dje

is,

icat

acc17

onto

mass transfer. In this paper the available procedures are reviewed and applied to food substrates: temperature, mass concentrationand velocity elds are computed even for non-linear couplings (i.e. when local species concentration depends on temperature) using aspecic solution strategy. Validity and limitations of the adopted notation and related integration into a proprietary software are dis-

localized, controlled and rapid surface transfer is desir-

air convection, a most energy-intensive process, which is

kinetics, also resulting in transport and storage costs reduc-

the air velocity. When hot air is locally blown over a moistfood, water vapor diuses through the boundary layer andis carried away (Fig. 1). A water vapor pressure gradient istherefore established from the moist interior to the externalfood surfaces. The boundary layer acts as a barrier to bothheat transfer and water vapor removal during drying.

* Corresponding author.E-mail address: ruocco@unibas.it (G. Ruocco).

Journal of Food Engineering 7able. Studies on JI have been performed extensively overthe past ve decades, nevertheless the coupling and inter-dependence between simultaneous mass/heat transferand uid dynamics still needs to be fully analyzed, withspecial reference to local distribution of transfer rates onsubstrates of dierent shape (see for example Olsson,Ahrne, & Tragardh, 2004; Sarghini & Ruocco, 2004).Additional diculties arise when in the subject impingedsolid a multi-phase transport is allowed. JI can be success-fully employed in drying or dehydration of foods by forced

tion. In turn, drying may cause deterioration of both eatingquality and nutritional value of the food. In food engineer-ing, the design and operation of drying equipment aim tominimize these changes by selection of appropriateconditions.

Dehydration involves a rather complex combination ofapplication of heat and removal of moisture from a foodmedium (Barbosa-Ca`novas & Vega-Mercado, 1996; Fel-lows, 2000). In addition to air temperature and relativehumidity, the rate of moisture removal is controlled bycussed. A comparison is also brought forth with the available literature data. 2005 Elsevier Ltd. All rights reserved.

Keywords: Jet impingement heat and mass transfer; Transient CFD; Food dehydration; Local water activity; Evaporation kinetics

1. Introduction

Among the available forced convection processes, thegaseous jet impingement (JI) is frequently used for itsexcellent heat and mass transfer characteristics, where

commonly used in food engineering to extend food shelf-life. Here, the majority of the unbound water normallypresent in a food is removed by applying heat under con-trolled conditions. The reduction in relative humidity(water activity) inhibits microbial growth and enzymeModelling local heat anslabs due to air

M.V. De Bon

CFDfood, DITEC, Universita degli studi della Basil

Received 24 March 2005;Available online

Abstract

Adequate design and verication of drying by a forced convectiby numerical analysis, but customary transport calculations need0260-8774/$ - see front matter 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.jfoodeng.2005.09.032mass transfer in foodt impingement

G. Ruocco *

a, Campus Macchia Romana, 85100 Potenza, Italy

epted 26 September 2005November 2005

enhanced technique (gaseous jet impingement) can be carried outbe integrated to account for complex (simultaneous) energy and

www.elsevier.com/locate/jfoodeng

8 (2007) 230237

Greek

of FNomenclature

aw water activity (dimensionless)c concentration (g solid/g water)cp specic heat at constant pressure (kJ/kg K)d jet diameter (m)D mass diusivity (m2/s)Ea activation energy (kJ/mol)k turbulent kinetic energy (J/kg)

M.V. De Bonis, G. Ruocco / JournalLocalized forced convection patterns, such as in JI,contribute to boundary layer destruction, hence in increaseof moisture removal, while equipment costs are kept to aminimum. Nonetheless, local conditions have to be care-fully monitored to ensure product uniformity.

Porous and multi-phase media drying has been longspeculated, and a large number of studies are available, fol-lowing the seminal works be De Vries (1958) and Whitaker(1977), that carry complete descriptions of physics, as inStanish, Schajer, and Kayihan (1986), Ben Nasrallah andPerre (1988) and Chen and Pei (1989). Boukadida andBen Nasrallah (1995) rst described a two-dimensional

K rate of production of water vapor mass per unitvolume (1/s)

K0 reference rate constant (1/s)l length (m)p pressure (Pa)r radial coordinate (m)R universal gas constant (kJ/mol K)S sucrose equivalent conversion factor (dimen-

sionless)Sct turbulent Schmidt number (dimensionless)t time (s)T temperature (K)u x-component velocity (m/s)v r-component velocity (m/s)x axial coordinate (m)

Fig. 1. A drying air jet onto a food slab: ow of moisture during process./ mass fraction (dimensionless)k thermal conductivity (W/m K)m kinematic viscosity (m2/s)q density (kg/m3)x specic dissipation rate (1/s)

Superscripts

f uid side, across the interfaces solid side, across the interface

Subscripts

0 initiala airi, m i-species in the mixturej jets solidsr solid, along rsx solid, along xt turbulentv water vaporw liquid water1r undisturbed, along rood Engineering 78 (2007) 230237 231progress of bulk convective drying of clay, but no contribu-tions have been found in the available literature, with ref-erence to localized convective drying in extended (i.e. atleast 2D) porous media.

A rst contribution of JI drying of a moist, porous solidwas presented by Francis and Wepfer (1996) with a thor-ough transient physical analysis, yet limited as one-dimen-sional. Furthermore, this model does not allow for a trulycoupled transfer mechanism, as the surface transfer ratesare externally implied. This limitations are also found inmore recent works by Moreira (2001) and Braud et al.(2001), who rst applied JI to food drying.

Within this framework, the numerical analysis by acomputational uid dynamics (CFD) approach can gainimportance as it leads to complete multi-dimensional andtransient process description, yet ancillary calculation pro-cedures are still needed to account for fully coupled energyand mass transfer. The present work has been performedwith the specic aim to merge an in-house computationroutine into a proprietary software (FLUENT 6.1 UsersGuide, 2003) in order to incorporate the multi-dimen-sional, transient calculation of an evaporation processdue a gaseous impinging, heating jet.

2. Problem formulation

A drying process of a thin food substrate is devised byusing JI: hot, fully turbulent air is discharged through a

production of water vapor in the substrate is determined

of Fnozzle with a given velocity distribution (upon recognitionof the nozzle internal geometry). Upon impact of the freejet on the substrate, the characteristic stagnation and walljet regions are rst formed, then a secondary pattern canbe identied in the lateral regions (Fig. 2). If the impingedfood is water saturated, liquid can be converted into vapordepending on the heat perturbation front within the sub-strate, which can then be modelled as a multi-phase med-ium (a mixture of bulk solid, liquid water and watervapor). Liquid water normally moves from the interior ofthe substrate to the surface (1) by capillary forces, and(2) by diusion caused by dierences in the concentrationof solutes at the surface and in the interior, while watervapor moves (3) by diusion in air spaces within the sub-strate caused by vapor pressure gradients. In this work,for the sake of simplicity, Fickian diusion is assumed onlyfor both liquid and water vapor, nevertheless a highly non-

Fig. 2. Characteristic regions in submerged, conned JI.

232 M.V. De Bonis, G. Ruocco / Journaluniform drying still results within the substrate, and a givenprocess time can lead to local overheating and/or incom-plete liquid conversion.

2.1. Driving assumptions

In Fig. 3 the subject geometry in cylindrical coordinatesis reported (only half section of the domain is considereddue to the geometry and transfer symmetries). The domainunder scrutiny consists in two interfaced uid-and-sub-strate multi-species sub-domains, sharing the biomaterialsexposed surface. The uid is a binary system comprising of

1. water vapor (v)2. air (a)

while the substrate is a ternary system comprising of

1. water vapor (v)2. liquid water (w)3. solid matter proper (s).The following additional assumptions are adopted:

1. The ow is axisymmetric, with constant properties andincompressible (negligible pressure work and kineticenergy).

2. The viscous heat dissipation is neglected.3. Due to the adopted ow regime, no body force is

accounted for.4. No-slip is enforced at every solid surface.5. Due to the nature of the interacting species, no diusion

uxes are accounted for in the energy equation.6. The dilute-mixture assumption is appropriate in each

sub-domain (the velocity components, temperature andpressure of each species are related to bulk mass in eachgoverning equation).

7. As the turbulence-chemistry interaction is neglected, the

Fig. 3. Geometry and nomenclature.

ood Engineering 78 (2007) 230237by an Arrhenius expressions (laminar-nite rate model).

2.2. Governing equations

With reference to the previous statements, the standardgoverningRANSand energy equations are enforced, to yieldfor velocity components, temperature, pressure mass frac-tions in both subdomains (Bird, Stewart,&Lightfoot, 2002)

Continuity, for each uid species

o/ot u o/

ox v o/

or vr

Di;m mtSct

1

roor

ro/or o

2/ox2

KT 1

where

Di,m (from the Ficks law) is the diusivity of the watervaporair system in the uid, and the water vaporliquid water system in the substrate sub-domain;

& Ruocco, 2005) its relative merit for the given ow cong-

of F in the substrate,K is the rate of production of water vapormass per unit volume (K = 0 in the uid sub-domain);

in the uid sub-domain, the overall mass fraction con-servation

P/ 1 apply, whereas in the solid sub

domain this condition is not required during the dryingprocess (

P/ < 1: voids formation).

Momentum in the axial direction, in the uid subdomain

ouot u ou

ox v ou

or op

ox oox

2m mt ouox

1roor

m mtr ouor ovox

2

Momentum in the radial direction, in the uid subdomain

ovot u ov

ox v ov

or op

or oox

m mt ouor ovox

1roor

2m mtr ovor

m mt vr2 3

Energy

qoot

Xcp/T

q u oox

Xcp/T v oor

Xcp/T

k kt o2

ox2X

cp/T 1roor

roor

Xcp/T

4In the substrate, the usual constraints of u = v = 0 apply inEqs. (1)(4), whereas mt and kt are zero (laminar mass andthermal diusions only).

2.3. Initial and boundary conditions

The food is initially in thermal equilibrium (T = T0)with the quiescent ambient (u0 = v0 = 0), and saturatedwith liquid water (/w = /w0,/v0 = 0); the mass fractionof solid is constant throughout the treatment (/s = /s0 =const; /w0 + /s0 = 1). Water vapor is allowed, duringtreatment, to ow through the interface, while no liquidwater is allowed in the uid subdomain.

With reference to Fig. 3, the mass, momentum and ther-mal boundary conditions are as follows:

Jet inlet (0 6 r 6 d/2,x = lsx + lj)/v 0; /a 1; u uj; v 0; T T j 5

Substrate symmetry axis (r = 0,0 6 x 6 lsx)o/v;wor

0; oTor 0 6

Fluid symmetry axis (r = 0, lsx < x 6 lj)

M.V. De Bonis, G. Ruocco / Journalo/v;aor

0; ouor 0; v 0; oT

or 0 7uration. Being its treatment beyond the scope of the pres-ent work, the Reader is referred to FLUENT 6.1 UsersGuide (2003) for its complete formulation.

2.5. Rate of production of vapor

In this paper a model of evaporation of unbound waterhas been adopted, based on a rst-order irreversible kinet-ics (Roberts & Tong, 2003). Liquid water to water vaporconversion can be generally taken as an Arrhenius rst-order reaction, with a rate dependent on temperature

KT K0eEa=RT 13where the reference rate constant K0 is 4.96 106 1/s andthe activation energy Ea is 48.7 kJ/mol.

2.6. Numerical method and additional considerations

The eect of the dierent values of domain radial lengthhas rst been monitored, to enforce the boundary conditionof undisturbed ow. A value of 20 nozzle diameters wasnally chosen along r. A triangular pave grid of approx.9800 cells has been employed (Fig. 4), highly stretched toFluid, at undisturbed distance (outlet) (r = l1r, 0 < x 5 mm) the surface vapor is blown away by the air ow,inducing more diusion within the food. The /v isolinesare densely packed along x, due to the high surface masstransfer rate. Far from stagnation, the mass fraction ofvapor decreases, and for r > 10.0 cm a small vapor cloud

fer mechanism is attributed at the surface), therefore thepresent relatively high uj value has been reconstructed usingthe cited bibliography through a local Nusselt number cal-culation based on jet diameter and height. In the presentconguration, after only 5 min the thin tortilla has lostalmost completely all liquid water, whereas a duration of20 min was reported in Braud et al. (2001). This dierenceis attributed to the strongly dierent models compared here.

Fig. 6. Quantitative plots of (a) /w and (b) /v isolines at t = 30 s.

M.V. De Bonis, G. Ruocco / Journal of Food Engineering 78 (2007) 230237 235appears.The eect of JI heating leads to complete /w drying after

t = 300 s. A residual /v transport in the wall jet region iswell evidenced in Fig. 7, while in the close-up of Fig. 8 anon-monotone behavior is detected along r, due to the jointeect of jet on the exposed surface, the internal diusion ofvapor along r and the removal from the side.

From the comparison with the available literature refer-ence (Braud et al., 2001), a discrepancy has been found onthe process duration. It must be recalled that (Braud et al.,2001) do not solve for the ow eld (an average heat trans-Fig. 7. Quantitative plots of

Fig. 8. /v map3.4. Evaluation of water activity

The importance of water activity aw in food processinghas been recalled earlier. aw is evaluated as the ratiobetween the vapor pressure in the substrate and the vaporpressure of pure water at the same temperature. The vaporpressure in a given product varies with the anity of waterwith food constituents: the greater the anity, the lower isthe vapor pressure as few water molecules are available tobe released upon processing. Solutes depress the vapor/v isolines at t = 300 s.

at t = 300 s.

can be attributed to the particular ow eld, which rela-

mechanism. The model shows how the integration of trans-

s at

of Fpressure of the solvent: this depression is usually given byRaoults law but in foods there are substantial deviationsfrom the ideal relationship.

A number of approaches have been taken insofar to esti-mate the water activity of a mixture, in order to predict itusing few characteristic parameters. But water activityhas never been calculated on a local basis: the knowledgeof the local distribution of aw is essential to food structure,consistence, perishability, and to yield for product/processoptimization.

One of the empirical equations for calculating wateractivity is the method of Grover (Barbosa-Ca`novas &Vega-Mercado, 1996). With this method, dierent ingredi-ents are assigned a sucrose equivalent conversion factorS. This factor was based on experimental vapor pressuresmeasured in such ingredient solutions, hence in part itincorporates corrections to Raoults law. Water activity isassessed by the concentration ci of each ingredient,multiplied by S factor for the specic ingredient, as inEq. (14)

aw 1:04 0:1X

Sici

0:0045X

Sici 2

14

Fig. 9. Water activity aw map

236 M.V. De Bonis, G. Ruocco / JournalFor the present case, S = 0.8 for corn starch. It must be ob-served, though, that as aw assessment is strongly dependenton temperature, it should be carried out in equilibrium con-ditions: only pseudo-aw transient values can be calculatedfor the drying process.

For the case at hand, after few seconds a rapid decre-ment is already detected, from an initial average value of0.800 0.760 in the stagnation region (not shown). Att = 20 s (Fig. 9a) the aw distribution is clearly inuencedby the jet-oset: the lowest value of 0.700 is detected underthe stagnation region (uniform along x due to the x-wiselimited extension). Its progress is monotone with r, increas-ing up to 2 cm from the edge (maximum value 0.729), thendecreasing again very slightly. The same progress is foundfor a later time t = 30 s (Fig. 9b). It is evident that evensuch a short duration increase contributes to decisive dehy-dration, as the lowest and highest values are 0.589 and0.625 in this case.port and biochemical notations in foods can be employedto pursue process optimization.

Acknowledgementstively favors vapor transport at the end-side, as seen inFigs. 6b and 7.

4. Conclusions

Dehydration in a food slab has been accomplished by animpinging heated air jet. Timedependent governingequations have been integrated to predict local moisture,temperature and velocity distributions. The evapora-tion kinetics has been tackled by a simple Arrheniusnotation.

Coupled moisture and temperature gradients have beenshown to determine a strong process non-uniformity. Alocal pseudo-water activity has also been computed, for athin corn tortilla. The non-monotone radial progress ofaw is attributed to the peculiar surface heat/mass transferThe local depletion near the lateral edge of the tortilla

(a) t = 20 s and (b) t = 30 s.ood Engineering 78 (2007) 230237This work was funded by MIUR Italian Ministry of Sci-entic Research, grant no. 2004090750003 entitled Analy-sis of transport phenomena due to jet impingement onsubstrates in industrial applications.

References

Angioletti, M., Nino, E., & Ruocco, G. (2005). International Journal ofThermal Science, 44(4), 349.

Barbosa-Ca`novas, G. V., & Vega-Mercado, H. (1996). Dehydration offoods. New York: Chapman & Hall.

Ben Nasrallah, S., & Perre, P. (1988). International Journal of Heat andMass Transfer, 31(5), 957.

Bird, R. B., Stewart, W. E., & Lightfoot, E. N. (2002). Transportphenomena. New York: John Wiley & Sons.

Boukadida, N., & Ben Nasrallah, S. (1995). Drying Technology, 13(3), 661.Braud, L. M., Moreira, R. G., & Castell-Perez, M. E. (2001). Journal of

Food Engineering, 50, 121.

Chen, P., & Pei, D. C. T. (1989). International Journal of Heat and MassTransfer, 32(2), 297.

De Vries, D. A. (1958). Transaction, American Geophysical Union, 39(5),909.

Fellows, P. J. (2000). Food processing technology. Boca Raton: CRC Press.FLUENT 6.1 Users Guide, Fluent Inc., 2003.Francis, N. D., & Wepfer, W. J. (1996). International Journal of Heat and

Mass Transfer, 39(9), 1911.Moreira, R. G. (2001). Journal of Food Engineering, 49, 291.

Olsson, E. E. M., Ahrne, L. M., & Tragardh, A. C. (2004). Journal of FoodEngineering, 63(4), 393.

Roberts, J. S., & Tong, C. H. (2003). International Journal of FoodProperties, 6(3), 355.

Sarghini, F., & Ruocco, G. (2004). International Journal of Heat and MassTransfer, 47(8-9), 1711.

Stanish, M. A., Schajer, G. S., & Kayihan, F. (1986). AlChE Journal,32(8), 1301.

Whitaker, S. (1977). Advances in Heat Transfer, 13, 119.

M.V. De Bonis, G. Ruocco / Journal of Food Engineering 78 (2007) 230237 237

Modelling local heat and mass transfer in food slabs due to air jet impingementIntroductionProblem formulationDriving assumptionsGoverning equationsInitial and boundary conditionsTurbulence treatmentRate of production of vaporNumerical method and additional considerations

ResultsConfiguration and materialFlow and temperature fieldMoisture contentEvaluation of water activity

ConclusionsAcknowledgementsReferences