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One-dimensional simulation of co-current, dairy spray drying systems — pros and cons

Simulation monodimensionnelle de systèmes de séchage par atomisation de produits laitiers en co-courant — avantages et inconvénients

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  • Published:
Dairy Science & Technology

Abstract

One-dimensional (1-D) simulation is a useful technique for the evaluation of dryer operating parameters and product properties before conducting real spray drying trials. The main advantage of a 1-D simulation tool is its ability to perform fast calculations with significant simplicity. Mathematical models can be formulated using heat, mass and momentum balances at the droplet level to estimate time-dependent gas and droplet parameters. One of the purposes of this paper is to summarize key mathematical models that may be used to perform 1-D simulation for spray drying processes, predict essential product-drying gas parameters, assess the accuracy of prediction using pilot-scale spray drying data and perhaps most importantly address the main benefits and limitations of the 1-D simulation technique in relation to industrial spray drying operations. The results of a recent international collaborative study on the development of spray drying process optimization software for skim milk manufacture are presented as an example of the application of 1-D simulation in milk processing.

Résumé

La simulation monodimensionnelle (1-D) est une technique utile pour évaluer les paramètres de séchage et les propriétés des produits avant de conduire les essais de séchage en réel. Le principal avantage de l’outil de simulation 1-D est sa capacité à réaliser des calculs rapidement et avec une grande simplicité. Les modèles mathématiques peuvent être formulés avec les équilibres de chaleur, de masse et de quantité de mouvement à l’échelle de la gouttelette pour estimer les paramètres de vapeur et de gouttelette qui varient au cours du temps. Un des objectifs de cet article est de présenter de façon synthétique les modèles mathématiques clés qui peuvent être utilisés pour réaliser une simulation 1-D, prédire les paramètres de vapeur essentiels pour le séchage du produit, évaluer la précision de la prédiction en utilisant les données du séchage par atomisation obtenues à l’échelle pilote, et enfin d’aborder les principaux bénéfices et limites de la technique de simulation 1-D en relation avec les opérations de séchage par atomisation industrielles. Les résultats d’une récente étude réalisée en collaboration internationale sur le développement d’un logiciel d’optimisation du procédé de séchage par atomisation pour la production de poudre de lait écrémé sont présentés pour illustrer l’application de la simulation 1-D.

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Abbreviations

a w :

water activity (−)

A :

surface area (m2)

A C :

cross-section area of atomizer pipe (channel) (m2)

b :

thickness of liquid jet at the orifice (m)

C :

GAB isotherm model parameter (−)

C 0 :

GAB isotherm model constant (−)

C D :

drag coefficient (−)

C p :

specific heat capacity (J·kg−1·K−1)

d p :

diameter of droplet or particle (m)

D 3/2 :

Sauter mean diameter (m)

D C :

diameter of atomizer pipe (channel) (m)

D e :

effective diameter of drying chamber (m)

D O :

orifice diameter (m)

D v :

air-vapor diffusion coefficient (m2·s−1)

E isi :

kinetic constant from solubility model (J·mol−1)

ΔE v :

apparent activation energy (J·mol−1)

ΔE v,b :

equilibrium activation energy (J·mol−1)

g :

universal gravitational constant (= 9.8 m·s−2)

h :

convective heat-transfer coefficient (W·m−2·K−1)

h m :

mass-transfer coefficient (m·s−1)

H :

enthalpy (J·kg−1)

ΔH 1 :

enthalpy parameter from GAB model (J·kg−1)

ΔH 2 :

enthalpy parameter from GAB model (J·kg−1)

ΔH L :

latent heat of vaporization (J·kg−1)

k :

thermal conductivity (W·m−1·K−1)

K :

GAB isotherm model parameter (−)

K 0 :

GAB isotherm model constant (−)

k g :

constant from the Gordon-Taylor model

k isi :

kinetic constant from solubility model (mL·s−1)

l :

axial distance in dryer (m)

m :

mass (kg)

m o :

monolayer moisture content (kg·kg−1)

m :

mass-flow rate (kg·h−1)

M :

molecular weight (g·mol−1)

Nu :

Nusselt number (−)

P :

pressure (kPa)

Pr :

Prandtl number (−)

r isi :

rate of insoluble material formation (mL·s−1)

R g :

universal gas constant (= 8.314 J·mol−1·K−1)

RH :

relative humidity (%)

Re :

Reynolds number (−)

Sc :

Schmidt number (−)

Sh :

Sherwood number (−)

t :

time (s)

T :

temperature (K)

T g :

glass-transition temperature (K)

T ∞ :

room temperature (K)

v :

velocity (m·s−1)

V :

volumetric-flow rate (m3·s−1)

U :

overall heat-transfer coefficient for heat loss (W·m−2K−1)

X :

average droplet moisture content (dry basis) (kg·kg−1)

X 0 :

initial moisture content (dry basis) (kg·kg−1)

X b :

equilibrium moisture content (dry basis) (kg·kg−1)

Y :

air absolute humidity (dry basis) (kg·kg−1)

β :

shrinkage model constant (−)

ω :

weight fraction (−)

θ :

number of droplets/particles (−)

μ :

viscosity (Pa·s)

ρ :

density (kg·m−3)

ρ v :

vapor density (kg·m−3)

b:

bulk drying gas

p:

particle, droplet

s:

solids

sat:

saturated conditions

v:

vapor

w:

water

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Authors and Affiliations

  1. Biotechnology and Food Engineering Group, Department of Chemical Engineering, Monash University, Clayton Campus, 3800, Victoria, Australia

    Kamlesh Patel & Xiao Dong Chen

  2. INRA, UMR1253, F-35042, Rennes, France

    Romain Jeantet & Pierre Schuck

  3. AGROCAMPUS OUEST, UMR1253, F-35042, Rennes, France

    Romain Jeantet & Pierre Schuck

Authors
  1. Kamlesh Patel
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  2. Xiao Dong Chen
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  3. Romain Jeantet
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  4. Pierre Schuck
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Correspondence to Xiao Dong Chen.

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Patel, K., Chen, X.D., Jeantet, R. et al. One-dimensional simulation of co-current, dairy spray drying systems — pros and cons. Dairy Sci. Technol. 90, 181–210 (2010). https://doi.org/10.1051/dst/2009059

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  • DOI: https://doi.org/10.1051/dst/2009059

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