization of flow, heat and mass transfer in CBRN protective clothing. In particular the influence of the actual geometrical struc-ture of the adsorbing filter layer and of the embedding textile layers on gas initial breakthroughs and ventilation conditions have been analyzed. For this purpose

meso-scale (i.e. at the scale of a limb) and micro-scale (i.e. at the scale of individual

carbon filter particles) CFD simulations were performed.

In the first part of this work we performed micro-scale simulations, in which the active carbon filter material in CBRN protective garments was modeled as a single layer array of parallel fibers or spheres, equidistantly or non-equidistantly spaced in a plane perpendicular to the flow direction. For free-stream Reynolds number (based on the particle diameter) between 0.01 and 600, and Schmidt numbers for the hazardous gas diffusion between 0.7 and 10, we studied mass transfer to such arrays as a function of the open frontal area fraction and the uniformity of the filter layer. Our CFD simulations showed that for these configurations two critical Reynolds numbers, based on the air velocity around the carbon particles and their diameters, Re1and Re2can be identified. Below Re1, all incoming hazardous gas

is transferred to the carbon filter material by diffusion and this mass transfer is independent of the inter-particle distances in this filter. Consequently, under these conditions, equidistantly and non-equidistantly spaced filters perform equally well. Above Re2, thin convective boundary layers are formed around the carbon particles.

These boundary layers are very thin compared to the inter-particle distances, and consequently mass transfer is again independent of the inter-particle distances and their uniformity. In fact, under these conditions the mass transfer to the filter layer is equal to that for a single particle. For Reynolds numbers between Re1and

Re2, there is a strong interaction between the boundary layers around the various

carbon particles. Consequently, the inter-particle distances and their uniformit-ies have a strong impact on the mass transfer. The latter may be up to a factor 3 lower for non-equidistantly spaced filter particles, as compared to equidistantly spaced particles. Based on elementary mass transfer reasoning and the results of our CFD simulations, analytical expressions for Re1and Re2have been proposed.

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posed. These new correlations fill a gap in the existing literature: whereas there have been many published data and correlations for mass transfer to single spheres and cylinders, to 1-dimensional arrays of spheres or cylinders aligned with the flow direction, and to 3-dimensional structured arrays of spheres or cylinders, no data were available yet on heat and mass transfer to 2-dimensional arrays of spheres or cylinders in a single plane perpendicular to the flow direction

The second step of our work was to analyze the influence of the two embedding textile layers on the performance of the active carbon filter layer. This has been done by modeling the textile layers as single layers of perpendicularly woven or parallel cylindrical bundles of fibers. These were placed upstream and downstream of the filter layer, resulting in three-layer configurations of protective material. We studied various positionings of the carbon filter particles with respect to the textile fiber bundles. We also varied the distance between the active and the passive layers, and switched from in-line to staggered alignments between the layers, for free-stream Reynolds numbers, based on the carbon particle diameter, between 0.1 and 100, Schmidt numbers between 0.7 and 10, and open frontal area fractions of 0.2, 0.4 and 0.6 for both the textiles and the filter layer. At fixed cross flow air velocity, the amount of tracer gas adsorbed onto the filter layer embedded between the two textile layer was found to be equal to the amount of tracer gas adsorbed onto the same filter layer when not embedded between textile layers, independent of the type of alignment and distance between the layers. However, the pressure drop across the three-layer protective material was found to be significantly higher than that of a single filter layer of the same open frontal area fraction. These results suggested that, when modeling CBRN protective material, the actual geometrical structure of inner and outer textile layers can be neglected, because they do not affect the adsorbing capacities of the active carbon layer. However, the additional pressure drop due to the textile layers must be taken into account. This can be done in two ways: (i) by modeling the textile layers as homogeneous porous layers of given permeability, or (ii) by modeling only the filter layer, using reduced velocities for the incoming air-flows.

Assured that, for given cross flow air velocity, the two embedding textile layers in CBRN protective clothing do not influence the gas adsorbing capacities of the garment, we used the results from our micro-scale simulations to propose a closed-form analytical model able to predict the protection factor and pressure drop coefficient for single layer filters of active carbon particles in cross-flow. Predic-tions from this model were found to be in excellent agreement with experimental observations and CFD simulations. A parametrical study with the proposed model

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showed that, for a given required protection factor, the lowest pressure drop is found for layers combining a high porosity and small particle diameter. Similarly, when a certain maximum pressure drop is allowed, the best protection is obtained when using small particles in a high porosity layer.

In the final stage of our work we performed a meso-scale study of the performance of CBRN protective clothing in one of its classical test setups. This is a solid cylinder - mimicking a human limb - in cross-flow sheathed at some small distance by the three-layer protective garment material. The two passive textile layers materials were modeled as homogeneous porous layers, whilst the active filter layers was modeled as a single layer of resolved adsorbing particles embedded between the two textile layers. For realistic conditions as used in published experimental tests of protective garments (Reynolds number 12, 000− 34, 000, based on the cylinder diameter and the free stream velocity, Schmidt number 3, and realistic values for the hydraulic resistance of the textile materials),the introduction of a single layer of activated carbon particles with an open area fraction as large as 0.6was found to reduce the mass deposition of tracer gas onto the cylinder surface by one to three orders of magnitude, whereas heat transfer is only decreased by tens of percents. The hydraulic resistance of a more dense carbon filter with an open area fraction as low as 0.2 was found to be still small compared to that of commonly used textiles, thus having little negative impact on the thermal comfort compared to a single layer of textile. The chemical protection, however, was improved by two to five orders of magnitude. These examples clearly illustrate that the combination of two relatively high permeability textile layers in combination with a single high porosity layer of active carbon filter particles enables highly effective CBRN protection together with high thermal comfort. The model presented in this chapter may be used to optimize such garments with respect to the hydraulic resistances of the textiles layers and the porosity and particles sizes of the carbon filter.

This thesis resulted in: (i) modeling rules for the actual geometrical structure of active and passive layers in CBRN protective clothing, (ii) as well as asymptotic scaling rules for the behavior of layers of active particles at small and large Reyn-olds numbers, and (iii) a closed-formed analytical model able to predict protection factor and pressure drop coefficient in CBRN protective clothing in cross-flow con-figurations.

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Samenvatting

De noodzaak tot het uitvoeren van taken in gebieden die besmet zijndoor giftige gassen heeft geleid tot de ontwikkeling van speciale beschermendekleding voor militairen.CBRN (Chemische, Biologische, Radiologische, Nucleaire) beschermendekled-ingstukken zijn een soort beschermende kleding die speciaal ontworpen zijnom bescherming te bieden tegen direct en indirect contact met radiologische,biologische, nucleaire en chemische stoffen in de vorm van giftige gassen engiftige dampen. In het algemeen zijn deze kledingstukken ontworpen voor eenlange gebruiksperiode. Tegenwoordig bestaat CBRN beschermende kleding uit eenenkele laag van actief koolstofmateriaal (bijvoorbeeld koolstofdeeltjes en/ofkoolstofvezels van ≈ 500 µm diameter), ingesloten tussen tweetextiellagen. Als ze aan besmette luchtstromen blootgesteld zijn, worden degiftige gassen die door de inkomende lucht getrans-porteerd zijn, door hetactieve koolstof materiaal geabsorbeerd. De resulterende schone lucht is vrij omdoor de beschermende kleding te stromen, waardoor ventil-atie en thermischcomfort voor de drager gegarandeerd zijn. Zelfs in de eerste uren van blootstelling (d.w.z. zolang het actievekoolstofmateriaal nog niet verzadigd is en dus nog actief is), kunnen kleinehoeveelheden van giftige gassen door het actieve materiaal stromen zondergeabsorbeerd te worden. Dit fenomeen is bekend als initial breakthroughen het wordt voornamelijk veroorzaakt door de geringe dikte en de hogeporositeit van de filterlaag. initial breakthrough wordt ookveroorz-aakt door “lekkages” bij de uiteinden van het kledingstuk, bijvoorbeeldbij nek, polsen en enkels. Hieruit blijkt dat een perfecte isolatie van deomringende omgev-ing lastig te bereiken is. Na dit eerste stadium wordt de actieve kool verzadigd door de giftige gassen. Deabsorberende eigenschappen van het koolstofmateriaal nemen dan met de tijddrastisch af. Uiteindelijk resulteert dit in een totaal verlies van defiltercapaciteiten van de kleding. Uiteraard is het gewenst dat dit tweedes-tadium zo laat mogelijk in werking treedt. Verder is de filterende werking vande kleding in dit tweede stadium van weinig interesse, omdat de kleding in ditstadium toch niet meer bruikbaar is. Van primair belang bij het ontwerp van CBRN

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bes-chermende kleding is dus hetverminderen van de hoeveelheid schadelijke gassen die de huid van de dragerkunnen bereiken tijdens initial breakthrough. Naast het verminderen vanlekkages, kan de toepassing van koolstoffiltermaterialen met een hogerepakkingdichtheid, ingesloten tussen textiellagen met lagere permeabiliteit, totdit gewenste effect leiden. Echter, de door de drager ervaren warmtestress zal hoger worden vanwege de resulterende lagere luchtpermeabiliteit van dekleding. Zulke tegenstrijdige eisen maken het ontwerp en de ontwikkeling vanCBRN bes-chermende kleding tot een ingewikkeld optimalisatieprobleem.

Daar waar experimenteel onderzoek aan CBRN beschermende kleding zeertijdrovend is en kostbare experimentele opstellingen vereist, kunnenComputational Fluid Dy-namics (CFD) simulaties een krachtig additioneelonderzoekhulpmiddel zijn. In dit proefschrift gebruiken we CFD modellering bijde bestudering en optimalisatie van de luchtstroming en het warmte- enmassatransport in CBRN beschermende kled-ing. Daarbij gaat onze bijzondereaandacht uit naar de invloed van de geometrie van de koolstoffilterlaag entextiellagen op de intial breakthrough van schadelijke gassen en op deventilatieëigenschappen van de kleding. Daartoe zijn meso-scale (op deschaal van een ledemaat) en micro-scale (op de schaal van enkelekoolstof-deeltjes) CDF simulaties uitgevoerd.

Het eerste onderdeel van het beschreven onderzoek betreftmicro-scale simulaties, waarin het actieve koolstoffiltermateriaal vanCBRN beschermende kleding is ge-modelleerd als een enkele laag parallelle,cilindrische vezels of bolvormige deeltjes, geplaatst in een regelmatig ofonregelmatig patroon in een vlak loodrecht op de stromingsrichting. Wijrapporteren de massaoverdracht door een dergelijk filterlaag als een functie vande open frontale oppervlaktefractie en de uniformiteit van de filterlaag, voorReynoldsgetallen (gebaseerd op de deeltjesdiameter en de vrije lucht-snelheid) tussen 0.01 en 600, en Schmidtgetallen tussen 0.7 en 10. werd De CFD simulaties lieten zien dat voor zulke configuraties twee kritischeReynoldsgetallen ,

Re1en Re2, bepaald kunnen worden. VoorReynoldsgetallen die veel kleiner zijn dan

Re1wordt het inkomendeschadelijke gas volledig door diffusie naar het

koolstoffil-termateriaalgetransporteerd en is de massaoverdracht onafhankelijk van de afstand tussen dedeeltjes. De filterende werking van de kleding is in dit regime daarom even goedvoor equidistant en niet-equidistant verdeelde filterdeeltjes. Voor Reynoldsget-allen die veel groter zijn dan Re2vormen zich dunne convectievegrenslagen rond

de koolstofdeeltjes. Deze grenslagen zijn heel dun vergelekenmet de afstand tussen de deeltjes, zodat de massaoverdracht weer onafhankelijkis van de (regelmatigheid van de) onderlinge afstand tussen de deeltjes. Voor Reynoldsgetallen tussen Re1

en Re2is er een sterke interactie tussen de grenslagen rond de koolstofdeeltjes.

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deelde filterdeeltjes, invergelijking met equidistant verdeelde deeltjes. Op basis van elementairemassaoverdrachtsbeschouwingen , gecombineerd met de resultaten van onze CFDsimulaties, hebben wij analytische uitdrukkingen voorgesteld voor de bepaling van Re1en Re2als functie van het Schmidtgetal en de open frontale

op-pervlaktefractie. Bovendien hebben wij analytische correlaties voorgesteldvoor de gemiddelde massaoverdracht in equidistante filters. Deze nieuwecorrelaties vullen een hiaat in de literatuur: terwijl er veel data encorrelaties zijn gepubliceerd voor massaoverdracht naar vrijstaande bollen encilinders, naar 1-dimensionele arrays van bollen of cilinders in destromingsrichting, en naar 3-dimensionele arrays van bollen of cilinders, zijner tot nu toe geen data gepubliceerd voor massaoverdracht naar 2-dimensionelearrays van bollen of cilinders, geplaatst in een vlak loodrecht op destromingsrichting.

Het tweede deel van ons werk betreft de analyse van de invloed van detwee tex-tiellagen op de prestaties van de actieve koolstoffilterlaag. Dit isgedaan door de kleding te modelleren als een drielaagssysteem, met enkele lagenvan parallelle of onderling loodrecht geweven cilindrische vezelbundels, stroomopwaarts en stroomafwaarts van de koolstoffilterlaag. Wij hebbenverschillende positioneringen van de koolstoffilterdeeltjes ten opzichte van devezelbundels bestudeerd, waarbij de koolstofdeeltjes recht achter devezelbundels, dan wel recht achter de poriën tussen de vezelbundels geplaatstwerden. We hebben ook de afstand tussen de actieve koolstoflaag en de passievetextiellagen gevarieerd. . Hierbij is het Reynolds-getal, gebaseerd op de deeltjesdiameter en de vrije luchtsnelheid, gevarieerd van 0.1 tot 100, het Schmidtgetal van 0.7 tot 10, en de open frontale oppervlaktefractie van detextiellagen en de filterlaag van 0.2 tot 0.6. . Voor een constanteluchtsnel-heid door de drielaagskleding was de hoeveelconstanteluchtsnel-heid schadelijke gassendie door de koolstofdeeltjes wordt geabsorbeerd gelijk aan die voor dezelfdefilterlaag zonder de twee textiellagen. De drukval over het drielaagsbeschermend materiaal was echter aanzienlijk hoger voor een enkele filterlaagmet dezelfde open frontale op-pervlaktefractie. Deze resultaten suggereren dat,bij het modelleren van CBRN beschermende kleding, de precieze geometrischestructuur van de binnenste en buitenste textiellaag genegeerd kan worden, omdatdeze lagen geen invloed hebben op de absorberende eigenschappen van de actievekoolstoflaag. De extra drukval, veroorzaakt door de textiellagen, moet echterwel in rekening worden gehouden. Dit kan op twee manier gedaan worden:(i) door de modellering van de textiellagen als homogene poreuze lagenvan gegeven permeabiliteit, of (ii) door de modellering van alleen defilterlaag, gebruikmakend van lagere luchtsnelheden.

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textiel-lagen geen invloed hebben op de absorberende eigenschappen debeschermende kleding, hebben wij de resultaten van onze micro-scalesimulaties gebruikt om een analytisch model voor te stellen dat de beschermingsfactor en de drukval-coëfficiënt kan voorspellen voor enkelefilterlagen van actieve koolstofdeeltjes in loodrechte stroming. Voorspellingenvan dit model stemden uitstekend overeen met experimentele resultaten en CFDsimulaties. Een parametervariatiestudie met dit model liet zien dat voor eengegeven beschermingsfactor de kleinste drukval wordt gevonden in lagen met eenhoge porositeit en een kleine deeltjesdiameter. Evenzo vinden we dat, voor eengegeven maximale drukval, de beste bescherming wordt verkregen bij een laagmet een hoge porositeit en kleine deeltjes.

In het laatste deel van ons werk hebben we met behulp vanmeso-scale CFD sim-ulaties onderzoek gedaan naar de beschermendeeigenschappen van CBRN bes-chermende kleding in een klassieke testopstelling.Deze bestaat uit een massieve cilinder – die een een menselijk ledemaatnabootst – in loodrechte stroming, op een vaste kleine afstand omgeven door eendrielaags beschermend materiaal. In onze simulaties hebben we de twee passievetextiellagen gemodelleerd als homogene poreuze lagen, terwijl de actievefilterlaag werd gemodelleerd als een enkele laag van absorberende deeltjes,ingebed tussen de twee textiellagen. Voor realistische condities zoals gebruikt in gepubliceerde experimentele tests van beschermende kleding (Reynoldsgetal 12, 000− 34, 000, gebaseerd op de diameter van de cilinder en vrijeluchtstromingssnelheid, Schmidtgetal 3, en realistische waarden voor de-hydraulische weerstand van de textiellagen) leidt de toevoeging van een enkele laag van koolstofdeeltjes met een open frontale oppervlaktefractie van 0.6 toteen vermindering van de massadepositie van het schadelijke gas op hetcilinderopper-vlak met circa één tot drie ordes van grootte, terwijl dewarmteoverdracht slechts met enkele tientallen procenten afneemt. Zelfs de hydraulische weerstand van een nog veel dichter koolstoffilter, met een open frontale oppervlaktefractie van slechts 0.2, bleek laag te zijn invergelijking met die van de meest voorkomende tex-tielmaterialen. Ook detoevoeging van een zodanig dichtgepakte koolstoffilterlaag heeft dus een geringnegatief effect op het thermisch comfort, terwijl de chemische beschermingverbeterde met twee tot vijf ordes van grootte. Deze voorbeelden laten zien datde combinatie van twee textiellagen met redelijk hoge permeabiliteit en eenenkele actieve koolstofdeeltjeslaag met hoge permeabiliteit leidt tot zeer goede CBRN bescherming en tegelijkertijd een hoog thermisch comfort. Het door onsvoorgetelde model kan gebruikt worden om de hydraulische weerstanden van detextiellagen en de porositeit en deeltjesgrootte van het koolstoffiltermateriaal in zulke kleding te optimaliseren met betrekking tot debeschermende werking het en thermisch comfort van de kleding.

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tuur van de actieve en passieve lagen in CBRNbeschermende kleding, (ii) asymptot-ische schalingsregels voor hetmassatransport in 2-dimensionale lagen van actieve kooldeeltjes bij relatieflage Reynoldsgetallen, en (iii) een analytisch model om debeschermingsfactor en de drukvalcoëfficiënt te voorspellen voor CBRNbescher-mende kleding in loodrechte stroming.

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I

NTRODUCTION

Chemical, Biological, Radiological and Nuclear (CBRN) protective clothing allows soldiers to perform tasks whenever hazardous gases represent a serious threat for human life. This type of clothing must offer high levels of protection and a proper ventilation which guarantees comfortable wearing conditions for the wearer at the same time. Understanding where the limits between these two highly demanding requisites are can improve the design and the development of CBRN protective garments. Whereas experimental studies of CBRN protective clothing are time consuming, and require expensive experimental setups, Computational Fluid Dynamics (CFD) simulations can be a powerful tool of investigation. The aim of this thesis is to understand the physics of the flow, heat transfer and mass transfer through CBRN protective clothing in order to predict and optimize the protection level and the ventilation quality of such garments.

1.1 Design, modeling and testing of CBRN protective

clothing

Among the several types of CBRN protective clothing available on the market, a three layer protection garment is widely used because of its favorable properties and ease of manufacturing[1]. In this particular configuration, a single layer of activated carbon spheres or fibres (typical diameter 500µm) is embedded between two layers of woven textile, i.e. the inner and the outer textile layer, as seen in

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Figure 1.1: CBRN protective clothing specimen (right) and schematics of its structure

(left).

Fig. 1.1. When such protective garments are exposed to contaminated air, the hazardous gases transported with the flow are adsorbed onto the single layer of ac-tivated carbon material, whilst the resulting cleaned air is free to stream through the protective clothing assuring proper ventilation for the wearer. The main purpose of the outer textile layer is that of decreasing the velocity of the incoming contam-inated air flow. The inner textile layer prevents contacts between the skin of the wearer and the carbon material, and redistributes the air flow inside the garment. In the first hours of exposure, i.e. before the active carbon becomes saturated, small amounts of hazardous gases can pass the adsorbing layer without getting adsorbed. In this period the concentration Cou t of hazardous gases that reaches the skin of the wearer is typically a low fraction of the concentration C∞which is transported

in the incoming air flow. This phenomenon is known as "initial breakthrough" and is mainly due to the high porosity of the carbon material layer.

At later stages, the carbon particles become saturated. Other than the requirement that this should happen as late as possible, this stage is of little relevance since the protective garment should not be worn anymore. Figure 1.2 illustrates the sat-uration process occurring in CBRN protective clothing in terms of dimensionless

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Figure 1.2: Illustrative example of saturation breakthrough curve for species

concen-tration in CBRN protective clothing against the exposition time[2].

species concentration Cou t/C∞and time of exposure. Increasing the packing

dens-ity of the carbon material layer might reduce the amount of initial breakthroughs. However, this might result in undesirable higher heat stresses on the wearer. For these reasons designing and developing CBRN protective clothing able to match the contradictory combination of high levels of protection and comfortable wear-ing conditions is a complex problem.

Experimental testing of protective clothing can take place at a wide range of scales, depending on the nature of the sought information. In the previous century experi-ments at meso and macro-scale level were the main tool of investigation.

At macro-scale a full clothed and moving manikin or human is employed to collect general data of comfort and protection offered under several environmental and operating conditions[3–5]. Such tests often involve complex configurations and require expensive experimental apparatus.

In the late ’90s , simplified and cheaper setups have been introduced, moving the focus of investigation from the macro-scale to the meso-scale. A widely used setup

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is a solid cylinder in cross-flow - representing a human limb - covered by protective material[6], where time and space averaged characteristics of the clothing such as hydraulic permeability, chemical protection and aerosol deposition, can be measured[7]. Analytical models based on this configuration have been developed [8, 9]. In these models the actual geometrical structure of the protective material is often replaced by ensemble properties, and the temporal and spatial dynamics of the airflow underneath the protective clothing are often neglected.

Information on the influence of the actual structure of the protective material on the initial breakthrough concentrations and ventilation conditions, can be ob-tained by moving the level of investigation to the micro-scale. Here time and spatial characteristics of the garment can be analyzed. Experiments on micro-structures of adsorbing spheres and textile fabrics are known to be extremely difficult to perform and expensive to realize[10, 11]. Therefore CFD simulations are believed to be a valid alternative tool of investigation. In the last two decades, due to improved computational tools and increased computational power, numerical simulations have been largely contributing to the research on CBRN protective clothing[12]. In the Transport Phenomena Group at the Chemical Engineer Department of Delft University of Technology, a research program on CBRN protective clothing in-volving numerical simulations was started at end of 2000 under the supervision of Prof. Kleijn, in close collaboration with the CBRN Protection Department of the Netherlands Organization for Applied Scientific Research TNO. Previous to the pro-ject described in this thesis, Sobera worked on the development of a computational model for CBRN protective clothing, focussing on flow and heat transfer in passive garments at micro and meso-scale[13]. In the present work we focused on flow, heat transfer and mass transfer in active (adsorptive) garments at the micro and meso-scale.

1.2 Motivation and aim

Initial breakthrough can drastically reduce the protection level offered by CBRN protective clothing in its first hours of use. The geometrical structure of the protect-ive material, e.g. carbon particle diameter, porosity of the adsorbing layer, position of the carbon particles etc., is one of the factors which largely influences this phe-nomenon. The aim of the project of this thesis is to explore the exact relationship between initial breakthrough concentrations, ventilation level and actual geometry

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of the protective material. For this purpose, micro-scale and meso-scale approaches are used together with CFD numerical simulations. These are used to construct an analytical model, capable of predicting protection and ventilation level in CBRN garments.

In chapters 2-4, we will consider the properties of protective garments under forced flow conditions, i.e. air with a prescribed velocity u∞and a given (small) trace

gas concentration C∞is forced to flow perpendicularly through a layer of

protect-ive garment material. After passing the layer of protectprotect-ive garment, the trace gas concentration will be Cou t , whereas the air velocity is still approximately equal to u∞. The garment properties of primary interest are so called protection factor

P F= C∞/Cou t and the pressure drop∆P over the garment.

Assuming that, before saturation, the adsorption of trace gas on the active carbon material is mass transfer limited with a mass transfer rate k, and that the surface area of carbon material per unit area of garment material equalχ, a simple steady state mass balance over the garment teaches that

u∞(C∞− Cou t) = k χC∞ (1.1)

or

P F = u∞

(u∞− k χ)

(1.2) which can be easily calculated once the mass transfer coefficient k to the carbon particles is known. The mass transfer coefficient k will depend of the air velocity

u_∞, the kinematic viscosityν of the air, the diffusivity D of the tracer gas in the air, a typical size L of the carbon particles, the porosityε of the carbon layer and the geometric configuration of the carbon and textile layers. Dimensional analysis now shows that

Sh= f (Re,Sc,ε, g eom e t r y ) (1.3) with Sh= k L/D the Sherwood number, Re = u∞L/ν, and Sc = ν/D the Schmidt

number. Therefore, in chapter 2 we will report Sherwood numbers as a function of free stream Reynolds number, Schmidt number, porosity of the carbon layer and the geometric configuration of the carbon layer.

The pressure drop∆P over the garment will be studied in terms of the dimension-less pressure drop coefficient Kw= ∆P/(0.5ρu2_∞), in which the pressure drop is

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scaled with the inertial pressure scale 0.5ρu_∞, and in terms of the Darcy num-ber Da= [∆P/(µu∞/d )]−1, in which the pressure drop is scaled with the viscous

pressure scaleµu∞/d .

1.3 Thesis outline

This thesis studies the influence of the geometrical structure of CBRN protective clothing on its protection and ventilation performances.The work of this project will be presented as follows:

• Chapter 2 describes the dependence of the mass transfer to two-dimensional (single layer) arrays of activate carbon fibers and spheres on the size and relative position of the particles inside the arrays, and on the free-stream conditions.

• Chapter 3 analyzes the influence of the textile material layers positioned in front and behind the adsorbing layer of carbon material on the mass transfer coefficient of the latter.

• In Chapter 4 an analytical model is proposed to predict and optimize protec-tion and ventilaprotec-tion levels in CBRN protective clothing.

• Chapter 5 illustrates a practical application of CBRN protective clothing. Here mass and heat transfer to a solid heated cylinder sheathed by a three-layer protective material is analyzed.

• In chapter 6 the most revelant conclusions from the project of this thesis are summarized.

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L

AMINAR FORCED CONVECTION MASS

TRANSFER TO ORDERED AND

DISORDERED SINGLE LAYER ARRAYS OF

CYLINDRICAL FIBERS AND SPHERES

1_{In this chapter we study laminar forced convection mass transfer to single layer}

arrays of equidistantly and non-equidistantly spaced parallel cylindrical fibers and spheres perpendicular to the flow direction. This serves as a model for the active carbon filter in CBRN protective garments. We report average Sherwood numbers as a function of the filter geometry and flow conditions, for open frontal area frac-tions between 0.04 and 0.95, Schmidt numbers between 0.7 and 10, and Reynolds numbers between 0.001 and 600. For equidistantly spaced cylindrical fibers and spheres we propose a general analytical expression for the average Sherwood num-ber as a function of the Reynolds numnum-ber, Schmidt numnum-ber and the open frontal area fraction, as well as asymptotic scaling rules for small and large Reynolds. For all studied Schmidt numbers, equidistantly space cylindrical fibers and arrays of

1_{This chapter is based on: D. Ambesi and C.R. Kleijn, Laminar forced convection heat transfer}

to ordered and disordered single rows of cylinders,International Journal of Heat and Mass Transfer, 55 (21-22), 2012, pp. 6170-6180; and D. Ambesi and C.R. Kleijn, Laminar-forced convection mass transfer to ordered and disordered single layer arrays of spheres, AIChE Journal, (published online) doi: 10.1002/aic.13904.

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spheres exhibit decreasing average Sherwood numbers for decreasing open frontal area fractions at low Reynolds numbers. At high Reynolds numbers, independently of the values of the open frontal area fraction, the Sherwood number approaches that of a single cylinder and that of a single sphere in cross-flow, respectively. For equal open frontal area fractions, the Sherwood number in non-equidistant rows of cylindrical fibers and arrays of spheres is lower than that of equidistant structures for intermediate Reynolds numbers. For very low and high Reynolds numbers, non-uniformity does not influence mass transfer.

2.1 Introduction

Despite their practical relevance for applications such as low pressure drop activ-ated carbon filters[14] and Chemical-Biological-Radiological-Nuclear protective clothing[2],where single layers of loosely packed carbon spheres and fibers are used to filter polluted air flows[15, 9], convective mass transfer to fibers and spheres arranged in a single 2-dimensional layer perpendicular to the flow direction have not yet been widely studied.

Due to the analogies between heat and mass transfer[16], it is widely accepted to relate mass transfer studies the heat transfer studies and vice versa. For this reason, and because of the limited amount of literature on mass transfer to single layer arrays of cylinders and spheres, our literature review will include studies for both mass and heat transfer problems.

Many studies have been devoted to heat transfer to or from periodic tube banks in the low and high Reynolds number regimes.

The effects of cylinder spacing, alignment and positioning on the average and local heat transfer have been the main objectives of these studies.

For cylinder based Reynolds numbers in the 103_-105_{range, ˘}_Zukauskas_{[17] reported}

how an increase in the turbulence intensity around the cylinders, leading to higher mean Nusselt numbers, can be obtained by decreasing the space between the cylinders along the streamwise direction.

Khan et al.[18] provided analytical expressions for heat transfer as a function of the longitudinal and transversal cylinder spacing in periodic banks of cylinders, for

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Reynolds numbers between 103_{and 10}5_{, and Prandtl numbers}_{≥ 0.7. It was found}

that higher heat transfer rates can be achieved when compact and staggeredly arranged tube banks are employed.

Seong-Yeon et al.[19] studied heat transfer in a staggered tube bank for air flow in the Reynolds number range from 7, 700 to 30, 300. The local heat transfer near the rear stagnation point of the first tube row was found to increase with decreasing tube spacing due to the appearance of strong vortices.

Martin et al.[20] studied air flow through sparse square and triangular arrays of cylinders with open volume fractions ranging from 0.80 to 0.99 and cylinder based Reynolds numbers from 3 to 160. Their numerical investigation showed that the Nusselt number increases for smaller cylinder spacings.

Wung et al.[21] numerically studied in-line and staggered arrays of cylinders with a longitudinal pitch two times larger than the transverse pitch, for Reynolds numbers between 40 and 800, and Prandtl numbers between 0.1 and 10. Increased Prandtl numbers led to an increase in the averaged Nusselt numbers. Staggered arrange-ments exhibited a relocation of the maximum local heat transfer rate, and higher average Nusselt numbers.

Ishigai et al.[22] visualized the flow around cylindrical tubes in tube banks in the Reynolds number range from 1, 400 to 13, 500 by using the Schlieren method. At small in-line pitches, the shear layer separated from the upstream cylinder and reattached onto the downstream cylinder without any vortex formation. In this flow situation stagnation regions between cylinders were formed, resulting in lower heat transfer rates.

For air flow around four equidistant cylinders in tandem, Shinya et al.[23] found the existence of a critical Reynolds number for which the heat transfer behaviour drastically changes. The vortex shedding behind the first cylinders determines the heat transfer to the downstream cylinders. In the absence of vortex shedding, a stagnant flow characterizes the region between the first and second row of cylin-ders, resulting in low heat transfer rates. In the Reynolds number range from 104_to

5· 104_{heat transfer correlated with the in-line pitch.}

Fewer studies have been devoted to single rows of equidistantly spaced cylinders. For cylinder based Reynolds numbers between 1, 000 and 15, 000, Ichimiya and coworkers[24] experimentally found that narrowing the inter-cylinder distance results in an increase of the local Nusselt number either upstream or downstream from the cylinder array. This was found to be due to the interaction of the wakes, that either contracted or extended behind cylinders.

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Yamamoto et al. [25] numerically, and Hattori et al. [26] experimentally, studied heat transfer from a water flow to single row of heated cylinders in the Reynolds number range from 75 to 500. For large spacings, vortex shedding was found to be similar to that around a single cylinder, whereas for small spacings vortices became more complicated and strongly interacting. The average Nusselt number was found to correlate with the local Reynolds number, based on the cylinder dia-meter and on the mean velocity at the minimum cross section of the flow channel between cylinders. For constant local Reynolds number, heat transfer was found to be independent of the cylinder spacing.

A vast amount of studies on heat and mass transfer in 3-dimensional packed beds of spheres[27–29, 11, 30–33] and on 1-dimensionallinear arrays of spheres aligned with the flow direction[34–42] can be found in literature.

Studies on 1-dimensional linear arrays of spheres aligned with the flow direction [34–42] ,cover a range of free-stream particle based Reynolds numbers from 1−1700, and Schmidt (or Prandtl) numbers from 0.7 to 70. The number of particles in the linear array varied from 2 to 8, and theinter-particle distance was varied from 1− 10 particle diameters. In most studies all particles were of equal size. Wang et al.[40] and Tsai et. al[38] additionally studied the influence of differences inparticle sizes. General conclusions from the mentioned studies are:

(i) The average Nusselt/Sherwood number increases with increasing

Reynoldsnum-ber;

(ii) The average Nusselt/Sherwood number increases with increasinginter-particle

distance;

(iii) At Peclet numbers below 50, the average Nusselt/Sherwood is smaller than that

for a single sphere;

(iv) The Nusselt/Sherwood for the leading sphere may exceed that of a single sphere.

Of the vast amount of studies on heat and mass transfer in 3-dimensional packed beds of spheres[27–29, 11, 30–33], relatively few studies have been devoted to the effect of the precise particle packing structure.

In their classic experimental study, Thoenes and Kramers[11]studied mass transfer to a single active sphere placed in various regularpacking arrangements of similar, but inactive spheres. For hydraulic diameter based Reynolds number between 1

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and 104_{and different gases and liquids as working fluids, it was found that the}

Sherwood number increases with increasing distancebetween active and inert spheres.

For a fixed bed of particles in a cylindrical tube and particle Reynolds number-sbetween 100 and 700, Dixon et al. [30] showed that the ratio betweenthe tube diameter and the particle diameter has a significant influence on heattransfer. In a computational study of the fluid flow through packed beds of spheres insimple cubic, rhombohedral and face or body-centred structures at particle based Reyn-olds numbers between 12 and 2000, Gunjal et al.[31] found thatthe local Nusselt number increases with increasing particle Reynolds numbers and increasing bed voidage.

Heat transfer in uniformly and non-uniformly packed beds of ellipsoidal and spher-ical particles was investigated by Yang et al.[32] for free stream particle based Reynolds numbers from1 to 5000 and a Prandtl number of 0.7. The average Nusselt number wasfound to be dependent on the particle shape and packing structure. For a particular particle shape, the overall heat transfer was found to be maximum for a simple cubic packing. For a fixed packing structure, longelliptic particles gave the highest heat transfer. Uniform packings were found to have higher heat transfer than non-uniform packings with the same particleshape and packing density. Whereas most work on packed bed has focused on average Sherwood numbers, Guo et al.[33]in their numerical study focus on local variations in mass transfer rates. The authorsconcluded that there is a clear relationship between local pore structure, streamlinepatterns and mass transfer rates.

From the above it is clear that information on convective mass and heat transfer to single rows of parallel cylinders (fibers) and2-dimensional arrays of spheres, perpendicular to the flow direction, for the low (<100) Reynolds number regime is still lacking. Also, in all previous studies, only equidistant arrays of cylinders and spheres have been studied. Particularly for sub-millimeter fibers and spheres, a perfect equidistant arrangement is hard to realize in practice.

We performed numerical simulations of the steady-state and oscillating laminar flow and mass transfer around uniformly spaced single rows of cylindrical fibers in cross-flow with an open frontal area fraction betweenε = 0.04 and ε = 0.95, and to 2-dimensional arrays of spheres in cross flow with an open frontal fraction between

ε = 0.25 and 0.95. We also studied non-uniformly spaced 2-dimensional arrays of

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The non-uniformly spaced arrays of cylindrical fibers and spheres were character-ized by the relative standard deviation in the inter-particle distance, which varied fromα = 0.5 to 1.5. The free-stream Reynolds numbers ρu∞d/µ, based on the

fiber and sphere constant diameter d and the free stream velocity u∞, was varied

between 0.001 and 600, and the fluid Schmidt number between Sc= 0.7 and 10.

2.2 Numerical approach

2.2.1 Studied configurations and boundary conditions

Figure 2.1 shows the computational domain for all the studied configurations,

viz.(i) equidistantly spaced cylindrical fibers arranged in a single row,

(ii)non-equidistantly spaced cylindrical fibers arranged in a single row, (iii)(ii)non-equidistantly spaced spheres arranged in a 2-dimensional square pattern, (iv) equidistantly spaced spheresarranged in a 2-dimensional hexagonal pattern, (v) non-equidistantly spaced spheres arranged in a 2-dimensional plane.In all cases, the particles are arranged in a plane perpendicular to the flow direction.

The cylindrical fibers and spheres are solid and non-permeable and all have the same, constant diameterd. The total length of the computational domain along the streamwise directionx is L1+ 41d , out of which L1upstream, and 40ddownstream

from the layer of spheres and cylindrical fibers. The upstream length L1was chosen

long enough to have a purely convective mass inflow through the inlet of the do-main, i.e. L1> 10D/u∞where D is the mass diffusivity and u∞the free stream

velocity.In the inlet we imposed a constant tracer species mass fraction C∞<< 1,

and a uniform inlet velocityu∞. The outlet plane was considered to be sufficiently

far downstreamfrom the layer of spheres and cylindrical fibers, such that a constant pressure, zero axial concentration gradientand uniform streamwise velocity could be assumed constant across the outlet.

On the sphere and fiber walls the tracer species is assumed to be consumed at infinite rate,so a zero concentration Cw= 0 and no-slip conditions for the velocity were imposed.The bounding sides of the computational domain, aligned with the streamwise direction x, were specified as symmetry boundaries in the case of

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equidistantly spaced spheres and cylindrical fibers, or as periodic boundaries for layers of non-equidistantly spaced spheres and cylindrical fibers.

Figure 2.1: Computational domain: for arrays of spheres (a);for arrays of cylindrical

fibers (b).

The fluid properties (densityρ, dynamic viscosity µ and mass diffusivity D)were assumed to be constant and buoyancy effects were neglected. The free stream Reyn-olds number was defined as Re∞= ρu∞d/µ, the Schmidt number as Sc = ν/(ρD).

We also define a Reynolds numberReL= ρ(u∞/ε)d /µ = Re∞/ε based on the

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2.2.2 Single layer arrays of cylinders

For arrays of cylindrical fibers the height H of the domain in the cross-flow direction

z corresponds to the set value of the open frontal area fractionε as ε =H− nd H = 1 H n X i=1 δi (2.1)

where n represents the total number of cylindrical fibers, andδi identifies the inter-fiber distances as shown in Fig.2.1. Whenδ1= δ2= ...δn, the cylindrical fibers are uniformly spaced,and symmetry properties can be applied in order to reduce the computational domain to one fiber with periodic boundary conditionsat z= 0 and

z= H.

Redistributing the cylindrical fibers for a given value ofε, such that δ16= δ26= . . . δn, results in a loss of symmetry, as seen in Fig. 2.1. We now study configurations with 4, 8 or 16 parallel cylindrical fibers, non-equidistantly distributed over the height H of the domain, and apply periodic boundary conditions at z= 0 and z = H. Sobera [43] introduced a dimensionless parameter α which gives a measure for the level of disorder in the wire spacing in such a configuration:

α =σ

δ (2.2)

whereσ and δ are the standard deviation and the mean value, respectively, of the inter-fiber distancesδi. The maximum obtainable value ofα for a periodically repeated row of n cylindrical fibers can be expressed in terms of n[43]

αm a x= p

n− 1 (2.3)

Forα = 0, the cylindrical fibers are equidistantly spaced, whilst increasing values ofα result in non-uniformly spaced cylindrical fibers and progressively more dis-ordered distributions. For a given value of the open frontal area fractionε = δ · n/H and the disorder measureα, an infinite number of different configurations can be generated that obey the following equations forδ and σ:

δ1+ δ2+ ... + δn−2+ δn−1+ δn= δn (2.4) δ2 1+ δ 2 2+ ... + δ 2 n−2+ δ2n−1+ δ2n= (σ 2_{+ δ}2_)n _(2.5)

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To obtain fiber distributions with a specificε and α, we draw the values of δ1,

δ2. . .δn−2from a normal probability distribution having the desired values ofσ

andδ. Subsequently, the values of δn−1andδnare obtained by solving Eqs.(2.4) and (2.5). Repeating this procedure for different random values ofδ1,δ2. . .δn−2

results in different realizations of the configuration with the sameε and α. All the possible realizations of one configuration can be distinguished from each other by means of higher statistical moments, such as the skewness g1and kurtosis g2.

g1= 1 n n P i=1 (δi− δ)3 σ3/2 (2.6) g2= 1 n n P i=1 (δi− δ)4 σ4 − 3 (2.7)

We generated a total number of 63 different configurations consisting of 4, 8 or 16 non-uniformly distributed cylindrical fibers, with non-uniformity parameters

α = 0.5, 1 and 1.5, and open frontal area fractions ε = 0.2, 0.4 and 0.8. As an example,

the 27 configurations forε = 0.8 are reported in Table 2.1.

For a fixed value ofε and α, the configurations differ in terms of the number of cylindrical fibers n in the periodic row, as well as the values of the higher statistical moments, such as g1and g2. As reported in[43], at given flow conditions and ε,

the hydraulic resistance of the row of cylindrical fibers is lower for higher values ofα.

2.2.3 Single layer arrays of spheres

For layers of equisized spheres arranged in a square or hexagonal pattern,as well as disordered layers of n= n2_Lequisized spheres, non-equidistantly distributed in a

single square layer of width and height H , the prescribed open frontal area fraction

ε follows from ε = 1 − nπ β  d H 2 (2.8) where we used n= 1 for ordered layers, and n = n2_L= 16 for the disordered lay-ers.For the (ordered and disordered) square layers,β = 4, while for the hexagonal

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Table 2.1: 27 studied row configurations for arrays of disorderedcylindrical fibers for ε = 0.8. n α = 0.5 α = 1 α = 1.5 g1 g2 g1 g2 g1 g2 −0.5890 −0.9327 0.9034 −0.9030 1.1500 −0.6702 4 0.1050 −1.0012 0.5064 −1.3433 1.1367 −0.6814 −0.1287 −1.5302 0.9943 −0.7721 1.1421 −.06767 0.0403 −0.1319 1.3304 0.6943 2.0419 2.5564 8 −0.4618 −0.8577 1.7545 1.8471 1.8456 1.8731 −0.5878 −1.1565 0.5337 1.4970 1.8932 2.0800 1.2971 1.6487 1.6478 2.3405 2.4951 5.5624 16 0.6676 −0.4140 2.1279 4.6268 2.8930 7.7442 0.7595 −0.0065 1.5091 1.2858 3.0905 8.7508 layer,β = 2p3.

To generate patterns with a controlled level of disorder, a procedure similar to that described for disorder arrays of cylindrical fibers was applied. With help of Fig. 2.2 this can be summarized as follows: first, the spheres are placed on a square grid of ny = nLcolumns by nz = nL rows. Inthis configuration the inter-sphere distances are constant and equal toδy = δz= δ = H/nL−d .Then, for each column, we redistribute the spheres such that the standardvariation in the inter-sphere distances equalsσ = αδ. As done for randomly distributed cylindrical fibers, we draw

the values ofδ1,z,δ2,z. . .δnL−2,zfrom a normal probability distribution with the

de-sired values ofσ and δ. Subsequently, the values of δnL−1,z andδnL,z are obtained

by solving Eqs.(2.4) and(2.5). Repeating this procedure for different random values ofδ1,z,δ2,z. . .δnL−2,z results indifferent realizations of the configuration with the

sameδand α. Again, all the possible realizations of one configuration can be distin-guished from each other by means of higher statistical moments skewness g1and

kurtosis g2as previously shown for arrays of randomly distributed cylindrical fibers.

After the spheres in each column have been randomly redistributed according to the above procedure, this is applied to redistribute the spheresin each row. We only

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Figure 2.2: Ordered and disorder arrays of n= 16 spheres for ε = 0.8: (a) ordered

(α = 0); (b) one realization for α = 0.5; (c) one realization for α = 1; (d) a second realization forα = 1.

accept those distributions in which no spheres overlap or touch, and all spheres lay within the H× H square. The first is physically impossible in a single layer distri-bution, the second is highly improbable and would create difficulties in creating a numerical mesh. The third restriction imposed on the distributions leads to some disturbance of the pure randomness of the distributions, as it may create larger voids near the edges, especially for largeα. However, the purpose of our study of non-uniform distributions is precisely to show the impact of such large voids. Figure 2.2 shows an ordered layer forε = 0.8 and nL= 4, as well as examples of

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disordered layers withε = 0.8, and α = 0.5 and 1.0, respectively.

2.2.4 Mesh generation

Meshing of the two-dimensional (for the case of cylinders) and three-dimensional (for the case of spheres) computational domain was performed in Gambit[44]. The structured meshes consisted of 20, 000 to 180, 000 grid nodes for uniformly distributed rows of cylindrical fibers, and of 250, 000 to 550, 000 grid nodes for non-uniformly distributed cylindrical fibers. For arrays of spheres the meshes consisted of 220, 000 to 1, 800, 000 hexahedral and tetrahedral gridcells. For all the studied configurations local grid refinement was applied in the regions nearby the surfaces of the particles and in the interstitial spaces between particles.

2.2.5 The solver

The flow was assumed laminar and incompressible, thus the continuity equation is expressed as

∇ · ~u = 0 (2.9)

where~u is the velocity field vector.

Assuming gravity effects negligible and no external body forces, the Navier-Stokes (momentum) equations can be written as

ρ∂ ~u

∂ t + ρ(∇ · ~u ~u ) = −∇P + ∇ · τ (2.10)

where∇P and τ are, respectively, the pressure field gradient and the viscous stress tensor for a Newtonian fluid.

The species transport equation, assuming constant species diffusivity, reads

∂ C

∂ t + ~u · ∇C = D∇2C (2.11)

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Equations (2.9−2.11) were solved in two-dimensional (three-dimensional for ar-rays of spheres),steady-state or transient formulation. The latter was needed for cases with large Reynolds numbers andsmall inter-particle distances, in which the interaction between the particle wakesleads to vortex instability behind the spheres as reported by Kim et al. [45] Hill et al. [46], and behindinfinitely long cylinders (cylindrical fibers) as reported by Slaouti et al.[47], Zdravkovich [48] and Ohya et al. [49].

A second order QUICK scheme[50] was used to discretize the equationsin space, whilst a second order implicit time discretization scheme was used[51].The pres-sure field was obtained by employing the SIMPLE algorithm[52].Convergence limits for the sum of the normalized absolute residuals (i.e. the absolute values of the residuals per grid point, summed over all grid points, and normalized by the value of thatsame summation at the beginning of the iterative solution procedure) for all theequations were set to 10−6_{. For the unsteady simulations, 10}−6_normalized

residuals convergence was assured at each time step. Unsteadysimulations were continued until a time-periodic, pseudo steady-state in thedownstream velocity and concentration profiles was reached.

For a number of representative cases (Re∞ = 0.1, ε = 0.8; Re∞ = 10, ε = 0.4;

Re∞= 100, ε = 0.25) with uniform sphere and fiber distributions, we studied the

dependence of our results on grid refinement, time step size and discretization scheme. For example for arrays of equidistantly distributed spheres doubling the number of grid cells in all coordinate directions (from 400, 000 to 3, 200, 000, from 230, 000 to 1, 800, 000, and from 300, 000 to 2, 312, 000 respectively), halving the time step size (from∆t = 0.3d /u∞to∆t = 0.15d /u∞), doubling the length

of the upstream and downstream domain (from L1 to 2L1and from 40d to 80d ,

respectively),and switching from QUICK to second order upwind schemes led to differences in the computed Sherwood number of less than 10% as shown in Table 2.2 for some of the above configurations.

2.2.6 Sherwood number

For arrays of cylindrical fibers, a steady-state mass balance over the domain sketched in Fig.2.1, assuming constant fluid properties, a purely convective inflow and

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out-Table 2.2: Dependence of Sh on grid refinements and domain length for uniformly

spaced spheres, Sc= 0.7.

ε Re_∞ ∆t Nr. of grid Upstream Downstream Sh

cells domain length domain length

0.25 100 0.3d/u∞ 300, 000 10u∞/D 40d 9.3411 0.25 100 0.15d/u∞ 300, 000 10u∞/D 40d 9.3425 0.25 100 0.3d/u∞ 2, 312, 000 10u∞/D 40d 9.3969 0.4 10 0.3d/u∞ 230, 000 10u∞/D 40d 2.4378 0.4 10 0.3d/u∞ 1, 800, 000 10u∞/D 40d 2.6914 0.8 0.1 0.3d/u∞ 400, 000 10u∞/D 40d 0.0752 0.8 0.1 0.3d/u_∞ 890, 000 20u_∞/D 80d 0.0775

flow, and a constant concentration Cw = 0 at the cylindrical fiber walls, leads to

nπd κC_∞= u_∞H(C_∞− Cou t) (2.12) where C_∞and Cou t are, respectively, the inlet species tracer concentration, and the mass weighted outflow species tracer concentration, n is the number of cylindrical fibers, d the cylindrical fiber diameter,κ the average mass transfer coefficient at the fiber walls, and u_∞the free stream velocity. With Eq.(2.1) this leads to the following relation for the average Sherwood number

Sh=κd D = u∞d πD(1 − ε) 1−Cou t C∞ (2.13) with D is the mass diffusivity of the species tracer into the fluid.

In a similar way, a steady-state mass balance over the domain sketched in Fig.2.1 coupled with Eq. (2.8), leads to the following expression of the Sherwood number for arrays of spheres

Sh=κd D = u∞d 4D(1 − ε) 1−Cou t C_∞ (2.14) In Eqs. (2.13) and (2.14), forε → 1, Cou t will approach C∞and the Sh values are

expected to approach that of a single cylinder or a single sphere. For transient simulations, time averaged Sh numbers were obtained from simulation results

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averaged over a time periodτ corresponding to τ ≈ 50d /u_∞.

2.3 Results and discussion

In the following four subsections, we present results for, respectively,equidistantly spaced parallel cylindrical fibers, equidistantly spaced spheres, non-equidistantly spaced parallel cylindrical fibers,and non-equidistantly spaced spheres, all ar-ranged in a single layerperpendicular to the flow direction. Sherwood numbers will be correlated withthe free-stream and local Reynolds numbers Re∞andReL=

Re_∞/ε and the Schmidt number, for various values of theopen frontal area fraction ε and the non-uniformity parameter α.The Schmidt number is varied from 0.7

to 10, and the free stream Reynolds numberRe∞from 0.001 to 600 for arrays of

cylindrical fibers, and from 0.1 to 100 for arrays of spheres.For equidistant rows of cylindrical fibers, we varied the open frontal area fraction fromε = 0.04 to

ε = 0.95, whilst for hexagonally and squarely arranged equidistant arrays of spheres ε was varied from 0.25 to 0.95. For the non-equidistant arrays of cylindrical fibers

we studied open frontal area fractionsε = 0.2,0.4 and 0.8 and non-uniformity para-metersα = 0.5,1.0 and 1.5. For the non-equidistant arrays of spheres we studied

ε = 0.4 and 0.8 and α = 0.5,1.0 and 1.5.

2.3.1 Equidistant arrays of cylindrical fibers

Figure 2.3 shows the obtained Sherwood number as a function of Re∞and the

open frontal area fractionε for equidistantly spaced cylindrical fibers at Sc = 0.7. In agreement with[20] and [24], Sh increases with decreasing ε for larger values of

Re∞. For lower values of Re∞, however, Sh decreases with decreasingε.

Since the mass transfer to individual cylindrical fibers is determined by local flow conditions near the cylindrical fibers, rather than the upstream free flow conditions, it is more informative to present Sh as a function of the local Reynolds number

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Figure 2.3: Sh number as a function ofε and Re∞for ordered rows of cylindrical

fibers and Sc = 0.7. Also shown is the correlation by McAdams [53] for a single cylinder.

Figures 2.4 and 2.5 show the obtained Sherwood numbers for equidistantly spaced rows of cylindrical fibers as a function of ReL, for different values of the open frontal area fractionε and Schmidt number Sc.

From these figures, three main observations can be made:

(i) Forlow ReL, Sherwood increases with increasing open frontal area fractionε.

(ii) For high ReL, the Sherwood number is close to that of a single cylinder (here evaluated by use of the empirical equation proposed by McAdams[53] Eq.( 2.19)re-placing Re∞by ReL), and independent of the open frontal area fractionε.

(iii) The Reynolds number ReL above which the Sherwood number is independent ofε and close to that of a single cylinder, decreases with increasing Sc and with

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Figure 2.4: Sh number as a function ofε,Sc and ReLfor ordered rows of cylindrical

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Figure 2.5: Sh number as a function ofε,Sc and ReLfor ordered rows of cylindrical

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increasingε.

The above three observations can be understood and more quantitatively analyzed by looking at the concentration distributions and concentration boundary layer formation around the cylindrical fibers, as shown in Figs. 2.6 and 2.7. These figures show contours of the dimensionless concentrationΘ = (C −Cw)/(C∞− Cw), which varies fromΘ = 1 in the inlet to Θ = 0 at the fiber walls.

For low ReL, as in Fig. 2.6, all incoming mass u∞HC∞is transferred by diffusion to

the fiber surfaces, and the fluid has essentially lost all of its tracer concentration once it has crossed the fiber plane, even for open frontal areas as large asε = 0.8. With u∞HC∞= ShDπκC∞and H/d = 1/(1 − ε) this leads to

Sh= 1 π Re_∞Sc 1− ε = 1 πReLSc ε 1− ε (2.15)

The low ReL behaviour as described above will occur when the convective time scale d/(u∞/ε) in which the fluid passes the fiber plane is large compared to the

transversal diffusion time scale(H − d )2_{/D = (εH)}2_{/D, or}

ReL Re1= 1 − ε

ε

2

Sc−1 (2.16)

The validity of Eq.(2.16) is shown in Fig. 2.8, in which all simulation results have been presented together.

The thicknessδC of the concentration boundary layers that are formed around the cylindrical fibers at high ReLdepends on the local fluid velocity uL= u∞/ε, rather

than the free stream fluid velocity u∞. For large ReLand large Sc , the dimensionless concentration boundary layer thicknessδC/d is expected to be small compared to the dimensionless inter-fiber distance(H − d )/d = ε/(1 − ε), and the concentration boundary layers will be non-interacting. We found this to be the case for:

ReL Re2≈ 400 1 − ε

ε

Sc−2/3 (2.17)

Figure 2.9, in which all simulations results have been combined, demonstrates that indeed the Sherwood numbers approach that of the McAdams correlation for a

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Figure 2.6: Dimensionless concentration contours for ordered cylindrical fibers at

Re∞= 0.1.

Figure 2.7: Dimensionless concentration contours for ordered cylindrical fibers at

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single cylinder when(1/400)ReLε/(1 − ε)Sc2/3 1.

In agreement with observation (iii), the critical value Re2above which single

cyl-inder mass transfer relations can be used decreases with increasing Sc and with increasingε.

Figure 2.10 shows the dependence of Sh on the Schmidt number Sc for all the studied cases.

All results presented in Figs. 2.4, 2.5 and 2.10 can be summarized by means of the correlation stated in Eq.(2.18) where Sh is described as a function of Re∞, Sc andε:

Sh= 1 π1−εε ReLSc r 1+ 1 π1−εε ReLSc ShM c Ad a m s 2 (2.18)

where ShM c Ad a m sis the Sherwood correlation for a single cylinder given by McAdams [53]. This is of course a simplyform of averaged ratios between Eq. (2.15) for low Re and Eq. (2.19) for high Re .

ShM c Ad a m s= (0.376Re_∞1/2+ 0.057ReL2/3)Sc1/3+ 0.92[l n 7.4055 Re_∞ + 4.18Re∞]−1/3Re_∞1/3Sc1/3 (2.19)

Sherwood numbers predicted by Eq.(2.18) have been included as solid lines in Figs. 2.4, 2.5 and 2.10, showing the good agreement with the simulation data.

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Figure 2.8: Illustration of Eq.(2.16) for 0.1≤ Re∞≤ 100, 0.7 ≤ Sc ≤ 10 and 0.04 ≤

ε ≤ 0.95 for ordered cylindrical fibers.

Figure 2.9: Ratio between Sh of ordered cylindrical wires and Sh of a single cylinder

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Figure 2.10: Sh number as a function ofε, and Re_L1/3Sc1/3 _{for ordered rows of}

cylindrical fibers. Also shown is the correlation by McAdams[53] for a single cylinder.

2.3.2 Equidistant arrays of spheres

In a similar way to what has been done for arrays of equidistant cylindrical fibers, we now analyze the mass transfer to arrays of equidistantly distributed spheres. For all studied values of Re∞,Sc andε, only smalldifferences were found between the

average Sherwood numbers in the ordered square and hexagonal arrays.Differences in Sherwood numbers between these two arrangements were less than15% for all studied cases, as shown in Fig. 2.11. Therefore, in the following, we will discuss in detail only the results obtainedfor square arrangements, and we will further focus our discussion on themuch larger differences between the ordered arrangements on the one hand, andthe disordered arrangements on the other hand. Figure 2.12 shows the obtained Sherwood numbers as a function ofRe∞and the open frontal

area fractionε for equidistantlyspaced spheres arranged in square structures at

Flow, heat and mass transfer through CBRN protective clothing

through

through

CBRN protective clothing

Davide AMBESI

Contents

Summary

Samenvatting

I

NTRODUCTION

1.1

Design, modeling and testing of CBRN protective

clothing

1.2

Motivation and aim

1.3

Thesis outline

L

AMINAR FORCED CONVECTION MASS

TRANSFER TO ORDERED AND

DISORDERED SINGLE LAYER ARRAYS OF

CYLINDRICAL FIBERS AND SPHERES

2.1

Introduction

2.2

Numerical approach

2.3

Results and discussion