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Control of Forced Convection Drying in Food Slabs
Ian David Lockhart Bogle and Michael Fairweather (Editors), Proceedings of the 22nd European Symposium on Computer Aided Process Engineering, 17 - 20 June 2012, London. © 2012 Elsevier B.V. All rights reserved.
Control of Forced Convection Drying in Food Slabs Vasile M. Cristea, Adele Irimita, George S. Ostace, Serban P. Agachi Chemical Engineering Department, Faculty of Chemistry and Chemical Engineering, Babes-Bolyai University, 11 Arany Janos, 400028, Cluj-Napoca, Romania, [email protected]
Abstract Reaching a desired quality of the dried product and reducing the convection drying energy costs of food are often related to practical or empirical evaluations, relaying on particular operator expertise and equipment conditions. First, the paper presents a forced convective drying simulator. The generalized conjugate multiphase transport model uses an exponential approach for the drying kinetics. The transient flow, temperature, pressure, liquid water and vapours fields are revealed by the simulator for a 2D geometry, in both air and porous solid domains. The simulation results are validated against experimental data, for the case study of convective drying of carrot slabs. Second, based on the simulator space and time predictions of water, temperature and velocity, in air and solid domains, a set of investigations are performed for improving drying operation by means of process control. The approach is used to minimize the duration of the drying process while reducing the energy costs. Keywords: drying, food, computational fluid dynamics, control.
1. Introduction Drying is a natural and healthy way of preserving food products while keeping their market appreciated properties and diminishing the manipulation costs. Dried foods are well preserved because the moisture content is less enough that undesired microorganisms can grow. One of the most important advantages of dried foods is that they take much less storage space than canned or frozen foods. But the drying process has to be performed under control as food that is underdried will decompose, and food that is overdried will lose its flavor and nutritive value. This is performed in special electrical or gas heated drying chambers, in order to achieve the desired moisture content and quality of the final product. The literature presents a large number of works addressing the porous and multi-phase drying, such as the reference studies in the field of air convective drying of BarbosaCanovas, Kowalski, Mujumdar [1-3]. Considering the basic approach of the drying process, the air temperature is controlled according to a special program mainly designed on the basis of experimental tests. Setting the appropriate drying rate reduces the drying time and leads to the desired quality of dried products. This may be performed by the support of a model involving simultaneous heat and mass transfer, both inside the drying body and between the body and the surrounding heating air. The drying process consists of several periods described by different mechanisms of drying. The mathematical modelling of the drying process enables appropriate equipment design, optimization and efficient control. First, the paper presents the development of a 2D CFD-based dynamic simulator for drying the carrot slab, subject to hot air flow. Then, temperature control of the drying
933
Control of forced convection drying in food slabs
slab is performed according to a desired temperature program, providing appropriate moisture removal.
2. Model description and simulator development The convective drying theoretical background and main considerations for the model used in the paper are presented by De Bonis [4]. The basic theoretical approach of the drying process considers several sequential steps: preheating, constant-rate and one or two falling-rate periods. Conjugate drying is considered in this study, as both mass and heat transfer are taking place in the solid and fluid phases. The model parameters are depending on moisture and temperature. The water content and temperature distribution in the solid interact with the forced laminar air flow. A first order irreversible kinetics is accounted for the vapour and liquid water production or depletion and transport. This approach eliminates the need for evaluating heat and mass transfer coefficients, usually considered as averaged values. Convection is considered for the heat transferred from air to the product surface and conduction for the heat transferred from the surface towards the porous solid interior. Moisture diffuses from the solid towards the surface, where it is vaporized, but nevertheless liquid water is also transformed in vapours within the solid. Water is basically transported in three ways: by diffusion, due to the liquid water concentration difference between the solid inside and its surface, by capillarity and by diffusion of water vapours from the interior of the porous solid to its surface, due to pressure differences. The most important assumptions of the 2D model are: laminar flow, dependence of model parameters on moisture content, inclusion of the capillary transport in the diffusion coefficient and considering the same diffusivity of the liquid water and vapours in the porous solid. The geometry of the porous solid and its air flow surroundings is presented in figure 1, with is associated CFD computation grid.
Fig. 1 Geometry of the drying slab and its surroundings (in m units), with the associated mesh
The system of equations describing the concentration and temperature of vapour and liquid water in the porous solid, pressure, drying air velocity, moisture concentration and temperature change in the air, are separately described in the two considered domains by the following equations [4]: - continuity for the liquid water in the porous solid:
wcl ( Dls cl ) wt
Kcl
(1)
-continuity for the water vapours in the porous solid:
wcv ( Dvs cv ) Kcv wt
(2)
934
V.M. Cristea et al. - heat balance in the porous solid:
U s c ps
. wT ( k s T ) e wt
(3)
- continuity for the water vapours in the drying air:
wcv ( Dva cv ) wt
u cv
(4)
- momentum balance in the drying air:
§ wu · u u ¸ w t © ¹
Ua ¨
p P 2 u
(5)
- heat balance in the drying air:
U a c pa
wT ( k a T ) wt
U a c pa u T ,
(6)
where cl and cv are the concentrations of liquid water and vapours; Dvl, Dvs, Dva, are the diffusivities of the liquid water, vapours in the porous solid and, respectively, the vapours diffusivity in the air; u is the air velocity vector; p is the pressure; ks and ka are the thermal conductivities in the porous solid and air; is the cooling rate due to evaporation, s and a are the solid and air densities, cps and cpa are the specific heats for the solid and air phases; is the dynamic viscosity; K=K0 e-Ea/RTK1 is an Arrhenius type evaporation relationship [5]. The associated boundary conditions assume full continuity for the vapours mass and temperature across the porous solid surface. The model equations have been implemented in the drying simulator using the COMSOL Multiphysics CFD software tool.
3. Simulation results Simulation results are presented in Figures 2 to 5. The simulator has been validated on the basis of literature data [4, 6]. For the inlet drying air placed at the left boundary of the rectangular domain, simulations have been made with constant inlet air temperature (T=343 K), moisture (cv=7 mol/m3) and velocity (u=3m/s). The presented results show the velocity, temperature, liquid water and vapours concentration fields, at the time t=18000s from the beginning of the simulation. As may be observed from the simulation results, the temperature and moisture fields inside the drying body are influenced by the flow and temperature patterns of the hot air flowing around it and by the geometry of the solid.
Fig. 2 Velocity field distribution around the porous solid, at time t=18000 s
Fig. 3 Temperature field distribution inside and around the porous solid at time t=18000 s
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Control of forced convection drying in food slabs
Fig. 4 Liquid water concentration distribution inside the porous solid, at time t=18000 s (detail)
Fig. 5 Vapours concentration distribution inside and around the porous solid at time t=18000 s (detail)
4. Drying control Based on the simulator space and time predictions of moisture, temperature and velocity, in the air and solid domain, a set of investigations have been performed for improving drying operation by means of process control. According to the designed approach, the PI temperature control in the solid has been considered and further presented. For solid temperature control a ramp-constant setpoint was imposed. This shape of the desired temperature change is providing, for the initial phase of the drying process, the slowly increasing of the solid heating while removing the water from the surface. Following a constant period, the setpoint temperature is increased in order to provide the necessary driving force for removing the moisture from the solid interior. Excessive heating should be avoided in order to prevent the crust formation, deformation of the solid or loosing its organoleptic properties. The manipulated variable used is the inlet air temperature. The simulation results presenting the temperature change in the point of spatial coordinates (0.11, 0.0025) is shown in figure 6. As the simulation results confirm, the controlled temperature follows the desired setpoint profile. The change of the liquid water concentration in the porous solid, for the same point, is shown in figure 7. 334 Controlled temperature Temperature setpoint
332
Temperature [K]
330 328 326 324 322 320 318
2000
3000
4000
5000 6000 Time [s]
7000
8000
Fig. 6 Temperature control in the porous solid
9000 10000
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V.M. Cristea et al.
Liquid water concentration, cl [mol/m3]
16000 14000 12000 10000 8000 6000 4000 2000
2000
4000
6000 Time [s]
8000
10000
Fig. 7 Liquid water concentration in the porous solid
The drying control study has been implemented in Matlab-Simulink using a special developed application for running the nonlinear dryer model in Comsol Multiphysics.
5. Conclusions The developed simulator is a useful tool for revealing the temporal and spatial moisture content and temperature distribution inside the food slab and surrounding air, during the forced convection dying process. Changes of the liquid water and vapours concentration in the porous solid are computed, together with the temperature and velocity fields. Gradient assessment of the moisture content and temperature in the solid may be determined, showing useful solutions for efficient operation. Good control of the temperature is performed using the PI controller. The simulator can be used with appropriate adjustments for other geometries of the porous solid and sorts of food materials. This study shows the way of using the complex drying CFD simulator in association to the control investigations in order to bring improvements in the drying process operation, as prerequisite for the its optimization aimed to achieve short drying time, minimum energy consumption, and prevent material deterioration.
6. Acknowledgements The authors gratefully acknowledge financial support from the research project PN Mod. III 409.
References [1] G.V. Barbosa-Canovas, H. Vega-Mercado, 1996. Dehydration of Foods. Chapman &Hall, New York. [2] S.J. Kowalski, 2007, Drying of Porous Materials, Springer, Dordrecht, The Netherlands. [3] A.S. Mujumdar (Ed.), 2007, Handbook of Industrial Drying, Taylor and Francis Group, New York. [4] M. V. De Bonis, G. Ruocco, 2008.A generalized conjugate model for forced convection drying based on an evaporative kinetics, Journal of Food Engineering, 89, 232. [5] S. Azzouz, A. Guizani, W. Jomaa, A. Belgith, 2002. Moisture diffusivity and drying mimetic equation of convective drying of graphes. Journal of Food Engineering 55, 323. [6] I.I. Ruiz-Lopez, A.V. Cordova, G.C. Rodriguez-Jimenes, M.A. Garcia-Alvarado, 2004. Moisture and temperature evolution during food drying: effect of variable properties. Journal of Food Engineering 63, 117.
Control of Forced Convection Drying in Food Slabs Vasile M. Cristea, Adele Irimita, George S. Ostace, Serban P. Agachi Chemical Engineering Department, Faculty of Chemistry and Chemical Engineering, Babes-Bolyai University, 11 Arany Janos, 400028, Cluj-Napoca, Romania, [email protected]
Abstract Reaching a desired quality of the dried product and reducing the convection drying energy costs of food are often related to practical or empirical evaluations, relaying on particular operator expertise and equipment conditions. First, the paper presents a forced convective drying simulator. The generalized conjugate multiphase transport model uses an exponential approach for the drying kinetics. The transient flow, temperature, pressure, liquid water and vapours fields are revealed by the simulator for a 2D geometry, in both air and porous solid domains. The simulation results are validated against experimental data, for the case study of convective drying of carrot slabs. Second, based on the simulator space and time predictions of water, temperature and velocity, in air and solid domains, a set of investigations are performed for improving drying operation by means of process control. The approach is used to minimize the duration of the drying process while reducing the energy costs. Keywords: drying, food, computational fluid dynamics, control.
1. Introduction Drying is a natural and healthy way of preserving food products while keeping their market appreciated properties and diminishing the manipulation costs. Dried foods are well preserved because the moisture content is less enough that undesired microorganisms can grow. One of the most important advantages of dried foods is that they take much less storage space than canned or frozen foods. But the drying process has to be performed under control as food that is underdried will decompose, and food that is overdried will lose its flavor and nutritive value. This is performed in special electrical or gas heated drying chambers, in order to achieve the desired moisture content and quality of the final product. The literature presents a large number of works addressing the porous and multi-phase drying, such as the reference studies in the field of air convective drying of BarbosaCanovas, Kowalski, Mujumdar [1-3]. Considering the basic approach of the drying process, the air temperature is controlled according to a special program mainly designed on the basis of experimental tests. Setting the appropriate drying rate reduces the drying time and leads to the desired quality of dried products. This may be performed by the support of a model involving simultaneous heat and mass transfer, both inside the drying body and between the body and the surrounding heating air. The drying process consists of several periods described by different mechanisms of drying. The mathematical modelling of the drying process enables appropriate equipment design, optimization and efficient control. First, the paper presents the development of a 2D CFD-based dynamic simulator for drying the carrot slab, subject to hot air flow. Then, temperature control of the drying
933
Control of forced convection drying in food slabs
slab is performed according to a desired temperature program, providing appropriate moisture removal.
2. Model description and simulator development The convective drying theoretical background and main considerations for the model used in the paper are presented by De Bonis [4]. The basic theoretical approach of the drying process considers several sequential steps: preheating, constant-rate and one or two falling-rate periods. Conjugate drying is considered in this study, as both mass and heat transfer are taking place in the solid and fluid phases. The model parameters are depending on moisture and temperature. The water content and temperature distribution in the solid interact with the forced laminar air flow. A first order irreversible kinetics is accounted for the vapour and liquid water production or depletion and transport. This approach eliminates the need for evaluating heat and mass transfer coefficients, usually considered as averaged values. Convection is considered for the heat transferred from air to the product surface and conduction for the heat transferred from the surface towards the porous solid interior. Moisture diffuses from the solid towards the surface, where it is vaporized, but nevertheless liquid water is also transformed in vapours within the solid. Water is basically transported in three ways: by diffusion, due to the liquid water concentration difference between the solid inside and its surface, by capillarity and by diffusion of water vapours from the interior of the porous solid to its surface, due to pressure differences. The most important assumptions of the 2D model are: laminar flow, dependence of model parameters on moisture content, inclusion of the capillary transport in the diffusion coefficient and considering the same diffusivity of the liquid water and vapours in the porous solid. The geometry of the porous solid and its air flow surroundings is presented in figure 1, with is associated CFD computation grid.
Fig. 1 Geometry of the drying slab and its surroundings (in m units), with the associated mesh
The system of equations describing the concentration and temperature of vapour and liquid water in the porous solid, pressure, drying air velocity, moisture concentration and temperature change in the air, are separately described in the two considered domains by the following equations [4]: - continuity for the liquid water in the porous solid:
wcl ( Dls cl ) wt
Kcl
(1)
-continuity for the water vapours in the porous solid:
wcv ( Dvs cv ) Kcv wt
(2)
934
V.M. Cristea et al. - heat balance in the porous solid:
U s c ps
. wT ( k s T ) e wt
(3)
- continuity for the water vapours in the drying air:
wcv ( Dva cv ) wt
u cv
(4)
- momentum balance in the drying air:
§ wu · u u ¸ w t © ¹
Ua ¨
p P 2 u
(5)
- heat balance in the drying air:
U a c pa
wT ( k a T ) wt
U a c pa u T ,
(6)
where cl and cv are the concentrations of liquid water and vapours; Dvl, Dvs, Dva, are the diffusivities of the liquid water, vapours in the porous solid and, respectively, the vapours diffusivity in the air; u is the air velocity vector; p is the pressure; ks and ka are the thermal conductivities in the porous solid and air; is the cooling rate due to evaporation, s and a are the solid and air densities, cps and cpa are the specific heats for the solid and air phases; is the dynamic viscosity; K=K0 e-Ea/RTK1 is an Arrhenius type evaporation relationship [5]. The associated boundary conditions assume full continuity for the vapours mass and temperature across the porous solid surface. The model equations have been implemented in the drying simulator using the COMSOL Multiphysics CFD software tool.
3. Simulation results Simulation results are presented in Figures 2 to 5. The simulator has been validated on the basis of literature data [4, 6]. For the inlet drying air placed at the left boundary of the rectangular domain, simulations have been made with constant inlet air temperature (T=343 K), moisture (cv=7 mol/m3) and velocity (u=3m/s). The presented results show the velocity, temperature, liquid water and vapours concentration fields, at the time t=18000s from the beginning of the simulation. As may be observed from the simulation results, the temperature and moisture fields inside the drying body are influenced by the flow and temperature patterns of the hot air flowing around it and by the geometry of the solid.
Fig. 2 Velocity field distribution around the porous solid, at time t=18000 s
Fig. 3 Temperature field distribution inside and around the porous solid at time t=18000 s
935
Control of forced convection drying in food slabs
Fig. 4 Liquid water concentration distribution inside the porous solid, at time t=18000 s (detail)
Fig. 5 Vapours concentration distribution inside and around the porous solid at time t=18000 s (detail)
4. Drying control Based on the simulator space and time predictions of moisture, temperature and velocity, in the air and solid domain, a set of investigations have been performed for improving drying operation by means of process control. According to the designed approach, the PI temperature control in the solid has been considered and further presented. For solid temperature control a ramp-constant setpoint was imposed. This shape of the desired temperature change is providing, for the initial phase of the drying process, the slowly increasing of the solid heating while removing the water from the surface. Following a constant period, the setpoint temperature is increased in order to provide the necessary driving force for removing the moisture from the solid interior. Excessive heating should be avoided in order to prevent the crust formation, deformation of the solid or loosing its organoleptic properties. The manipulated variable used is the inlet air temperature. The simulation results presenting the temperature change in the point of spatial coordinates (0.11, 0.0025) is shown in figure 6. As the simulation results confirm, the controlled temperature follows the desired setpoint profile. The change of the liquid water concentration in the porous solid, for the same point, is shown in figure 7. 334 Controlled temperature Temperature setpoint
332
Temperature [K]
330 328 326 324 322 320 318
2000
3000
4000
5000 6000 Time [s]
7000
8000
Fig. 6 Temperature control in the porous solid
9000 10000
936
V.M. Cristea et al.
Liquid water concentration, cl [mol/m3]
16000 14000 12000 10000 8000 6000 4000 2000
2000
4000
6000 Time [s]
8000
10000
Fig. 7 Liquid water concentration in the porous solid
The drying control study has been implemented in Matlab-Simulink using a special developed application for running the nonlinear dryer model in Comsol Multiphysics.
5. Conclusions The developed simulator is a useful tool for revealing the temporal and spatial moisture content and temperature distribution inside the food slab and surrounding air, during the forced convection dying process. Changes of the liquid water and vapours concentration in the porous solid are computed, together with the temperature and velocity fields. Gradient assessment of the moisture content and temperature in the solid may be determined, showing useful solutions for efficient operation. Good control of the temperature is performed using the PI controller. The simulator can be used with appropriate adjustments for other geometries of the porous solid and sorts of food materials. This study shows the way of using the complex drying CFD simulator in association to the control investigations in order to bring improvements in the drying process operation, as prerequisite for the its optimization aimed to achieve short drying time, minimum energy consumption, and prevent material deterioration.
6. Acknowledgements The authors gratefully acknowledge financial support from the research project PN Mod. III 409.
References [1] G.V. Barbosa-Canovas, H. Vega-Mercado, 1996. Dehydration of Foods. Chapman &Hall, New York. [2] S.J. Kowalski, 2007, Drying of Porous Materials, Springer, Dordrecht, The Netherlands. [3] A.S. Mujumdar (Ed.), 2007, Handbook of Industrial Drying, Taylor and Francis Group, New York. [4] M. V. De Bonis, G. Ruocco, 2008.A generalized conjugate model for forced convection drying based on an evaporative kinetics, Journal of Food Engineering, 89, 232. [5] S. Azzouz, A. Guizani, W. Jomaa, A. Belgith, 2002. Moisture diffusivity and drying mimetic equation of convective drying of graphes. Journal of Food Engineering 55, 323. [6] I.I. Ruiz-Lopez, A.V. Cordova, G.C. Rodriguez-Jimenes, M.A. Garcia-Alvarado, 2004. Moisture and temperature evolution during food drying: effect of variable properties. Journal of Food Engineering 63, 117.