data based mechanistic modelling of three dimensional temperature ...

Katholieke Universiteit Leuven Faculteit Bio-ingenieurswetenschappen

DISSERTATIONES DE AGRICULTURA Doctoraatsproefschrift Nr. 796 aan de Faculteit Bio-ingenieurswetenschappen van de K.U.Leuven

DATA BASED MECHANISTIC MODELLING OF THREE DIMENSIONAL TEMPERATURE DISTRIBUTION IN VENTILATED ROOMS FILLED WITH BIOLOGICAL PRODUCTS

Promotor:

Proefschrift voorgedragen tot het

Prof. Daniel Berckmans, K.U. Leuven

behalen van de graad van Doctor in de Toegepaste

Leden van de Examencommissie:

Biologische Wetenschappen

Prof. Marc Hendrickx, KU Leuven

Door

Prof. Erik Vranken, KU Leuven

Võ Tấn Thành

Prof. Jean Lebrun, Liege University Dr. Ha Thanh Toan, Cantho University

May 2008

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Acknowledgment Firstly, I would like to express my sincere gratefulness to my advisor, Prof. Daniel Berckmans for his great suggestions, endless support and encouragement, and professional guidance throughout my PhD study.

My sincere thanks to Prof. Erik Vranken for his daily help during my working time in Leuven. I would like to thank my committee members, Prof. Rony Geers, Prof. Marc Hendrickx, Prof. Jean Lebrun and Dr. Ha Thanh Toan for their valuable suggestions and kind support during my research work. Special thanks to Mr. Jean-Lou Lemaire and Mr. Ludo Happaerts for their assistance in building the experimental installation and guidance to collect the equipments during my research.

I would like to thank all my friends and colleagues at M3-BIORES for helping me during the time I was in Leuven.

I would also like to thank the Belgian government for giving me an opportunity to pursue my study. My specially thanks to VLIR through the Institutional University Cooperation program with Cantho University for their financial support to this study. Special thanks to the Vietnamese student community at Catholic University of Leuven for their friendship and great time we have spent together.

Lastly, the deepest appreciation goes to my dear parents and my lovely wife in Vietnam for their unconditional love, encouragement, and support.

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Abstract In this PhD research, a data based mechanistic modelling approach was developed for real time monitoring (non-invasive measurement method) and online adaptive control of threedimensional temperature distribution in the room filled with biological products.

An empty room and room filled with obstacles and a room filled with biological products were selected for the model development. During the experiments, step inputs on an air inlet temperature were applied while airspace, obstacles and biological product temperature were recorded. The continuous-time simplified refined instrument variable algorithm (SRVIC) in the CAPTAIN Toolbox for Matlab was used to identify the model parameters and select the best model order.

In a first step was analysed wherever the data based mechanistic method, as developed for an empty room, could be applied in a ventilated room filled with obstacles. An empty room and a room filled with plastic balls as simulative products were used, and 36 thermocouples were installed in two vertical planes in a process room. The results showed that the temperature uniformity index in the empty and in the room filled with balls was dependent on the ventilation rates. High ventilation rates in combination with high acceptable temperature differences resulted in a high temperature uniformity index. The temperature uniformity index in both cases reached 100% with a ventilation rate of 240 m3 h-1 and an acceptable temperature difference of 1oC, due to adequate mixing. By adopting the mechanistic phase from an empty room to a room filled with obstacles, to model the dynamic response of airspace from inlet air temperature was shown that data based mechanistic modelling (DBM) approach worked in a room filled with obstacles.

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In the second step, the data based mechanistic modelling was further developed for a ventilated room filled with 480 balls. The dynamic response of airspace temperature and air inside the balls after steps on the air inlet temperature were used to find a best fitted model based on the coefficient of determination ( RT2 ), Young Information Criterion (YIC) and standard error (SE). A third order transfer function from the dynamic response of airspace temperature from steps inlet air temperature was found as the best fitted model in correspondence with the general theory of heat transfer from airspace to the balls. Physically meaningful parameters were found from the fitted model: there were the local volumetric of fresh air concentration (β1), and α2 value which was related to a local overall heat transfer coefficient from the airspace to the air inside the balls, it is the same structure of “cooling rate” term in Newton’s law for cooling processes. The local volumetric of fresh air concentration values (β1) in a room filled with obstacles represented an airflow pattern as in an empty room, and α2 was explained as the amount of energy which transfers from airspace to the air inside the ball, and it can be used to predict the temperature of air inside the ball.

In the third step, the data based mechanic model was developed for a room filled with solid material with different shapes as biological products. The dynamic response of airspace and product temperature from steps on inlet air temperature was recorded. The temperature uniformity index of airspace and the bulk of potatoes were calculated at different acceptable temperature differences and ventilation rates. The calculated temperature uniformity index for airspace varied from 2.7 to 66%, and the bulk of potatoes from 8.0 to 66%. The cumulative energy in the potatoes during the process is not only dependent on airspace temperature but also on the air velocity. A third order transfer function was obtained from the dynamic response of airspace temperature from step on inlet air temperature. This equation explained a heat transfer process in the room filled with biological products. Two important physically vi

meaningful parameters found from the model parameters are a local volumetric of fresh air concentration value (β1) and a local ‘cooling rate’ value (α2). The local cooling rate value in the model explained the rate of energy transfer to the product from the airspace. The local cooling rate value contains both a temperature difference (between airspace and product) and the airspace velocity. This is an important model parameter which existing in the model could be used for online prediction of product temperature and real time control of the 3D temperature distribution in a room filled with biological products.

The last step of this research was the evaluation of the model. Two methods to calculate the local cooling rate value to estimate the product temperature from the DBM model were found in the second and third steps. Results of local cooling rate values with several kinds of material and several levels of ventilation rates showed that the differences of the local cooling rates between the two methods at the different ventilation rates were 22 to 26%. A new method to calculate a cooling rate or heat transfer coefficient was found in this step, it was calculated under unsteady conditions with the information of the dynamic response of the product from airspace temperature that can be used to real time calculation of product temperature during heating/cooling applications.

Finally, the data based mechanistic model approach was successfully applied to model the temperature in a room filled with biological products and it extends for the 3D temperature distribution by using a well-mixed zone approach. Physically meaningful parameters were found such as a local volumetric of fresh air concentration and a local ‘cooling rate’. Their existence in a model are a key factor to explain an energy transfer within a fluid flow, a rate of energy transfer from fluid flow to products and a fluid flow velocity around products during heating/cooling processes. A local cooling rate is a physically meaningful parameter

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in the model, which can be used in a control algorithm to predict the product temperature, and be applied for real time controlling of 3D temperature uniformity index in heating and cooling applications.

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Table of content Acknowledgment Abstract Table of Content List of tables List of figures List of symbols and abbreviations

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Chapter 1 Introduction and Objectives ............................................................................... 1  1.1  Introduction ................................................................................................................ 3  1.2  Objectives ................................................................................................................. 16  1.3  Brief outline of next chapters ................................................................................... 18  Chapter 2 Materials and Methods..................................................................................... 21    2.1  Introduction .............................................................................................................. 23  2.2  Technical descriptions .............................................................................................. 23  2.3  Materials and methods .............................................................................................. 34  2.3.1.  Material ............................................................................................................. 34  2.3.2.  Methods ............................................................................................................ 35  Chapter 3 Modelling of Three-dimensional Air Temperature Distributions in Porous   Media ........................................................................................................................................ 45  3.1  Introduction .............................................................................................................. 47  3.2  Materials and methods .............................................................................................. 48  3.2.1.  Laboratory test room ........................................................................................ 48  3.2.2.  Experiments ...................................................................................................... 48  3.2.3.  Data-based mechanistic modelling approach ................................................... 52  3.3  Results and discussions ............................................................................................ 59  3.3.1.  Uniformity of air temperature in the empty test installation ............................ 59  3.3.2.  Data-based phase in the empty room................................................................ 63  3.3.3.  Uniformity of air temperature in the test installation filled with obstacles ...... 66  3.3.4.  Data-based mechanistic modelling approach in the obstacles room ................ 68  3.3.5.  Comparison between the empty test installation and the test installation filled with obstacles ................................................................................................................... 72  3.4  Conclusions .............................................................................................................. 74  Chapter 4 Data Based Mechanistic Modelling for Control of Three Dimensional   Temperature distribution in a Ventilated Room Filled with Obstacles ................................... 75  4.1  Introduction .............................................................................................................. 77  4.2  Materials and methods .............................................................................................. 78  4.2.1.  Laboratory test room ........................................................................................ 78  4.2.2.  Experiments ...................................................................................................... 79  4.2.3.  Data based mechanistic modelling approach.................................................... 81  4.2.4.  Data based identification and estimation .......................................................... 81  4.2.5.  Mechanistic phase in the ventilated porous media ........................................... 82  4.3  Results and discussions ............................................................................................ 89  4.3.1.  The third order transfer function in ventilated porous media ........................... 89  4.3.2.  Physical meanings of estimated parameters ..................................................... 90  4.4  Conclusions .............................................................................................................. 96  Chapter 5 Data Based Mechanistic Modelling of Three Dimensional Temperature   Distribution in Ventilated Rooms Filled with Biological Material .......................................... 97  5.1  Introduction .............................................................................................................. 99   

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5.2  Material and method ............................................................................................... 101  5.2.1.  Laboratory test room ...................................................................................... 101  5.2.2.  Data based mechanistic modelling approach.................................................. 103  5.3  Results and discussion ............................................................................................ 110  5.3.1.  Temperature distribution in airspace and potatoes during experiment........... 110  5.3.2.  Uniformity of air and potato temperature in experiment ................................ 113  5.3.3.  Data based phase ............................................................................................ 114  5.3.4.  Mechanistic phase........................................................................................... 115  5.3.5.  Analysis and suggestion of the order of transfer function .............................. 117  5.4  Conclusions ............................................................................................................ 119  Chapter 6 Validation of a Data Based Mechanistic Model for Online Calculation of the   Cooling Rate during Cooling Processes ................................................................................. 121  6.1  Introduction ............................................................................................................ 123  6.2  Material and method ............................................................................................... 124  6.2.1.  Laboratory test room ...................................................................................... 124  6.2.2.  Experiment ..................................................................................................... 125  6.3  Data based mechanistic model approach ................................................................ 125  6.3.1.  Data based phase ............................................................................................ 125  6.3.2.  Mechanistic phase........................................................................................... 125  6.4  Results and discussions .......................................................................................... 128  6.4.1.  The third order transfer function for the heat transfer in a room filled with products 128  6.4.2.  Cooling rate from the first order transfer function ......................................... 129  6.4.3.  Cooling rate as found from the estimated parameters of the third order transfer function 130  6.4.4.  Comparison of ‘Cooling rate’ values obtained by two methods .................... 130  6.4.5.  Calculation of a heat transfer coefficient from ‘Cooling rate’ with known physical properties of material ....................................................................................... 131  6.4.6.  An example for biological products ............................................................... 132  6.5  Conclusions ............................................................................................................ 133  Chapter 7 General conclusions and Suggestions for future research ............................. 135    7.1  General conclusions................................................................................................ 137  7.2  Suggestions for future research .............................................................................. 142  References Appendices

137 148 -Appendix A -Appendix B -Appendix C

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List of tables Table 1-1 Researches related to the improvement of product temperature during heat treatments ........................................................................................................................... 9  Table 2-1 Physical characteristics of materials used in this research ....................................... 34  Table 2-2 Comparison between mechanistic, data based and data based mechanistic modelling .......................................................................................................................................... 39  Table 3-1 Overview of the dynamic experiments .................................................................... 51  Table 3-2 The model parameter estimates with for sensor position (1) and (32) in the empty room with ventilation rate is 280 m3 h−1........................................................................... 63  Table 3-3 The model parameter estimates with for sensor position (1) and (32) (in the obstacle room with ventilation rate is 280 m3 h−1) ......................................................................... 70  Table 4-1 Overview of the dynamic experiments .................................................................... 81  Table 4-2 Third order model parameter associated statistical measures for step up experimental data at 280 m3 h-1 inlet flow rate ................................................................. 89  Table 4-3 First order model parameters in a relationship between temperature in WMZ1 ( ti (t ) ) and material temperature ( tm (t ) ) with associates statistics measure for step up experiment at 280 m3 h-1................................................................................................... 92  Table 4-4 Calculated parameters at position (33) with ventilation rate from 220 to 280 m3 h-1 .......................................................................................................................................... 95  Table 5-1 Overview of the dynamic experiments .................................................................. 103  Table 5-2 Temperature uniformity index as a function of acceptable temperature difference and ventilation rates in the airspace................................................................................ 113  Table 5-3 Temperature uniformity index as a function of acceptable temperature difference and ventilation rates in bulk of potatoes ......................................................................... 113  Table 5-4 Estimated parameters from the third order of transfer function at position (6) and (30) with ventilation rate of 280 m3 h-1 as an example of calculating method ............... 115  Table 5-5 α2 values from numerator of the third order transfer function at ventilation rate 200 m3 h-1 ............................................................................................................................... 116  Table 5-6 Analysis and suggestion of the order of transfer function in several processes..... 118  Table 6-1 Estimated parameters from the third order transfer function at the different ventilation rates .............................................................................................................. 128  Table 6-2 Estimated parameters from the first order transfer function .................................. 129  Table 6-3 Cooling rate values at the different ventilation rates (1st order TF) ....................... 129  Table 6-4 Roots of second order equation .............................................................................. 130  Table 6-5 Comparison cooling rate values from two methods at different ventilation rates 130  Table 6-6 Estimated bulk heat transfer coefficient from known physical characteristics of material and ‘Cooling rate’ term from model parameters at different ventilation rates . 131  Table 6-7 Estimated parameters from Data based mechanistic model for forced air-cooling of apples at ventilation rate 20 m3 h-1 ................................................................................. 132 

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List of figures Fig. 1-1 Scheme of model predictive control of 3D temperature distribution in a room filled with biological product ..................................................................................................... 14  Fig. 1-2 Energy exchanges in the Well Mixed Zone (WMZ) .................................................. 16  Fig. 2-1 First of the laboratory test installation ........................................................................ 25  Fig. 2-2 Slot of air inlet ............................................................................................................ 26  Fig. 2-3 Air outlet systems ....................................................................................................... 26  Fig. 2-4 Air outlet tube ............................................................................................................. 26  Fig. 2-5 Holes on the air outlet system ..................................................................................... 26  Fig. 2-6 Control of the ventilation rate through the test room.................................................. 27  Fig. 2-7 Cooling unit (a) and heat exchanger (b) ..................................................................... 28  Fig. 2-8 Numbered sensors in the test installation.................................................................... 28  Fig. 2-9 Room filled with balls................................................................................................. 30  Fig. 2-10 Room filled with boxes of potatoes .......................................................................... 31  Fig. 2-11 Position of balls in the test room and measuring air temperature inside the ball ..... 31  Fig. 2-12 Product temperature measurements ......................................................................... 31  Fig. 2-13 Test installation for validating the obtained model................................................... 33  Fig. 2-14 Air extracted system ................................................................................................ 33  Fig. 2-15 Researching methods to control 3D product bulk temperature in heating/cooling applications ....................................................................................................................... 36  Fig. 2-16 Step up (a) and step down (b) experiments:.............................................................. 36  Fig. 2-17 Step up inlet air temperature and dynamic temperature changes in airspace and potatoes at ventilation rate 280 m3 h-1 .............................................................................. 37  Fig. 2-18 Data-based mechanistic (DBM) modelling technique (Young et al., 2002)............. 40  Fig. 2-19 Diagrammatic representation of the continuous time SRIVC algorithm .................. 41  Fig. 3-1 Step up (a) and step down (b) experiments (c) The measured dynamic response of airspace and buffer temperature from the inlet air temperature for a ventilation rate 280m-3 h-1.......................................................................................................................... 50  Fig. 3-2 Three-dimensional view of the test installation. (1) Air inlet, (2) Air outlet, ............. 52  Fig. 3-3 Schematic representation of the well-mixed zone concept: ........................................ 54  Fig. 3-4 Block diagram of the feedback connected the second order transfer function: .......... 58  Fig. 3-5 (a) Visualisation of measured three-dimensional temperature distribution in the empty room under the following steady-state conditions: ventilation rate 120 m3 h−1, air supply temperature 17°C and internal heat production 300W; (b) visualisation of the 3D zone in the empty room with acceptable temperature difference 0.2°C and average temperature in a well mixed zone 23.1±0.2 oC................................................................. 61  Fig. 3-6 Temperature uniformity index (Itemp) of the empty room: (a) low ventilation rates (120–160 m3 h−1); (b) high ventilation rates (240–280 m3 h−1) with an acceptable temperature difference from 0.2 to 1°C ............................................................................ 62  Fig. 3-7 Partial contours of parameter β1 in the empty chamber: (a) front plane at the ventilation rate is 120 m3 h−1; (b) front plane at the ventilation rate is 280 m3 h−1 .......... 64  Fig. 3-8 Visualisation of the airflow pattern with smoke: (a) 120 m3 h−1; (b) 280 m3 h− ........ 65  Fig. 3-9 (a) Visualization of measured three-dimensional airspace temperature distribution in obstacle room under the following steady state conditions: ventilation rate 120 m3 h−1, air supply temperature 17 °C and internal heat production 300 W; (b) Visualisation of the 3D zone in the obstacle room with acceptable temperature difference 0.2°C, a well mixed zone 23.6±0.2 oC ................................................................................................... 67  Fig. 3-10 Temperature uniformity index of airspace (Itemp) of the obstacle chamber at (a) low ventilation rates (120–160 m3 h−1); (b) high ventilation rates (240–280 m3 h−1) ............. 68  xiii

Fig. 3-11 (a) The output of the first-order, second-order transfer function model compared with the measured airspace temperature response at the sensor position (1); (b) at the sensor position (32) in the obstacle chamber at ventilation rate 280 m3 s−1; , first order; , second order; noise line, experiment data ...................................................................... 69  Fig. 3-12 Residual plots of the first, second and third order model at the sensor position (32) in the obstacle room with the ventilation rate 280 m3 h−1 ................................................ 71  Fig. 3-13 Partial contours of parameter β1 in the obstacle chamber at the front plane with the ventilation rate 280 m3 h−1 ................................................................................................ 72  Fig. 3-14 Comparison between the temperature uniformity index of airspace (Itemp) for two values of the acceptable temperature difference 0.2°C (a) and 1°C (b); .......................... 73  Fig. 4-1 Numbered sensors in the test chamber........................................................................ 79  Fig. 4-2 Step up (a), step down (b) of dynamic experiments,(c) The measured dynamic response of airspace and air inside ball temperature from the inlet air temperature for a ventilation rate 280m-3 h-1 ................................................................................................ 80  Fig. 4-3 Schematic representation of the well-mixed zone concept in ventilated room filled with obstacles ................................................................................................................... 83  Fig. 4-4 The third order block diagram of system .................................................................... 87  Fig. 4-5 Third order fitted model and residual plot for 280 m3 h-1 inlet air flow rate (63.6 volume changes per hour): (a) position 27; (b) position 30 ............................................. 90  Fig. 4-6 Two dimensional contours of parameter β1 in the obstacle chamber at the ventilation rate 280 m3 h-1 at positions of vertical planes: (a) rear plane; (b) front plane .................. 91  Fig. 4-7 Comparison of parameter β1 at the different ventilation rates (160-280 m3 h-1) ........ 92  Fig. 4-8 Parameter α2 at several positions at ventilation rates 160 m3 h-1 and 280 m3 h-1 ...... 94  Fig. 4-9 Parameters β1 and α2 value at the difference of ventilation rates (position 33) ........ 95  Fig. 5-1 Boxes of potatoes and inserted sensor in potato Experiments .................................. 101  Fig. 5-2 Step up air inlet (a) and step down air inlet (b) of dynamic experiment ;(c) The measured dynamic response of the airspace and potato temperatures from the air temperature inlet at ventilation rate 280m3 h-1 ............................................................... 102  Fig. 5-3 Scheme of heat transfer in a selected well mixed zone containing several potatoes 105  Fig. 5-4 Third order block diagram of system ........................................................................ 109  Fig. 5-5 Temperature distribution in airspace with ventilation rate 200 m3 h-1 ...................... 112  Fig. 5-6 Temperature distribution in bulk of potatoes with ventilation rate 200 m3 h-1 ......... 112  Fig. 5-7 Dynamic temperature data at position 6 (a) and 30 (b) ............................................ 114  Fig. 5-8 Partial contour of parameter β1 (s-1) at front plane with ventilation rate 200 m3 h-1 116  Fig. 5-9 Comparison β1 and α2 at position (1) at ventilation rate from 160 to 320 m3 h-1 ... 117 

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List of symbols and abbreviations Cp,0 heat capacity of air supply, J kg-1 oC-1 Cp,buff heat capacity air in the WMZ2, J kg-1 oC-1 Cp,i heat capacity air in the WMZ1, J kg-1 oC-1 Cp,m heat capacity of air in the ball, J kg-1 oC-1 heat capacity of material, J kg-1 oC-1 K1 model parameter K2 model parameter K3 model parameter Km model parameter k1 heat transfer coefficient between WMZ1 and WMZ2, J s-1 m-2 oC-1 k2 heat transfer coefficient between buffer zone and environment, J s-1 m-2 oC-1 km heat transfer coefficient between WMZ1and inside ball, J s-1 m-2 oC-1 heat transfer coefficient between WMZ1and material, J s-1 m-2 oC-1 m mass of material, kg qc part of internal heat production entering WMZ1, J s-1 S1 surface area between WMZ1 and WMZ2, m2 S2 surface area between WMZ2 and environment, m2 Sm surface of one ball, m2 surface of one material, m2 T0(t) inlet temperature, oC t0(t) inlet temperature at small temperature perturbations about steady state, oC o T0(t-τ) supply air temperature, C o t0(t-τ) supply air temperature at small temperature perturbations about steady state, C o Tbuff(t) temperature in the buffer zone (WMZ2), C tbuff(t) buffer temperature at small temperature perturbations about steady state, oC Ti(t) temperature in the well mixed zone i (WMZ1), oC Tlab temperature of environment, oC Tm(t) temperature inside ball, oC temperature of material, oC tm(t) temperature inside ball at small temperature perturbations about steady state, oC temperature of material at small temperature perturbations about steady state, oC − temperature in the WMZ1 at the steady state condition, oC Ti −

temperature inside material at the steady state condition, oC

−

input temperature at the steady state condition, oC

Tm

T0 −

T buff V Vin V1 VOL vol buff

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buffer temperature at the steady state condition, oC part of the ventilation rate entering the WMZ1, m3 s-1 ventilation rate, m3 s-1 volume of well mixed zone, m3 considerable volume, m3 volume of the buffer zone WMZ2, m3 volume of air in the WMZ1, m3

3 volm volume of potato, m -1 ζ ratio of volume and surface of material, m ε porosity of bulk material

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α1 model parameter -1 α2 parameter related to overall heat transfer coefficient, s β1 γ0

γbuff γi γm

cooling rate, s-1 local volumetric concentration of fresh air rate, s-1 density of air supply, kg m-3 density of air in the buffer zone (WMZ2), kg m-3 density of air in the WMZ1, kg m-3 density of air in the ball or density of material kg m-3 density of material kg m-3

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1 Chapter 1 Introduction and Objectives

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Chapter 1 Introduction and Objectives 1.1 Introduction Heating and cooling are common thermal processes in the post harvest and food industry. These thermal processing techniques are widely used to maintain quality and safety of food products and to extend shelf life of products (Wang & Sun, 2003). During heating/cooling applications, temperature, particularly the fluctuating temperature during the process, was found to be a major factor contributing to product losses during processing, storage and distribution of food (Vigneault et al., 2006). Postharvest losses of horticultural crops are estimated to be as high as 25% to 50% of the production due to poor postharvest handling techniques, mainly poor temperature management (Nunes & Emond, 2003).

In post harvest, temperature is the variable of the postharvest environment that has the greatest impact on the storage life of vegetables (Nunes & Emond, 2003). Keeping fruits and vegetables within their optimal ranges of temperature and relative humidity is the most important factor in maintaining their quality and minimizing postharvest losses (Michael Knee, 2002). Lower temperatures may cause chilling injury (the lowest safe temperature depend on the type of fruit or vegetable, e.g. lower than 11.5-13oC for bananas, 2-3oC for apples, 3oC for oranges, etc. (Wang, 2004)), and higher temperatures can reduce the storage life of the product. Kader (1991) reported that every 10°C increase in temperature accelerates deterioration and the rate of loss in nutritional quality by two to threefold. In storage of meat, Olafsdottir et al. (2006) found that reducing the storage temperature of cold fillets from 1.5oC to 0.5oC increased the minimum sensory life from 12.5 to 15 days.

The variation of temperature as a function of time or fluctuating temperature in processes is also a problem that needs to be controlled during heating and cooling. The temperature variability caused by poorly designed or controlled heating, ventilating, and air conditioning 3

(HVAC) equipment, is often taken into account by the evaluation of safety factors. In the storage of grain, temperature fluctuations may result in increased water loss, and condensation may develop on the product from the surrounding air, leading to the growth of microorganisms (Wills et al., 1998). Temperature fluctuations cause different other problems in relation to food storage and processes. They cause heat shock proteins in living cells in the post harvest of fruits and vegetables resulting in variation of the rate of moisture losses (Morimoto et al., 2003). The shelf life of frozen food is a complex concept that depends on the characteristics of the food product and the environmental conditions (Giannakourou et al., 2006). When temperature fluctuations occur during frozen storage, the crystal ice in a system will be varied (increasing the size or amount of ice crystal) (Reid, 1997) and influence the quality loss during frozen storage (Giannakourou et al., 2006) (e.g. moisture absorption and redistribution in foods, drip loss during thawing etc.). Additionally, the variation of temperature is also a cause of the growth of different pathogen particles as micro-bacteria and other deteriorations in the cold chains (Bogataj et al., 2005). In thermal processing, the variation of temperature with 1oC will lead to the change about 25% in the process lethality (Lewis, 2006). The retort temperature changes occasionally during the production. This results in an incomplete sterilization of the cans, which could lead to growth of nonpathogenic spoilage organisms or to toxic production of Clostridium botulinum. Therefore, temperature deviations represent a possible threat to the health of the consumer as well as to the economic survival of the food processor (Houlzer and Hill, 1977).

The spatial variation of temperature or the three dimensional distribution of product temperature in a process room during the heat treatment, is strongly dependent on the uniformity of the environment because of heating and cooling actions. In many cases, environmental temperature and fluid flow velocity around the products are not

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homogeneously distributed throughout the volume of a process room. This results in an imperfect mixed fluid, and a non-uniformity of the product temperature occurs during the heat treatment (Sun, 2007).

Uniformity of product temperature is one of the most important considerations in food processing. Non-uniform temperature distributions during heating, cooling, and storage may reduce the quality of food, safety level and thus cause economical losses. For example, in thermal processing of food, uniform heating is desirable to achieve a predetermined level of sterility with minimum destruction of the colour, texture, and nutrients of food products (Sun, 2007). Thermal equipments always contain regions in which the temperature of the heating medium is lower than the control temperature due to poor circulation of steam or steam/air mixtures (Tucker et al., 2001), Smout et al. (2000) reported that the coefficient of variation ranging from 14.9% to 63.1% for the thermal death time (F values) at different positions within the retort. DHSS (1994) suggested that the medium temperature should be the same for all the containers within the process vessel to within 0.5oC (no two points should be more than 1oC apart). In grain storage, the temperature difference within the grain bulk causes natural convection within the grain bulk, which results in moisture movement from a high to a low temperature area, and increases the chances for the distribution of insects, mites and fungi and thus brings about the deterioration of grain quality (Brooker et al., 1992, Canchun et al., 2000).

Consequently, control of 3D uniformity of product temperature during heating/cooling applications need to be realised to: - Reduce the product temperature gradient to control exact reactions occurring in food during the processing (inactivate microorganism, biological and chemical reactions, etc).

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- Control the hazard and food loss due to the non-uniformity of the temperature like coolest or hottest points because of inadequate heating and cooling (prevent a local heat respiration, chilling injury, air movement, etc.). - Optimize the process to save energy and to prevent weight loss during the heat treatment (Simpson, 2004, Canchun et al., 2000). - Create products coming to market with uniform characteristics.

Several mathematical modelling approaches have been applied to model temperature distribution in food processes and storage (i.e. Computation fluid dynamic (CFD), zoned models, multi zoned model, data based modelling, etc.). In these methods, CFD (based on the continuity equation and the set of the Navier-Stokes equations) offers a powerful design and analysis tool for the agri-food industry (Sun, 2002). Zoned modelling (based on the conservation equations of mass and energy to each cell where the air is treated as a perfect gas (Daoud and Galanis, 2007)) is used for predicting indoor temperature in a displacement ventilated room (Song et al., 2008). Data based modelling (based on quantitative data analysis) is a tool for predicting and control. Table 1.1 shows that most studies focused on modelling the temperature distribution to predict 3D airspace temperature and airflow pattern for optimal design under steady state conditions (i.e. Hoang et al. (2000), Nahor et al. (2005), Mirade and Picgirard, (2006), etc.) and unsteady state conditions (i.e. Ozcan et al. (2003), Therdthai et al. (2004)). In these studies, uniformity of medium temperature was used as a condition to realise the uniformity of product temperature. In reality however, there is no unique relationship between the uniformity of product temperature and medium temperature because of the local differences in the heat transfer coefficient.

6

Dynamic modelling of the temperature of a process room filled with biological products was introduced in several studies. Mirade (2003) used a two-dimensional computational fluid dynamics model with time-dependent boundary conditions (i.e. an unsteady model). The CFD code Fluent v.5.4.8 was used to build a numerical model in this research. The homogeneity of the distribution of the air velocity in an industrial meat dryer was discussed and this research provided a rational approach to help in the operation and design of modern dryers. A three-dimensional computational fluid dynamics (CFD) model with moving grids was developed by Therdthai et al. (2004) to simulate the dynamic response during an industrial continuous baking process. This model can be used to optimise temperature profile in design to reduce the variations in product quality. Verdijck (1999), Verdijck and Straten (2002), Verdijck et al. (2005) developed a control methodology for model-based product quality control applied to climate controlled processing of agro-material. Model Predict Control (MPC) algorithm was used based on the non-linear control algorithm. This is the local controller to optimise energy efficiency without harming the product, and can be applied in storage, transportation, and drying processes etc. This model is limited to control directly the product quality (e.g. sugar in potato storage) and its quality variation in local climate controlled operations (e.g. optimisation of temperature), there is no information about the control input. Van Brecht et al. (2003) developed a control algorithm to increase the 3D uniformity in temperature during the entire incubation process. The uniformity of air temperature, airflow pattern and air quality are factors that need to be controlled in this process. The effect of heat flow direction to eggs was also considered in this research, a heat transfer coefficient was obtained from the air velocity, physical characteristics of air and egg, and temperature difference between air and egg. In practise, it is quite impossible to place a sensor exactly perpendicular to the airflow direction in a porous medium. The air circulation is continuously changing direction and the measuring device insertion generally disturbs the

7

air pathway (Alvarez and Flick, 1999). Additionally, it is not easy to measure the egg temperature during the incubator process.

From the state of the art in literature (see Table 1.1), we can see that 19 of 32 existing models for this problem are focussing on temperature in steady state conditions. Out of 19 models in literature, only seven models handle the dynamic behaviour of temperature but only six models were used for control purposes. No model was developed to control 3D temperature distribution in the bulk of products in heating/cooling operations.

From this literature survey, we can conclude that no dynamical models have been used that focus on controlling the dynamic behaviour of 3D temperature distribution in the bulk of products during heating/cooling processes and that contain physically meaningful parameters.

8

Table 1-1 Researches related to the improvement of product temperature during heat treatments No.

Authors

1

Alvarez & Flick, 1999

2

Alvarez & Trystram, 1996

3

Canchun et al., 2000

4

Gill et al., 1996

5

Feustel & Dieris, 1991 Hoang et al., 2000

6 7

Inard et al., 1996

8

Fukuyo et al., 2003 Keesman et al., 2003

9

Studies

Objectives

Design

Predict

Control

Analysis of heterogeneous cooling of agricultural products inside bins Part I: aerodynamic study Design of a new strategy for the control of the refrigeration process: fruit and vegetables conditioned in a pallet

Analysis air flow pattern to improve the uniformity of airspace temperature

Yes

No

Using numerical model to describe the refrigeration process between the air and agricultural products. Finding the hottest and coldest points to control over treatment Finite element method to calculate the temperature distribution in airspace during storage Using temperature history in the microbiology model to control product quality during storage

Yes

Finite element prediction of transient temperature distribution in a grain storage bin Control of product temperatures during the storage and transport of bulk containers of manufacturing beef. A survey of air flow models for multizone structures Analysis of the air flow in a cold store by means of computational fluid dynamics Prediction of air temperature distribution in buildings with a zonal model Thermal uniformity and rapid cooling inside refrigerators Optimal climate control of a storage facility using local weather forecasts

Dimension

Dynamic

No

Air space or products Airspace

3D

No

Yes

Yes

Airspace

-

No

Yes

Yes

No

Airspace

2D

No

No

Yes

Yes

Products

Random points

No

Zonal model

Yes

Yes

No

Airspace

3D

No

CFD to calculate air flow pattern in cool store

Yes

Yes

No

Airspace

3D

No

Calculation of mass air flows between two zones based on zonal method Using CFD to calculate the temperature distribution Optimal climate control of a potato storage facility by controlling air inlet

Yes

Yes

No

Airspace

3D

No

Yes

Yes

No

Airspace

3D

No

No

Yes

Yes

Point

No

9

Table 1.1 Researches related to the improvement of product temperature during heat treatments (Continuous) No.

Authors

Studies

Objectives

Design

Predict

Control

Find a spatial homogeneity of the air velocities above the product based on the pressure profiles and the air velocities in the drying chamber by CFD Predict air velocity and optimize design by using CFD method

Yes

Yes

Yes

Predict 3D temperature and velocity profiles in baking process

10

Mathioulakis et al., 1998

Simulation of air movement in a dryer by computational fluid dynamics: Application for the drying of fruits

11

Mirade and Picgirard, 2006

12

Mirade et al., 2004

13

Mirade, 2003

14

Moureh et al., 2002

15

Moureha & Flick, 2004

16

Nahor et al., 2005

Improvement of ventilation homogeneity in an industrial batch-type carcass chiller by CFD investigation Characterization and CFD modelling of air temperature and velocity profiles in an industrial biscuit baking tunnel oven Prediction of the air velocity field in modern meat dryers using unsteady computational fluid dynamics (CFD) models Numerical and experimental study of airflow in a typical refrigerated truck configuration loaded with pallets Airflow pattern and temperature distribution in a typical refrigerated truck configuration loaded with pallets CFD model of the airflow, heat and mass transfer in cool stores

Dimension

Dynamic

No

Air space or products Airspace

3D

No

Yes

No

Airspace

3D

No

Yes

Yes

No

Airspace

3D

No

the homogeneity of the distribution of the air velocity in an industrial meat dryer by using CFD

Yes

Yes

No

Airspace

2D

Yes

Using CFD to improve and to optimise air-distribution systems in refrigerated vehicles

Yes

Yes

No

Airspace

3D

No

Using CFD to improve and to optimise air-distribution systems in refrigerated vehicles

Yes

Yes

No

Airspace

3D

No

Using CFD to calculate velocity, temperature distribution in cool stores. Using model to predict airspace and product temperature

Yes

Yes

No

Airspace

3D

No

10

Table 1.1 Researches related to the improvement of product temperature during heat treatments (Continuous) No.

Authors

Studies

17

Ozcan et al., 2005

18

Smout et al., 2000

19

Therdthai et al., 2004

20

Várszegi, 2001 Van Brecht et al., 2003

Predicting 3D spatial temperature uniformity in food storage systems from inlet temperature distribution Non-uniformity of lethality in retort processes based on heat distribution and heat penetration data. Three-dimensional CFD modelling and simulation of the temperature profiles and airflow patterns during a continuous industrial baking process Modelling cooling methods for horticultural produce. Quantification and control of the spatiotemporal gradients of air speed and air temperature in an incubator. A modelling and control structure for product quality control in climate-controlled processing of agro-material Optimisation of product quality and minimisation of its variation in climate controlled operations Direct product quality control for energy efficient climate controlled transport of agromaterial

21

22

Verdijck & Van Straten, 2002

23

Verdijck et al., 2005

24

Verdijck et al., 2005

Objectives

Design

Predict

Control

Dimension

Dynamic

No

Air space or products Airspace

Control air space

No

Predict

3D

Yes

Relation of non-uniformity of environment and non-uniformity of product temperature.

Yes

No

No

Products

3D

No

Using CFD to predict temperature distribution in baking process

Yes

Yes

No

Airspace

3D

Yes

Calculate cooling rate

Yes

Yes

No

Products

1D

No

DBM to control airspace temperature

Yes

Yes

Yes

Airspace

3D

Yes

Control airspace temperature in storage room in relation to product quality parameters

No

Yes

Yes

Products

Point

Yes

Direct control of product quality of agro-material and minimisation of its quality variation Control product quality by climate control

Yes

Yes

No

Airspace

1D

No

No

Yes

Yes

Airspace

Point

Yes

11

Table 1.1 Researches related to the improvement of product temperature during heat treatments (Continuous) No.

Authors

Studies

Objectives

Design

Predict

Control

25

Verdijck, 1999

Yes

Verboven et al., 2000

Optimal storage conditions based on a model of product quality under an effect of the storage conditions. CFD to predict the temperature distribution in oven

Yes

26

Yes

27

Vigneault C., 2005

Calculate air velocity based on the cooling rate value

28

Delgado and Sun, 2001

29

Janssens ,1999

30

De Moor, 1996

Model-based product quality control for a potato storage facility Computational fluid dynamics modelling and validation of the temperature distribution in a forced convection oven A new approach to measure air distribution through horticultural crop packages. Heat and mass transfer models for predicting freezing processes – a review Dynamic modelling of heat and mass transport in imperfectly mixed fluid: A comparison of two approaches Modelling and control of energy and mass transfer in imperfectly mixed fluid

31

Berckmans et al., 1992

Methods to predict moisture and temperature in product during freezing process Using Data based mechanistic modelling approach to modelling the spatio-temporal temperature distribution in an empty room. Dynamic modelling approach was used to evaluate the dynamic behaviour of the microenvironmental factors (temperature and humidity) within an imperfect mixed space. Data based mechanistic model to find a physically meaning parameter to control 3D imperfectly mixed spaces

32

Patrick et al., 1995

New model concept to control the energy and mass transfer in a three-dimensional imperfectly mixed ventilated space Climatic Control of a Storage Chamber Using Fuzzy Logic

Using fuzzy logic for the control of MIMO in storage chamber (temperature and humidity of airspace)

12

Dimension

Dynamic

Yes

Air space or products Product

1D

Yes

Yes

No

Airspace

3D

No

Yes

Yes

No

Products

3D

No

No

Yes

No

Products

Point

-

No

Yes

Yes

Airspace

3D

Yes

No

Yes

Yes

Airspace

3D

Yes

No

Yes

Yes

Airspace

3D

Yes

No

No

Yes

Airspace

-

-

There are many methods to control a process. The Model predictive control (MPC) is an advanced method of process control (usually understood as techniques more advanced than a standard PID control (Tatjewsky et al., 2007)) that has been used in the process industries since the 1980s, such as in chemical plants and oil refineries. Models used in MPC include white-box models, black-box models, and grey-box models (some physical insight is available, but several parameters remain to be determined from observed data).

Several reasons to use MPC were listed by Tatjewski (2007). -

Firstly, the MPC algorithms can directly take into account constraints on both process inputs and outputs, which often decide on the quality, effectiveness, and safety of the production.

-

Secondly, they generate process inputs taking into account internal interactions within the process, due to the direct use of the model. Thus, they can be applied to processes with difficult dynamics and to multivariable control, even when numbers of manipulated and controlled variables are uneven.

-

Thirdly, the principle of operation of these algorithms is comprehensible and relatively easy to explain to engineering and operator staff, which is a very important aspect when introducing new techniques into industrial practice.

Using the model predictive control concept to control the uniformity of 3D product temperature in process room is shown in Fig. 1.1.

13

Control output 3D temperature of the bulk of products Control inputs -Ventilation rate -Inlet temperature

Measuring

Measuring Dynamic Modelling

Physically meaningful parameters for control

Model Predictive Control (MPC)

Fig. 1-1 Scheme of model predictive control of 3D temperature distribution in a room filled with biological product In Fig. 1.1, to control the 3D temperature of the bulk of products we need: (1) To use real time feedback of 3D product temperature by using multiple sensors to obtain product temperature during processing, (2) To predict the 3D product temperature at several positions in the process room by changing inputs, (3) To use a model predictive controller to control 3D product temperature distribution.

To control the product temperature at a specific position in a process room, we can use a single temperature sensor with a feedback loop in a temperature or ventilation rate controller with a black-box model. To control the uniformity of 3D product temperature in a process room, all product temperatures in 3D should be measured by the controller. This is not realistic in practice, especially in case of biological products (damage of product due to the high respiration rate and internal heat production when temperature sensors are inserted inside products). To avoid damaging of products, product simulators (Vigneault et al., 2002) can be 14

applied but without physically meaningful parameters in a model, it is impossible to predict and control the product temperature around simulators.

The Data Based Mechanistic (DBM) model approach has been shown to allow accurate modelling (e.g. De Moor and Berckmans, 1993; Janssens et al., 2000) which was applied to the problem of modelling imperfect mixing in the forced ventilated buildings (Janssens et al., 2004), cars (Quanten et al., 2004), incubators (Van Brecht et al., 2002). This approach is unique for controlling imperfectly mixed fluids since it is a hybrid between the extremes of mechanistic and data based modelling, and provides a physically meaningful description of the dominant internal dynamics of heat and mass transfer in the imperfectly mixed fluid. Physically meaningful parameters obtained from DBM could be used to predict and control 3D temperature distribution in ventilated room. The dynamics models from Berckmans et al. (1992a,b), De Moor (1996), Janssens (1999), and Van Brecht (2004) were developed from the heat and mass transfer in an empty room (heat transfer from airspace to products is neglected). Therefore, the ability of models was limited in an empty room and in a room filled with biological products where energy transfer from airspace to material is not important (i.e. in egg incubator). So far, it is impossible to predict product temperature and control dynamic behaviour of the 3D product temperature during cooling/heating processes.

15

1.2 Objectives The general objective of this PhD is to study the possibility of real time monitoring and control of the three dimensional (3D) temperature distribution in a room filled with biological products to improve the uniformity of product quality during heating/cooling applications.

The first objective consists of investigating the 3D temperature distribution in a ventilated room filled with obstacles and analyse the effect of the varying inlet temperature and ventilation rate on the dynamic behaviour of the 3D temperature distribution the airspace (airspace was defined as air surrounding the products in Figure 1.2) and the product temperature. Energy exchange between airspace and products Air inlet Product Product Product

Airspace Product Product

Air outlet

Volume of well-mixed zone voli

Product Temperature Tp(t)

Airspace Temperature Ti(t)

Figure 1.2 Fig. 1-2 Energy exchanges in the Well Mixed Zone (WMZ)

16

The second objective focuses on developing a model for controlling the 3D temperature distributed in airspace and product temperature by air inlet temperature.

The third objective is to find physical meaningful parameters in the model for the dynamic behaviour of the 3D temperature distribution in the airspace and product temperature that could be used for control purposes.

17

1.3

Brief outline of next chapters

In previous studies the dynamic response 3D distribution of the air temperature was studied in empty rooms and in incubators. Second order transfer function models were made with physical meaning in the parameters. These models were made for control purposes and this mainly to control the uniformity of airspace temperature in a building, car, incubator, etc. In these models however the heat transfer from the airspace to the products is not considered. Consequently so far it is not possible to control the 3D temperature distribution of the product by using control inputs.

The main objective of this research is the real time modelling of the dynamic response of 3D temperature distribution of the product in conditioned rooms filled with biological products. In order to archive to this objective, this PhD works is organized as follows

In chapter 1 a literature review is given of existing models in the field of ventilation and control of temperature distribution in conditioned process rooms and ventilated buildings. This will lead to a more detailed formulation of the objectives of this thesis.

Chapter 2 describes the test installations and the modelling methods that were used in this research. - First we did measurements in an empty ventilated room equipped with all sensors and requirements to measure and visualise dynamic responses of 3D temperature distribution to variations of the air inlet temperature. - Than the room was filled with obstacles with regular shape and well known characteristics: plastic balls. In a next step these balls were filled with water to increase the 18

complexity of the heat transfer in the system. After this we did experiments with real biological products (potatoes, apples) to gain mechanistic understanding of the process. In a last step we used different size and type of balls for validation purposes. - A simplified refined instrumental variable method (SRIV) will be used to estimate the parameters in a fitted model that related the control inputs to the temperature distribution in the room. - A Data based mechanistic model was used to explain the physical meaning of the parameters in the model.

In chapter 3, the three-dimensional temperature distributions in a ventilated empty room and a room filled with obstacles are compared experimentally to evaluate the presence of stored products, on the temperature uniformity. During experiments, step inputs in inlet air temperature are applied and temperature responses at 36 sensor locations in the room are recorded to develop a data-based mechanistic (DBM) model of the temperature response at different positions in the room. To study the influence of stored product and obstacles on 3D temperature distribution we had to start with the modelling of an empty room for comparison reasons.

In chapter 4, a data-based mechanistic model for temperature responses at different positions in both airspace and obstacles was developed. Plastic balls with known characteristics are used as obstacles. Step increases in air inlet temperature are applied while the airspace temperature and the air inside the balls are recorded. Using a compact model several physically meaningful parameters are found to represent the temperature distribution in the airspace and in the obstacles as well. This is different from all work that has been done in the past with the well mixed zone principle. 19

In chapter 5, a data-based mechanistic modelling approach is developed for room filled with real biological products. Boxes of potatoes are used as biological material. Step inputs on an air inlet temperature were applied while airspace and the dynamic responses of potato temperatures were recorded. Several physically meaningful parameters are found to present the temperature distribution in airspace and in the bulk of products.

In chapter 6, the evaluation of the model and an example of using a data based mechanistic model in case of the cooling of apples. Two methods to calculate the cooling rate are conducted and the comparisons of the estimated cooling rate and heat transfer coefficient are made.

Finally, the main conclusions and suggestions for further studies will be formulated in chapter 7.

20

2 Chapter 2 Materials and Methods

21

22

Chapter 2 Materials and Methods 2.1 Introduction First the 3D temperature distribution was modelled in an empty room based on temperature measurements in 36 positions in dynamic experiments. Then, the room was filled up with obstacles. To have obstacles with well known characteristics and similar shape plastic balls filled with air where used. To study the increase of the model order the ball in next step where filled with water this implies a new thermal buffering capacity For validation experiments a different size of ball with water was used to test the model performances in a new situations. 2.2 Technical descriptions Two installations (Figs. 2.1 and 2.9) were used in this research. They were installed at the Laboratory of Measure, Model & Manage Bioresponses (M3-BIORES), Katholieke Universiteit Leuven, Belgium. For the model development, the test chamber in Fig. 2.1 was used. This chamber is based on the test installation which was described in several publications (e.g. De Moor & Berckmans, 1996; Price et al., 1999; Van Brecht et al., 2000, 2004; Young et al., 2000; Zerihun Desta et al., 2004, 2005; Özcan et al., 2005; Van Buggenhout et al., 2005, 2006), with some adaptations, as described below.

The laboratory test chamber (Fig. 2.1) was a mechanically ventilated room with a length of 3 m, a height of 2 m, a width of 1.5 m and a volume of 9 m3. It has a slot inlet (Fig. 2.2) in the left sidewall just beneath the ceiling. The slotted air inlet, which has a width of 0.6 m and a height of 0.036 m, was positioned 1.55 m above the floor. The initial direction of the incoming air jet is not horizontal, but downward. The inlet angle with the horizontal is -10°. On the floor of the test installation, 12 large tubes with a diameter of 90 mm were installed (Fig. 2.3) and were connected to the air outlet (Fig. 2.4). These tubes were perforated with 24 holes with a diameter of 0.01 m and the holes positions were as in Fig. 2.5. A series of five 23

aluminium-heating elements (300 W totals) was installed at the bottom to physically simulate the internal heat production

An envelope chamber of length 4 m, width 2.5 m and height 3 m was constructed around the test chamber to minimise disturbing effects of varying laboratory conditions (fluctuating temperature, opening doors, etc.). The enveloping chamber was not ventilated. The volume of the buffer zone was 21 m3. The main test room and the envelope chamber were both constructed of transparent plexiglas in order to be able to visualise the airflow pattern. The thickness of the plexiglas walls is 0.075 m. The heat conduction coefficient is 0.16 W m-1 oC-1.

.

24

2.5m

3m

1.5m

  Thermocouples 3m

 

Air inlet 0.036m

0.8m

0.6m

Rear sensor plane

Front sensor plane

2m

1.6m 1.55m

0.4m

Heat generation elements

Air outlet

Holes Φ 0.01m

Ducts Φ 0.09m

Fig. 2-1 First of the laboratory test installation

25

Envelope chamber

Fig. 2-2 Slot of air inlet

Fig. 2-3 Air outlet systems

Fig. 2-4 Air outlet tube

0.04m

Φ 0.09m 0.1m

Φ 0.01m

Fig. 2-5 Holes on the air outlet system

26

The laboratory test chamber was provided with a mechanical ventilation system. The air was extracted from the laboratory by a centrifugal fan. To achieve a desired ventilation rate, a movable cone was used (Fig 2.6). The position of the cone was regulated by a computercontrolled step motor.

Fig. 2-6 Control of the ventilation rate through the test room The mechanical ventilation system enables an adequate control of the ventilation rate in the range 70 - 420 m3 h-1 and this with an accuracy of 10 m3 h-1. These ventilation rates result in rather high inlet velocities (0.44 - 2.61 m s-1), air refreshment rates (7.6 - 46.6 refreshments per hour), and Reynolds numbers (1837 - 11021 at the inlet section of the test chamber). The high Reynolds numbers indicated that turbulent airflow prevails in the ventilation chamber (Welty et al., 1984).

The ventilation rate was measured in the supply duct from the pressure drop over an orifice and feedback to the ventilation PID-control system. The measurement error is 10 m3 h-1. To avoid that the thin plexiglas walls of the test chamber are subject to overpressure during the experiments (up to 100 Pa at a ventilation rate of 300 m³ h-1), an exhaust fan was provided in the outlet terminal.

A heat exchanger (Fig. 2.7 (b)) was provided in the supply air duct to regulate the temperature of the inflowing air. The supply air temperature is measured by a thermocouple in the inlet 27

section of the test chamber (in range 10 - 30°C), which was fed back to the on/off control system.

(a)

(b)

Fig. 2-7 Cooling unit (a) and heat exchanger (b) To measure the spatio-temporal temperature distribution in the test chamber, 36 temperature sensors were positioned in a 3-D measuring grid covering a large part of the room. The configuration of the 3-D sensor grid consisting of temperature in the test chamber was shown more detailed in Fig. 2.8. Air inlet

34

28

22

10

16

4 0.8m

35 31

29 25

23 19

11

17 7

13

5 1 0.8m

36 Height

30

24

12

18

6

32

26

20

14

8

2

33

27

21

15

9

3

Width 0.5m

0.8m Air outlet

0.375m

0.4m Length Front plane

Rear plane

Fig. 2-8 Numbered sensors in the test installation 28

The sensors are located in two vertical xy-planes: a front sensor plane (0.375 m from the front wall) and a rear sensor plane (0.375 m from the back wall) (Fig. 2.1). The temperature sensors have an average accuracy of respectively 0.1°C. The time constant of the sensors is less than 3 seconds. In addition to the 3-D distribution of temperature, the ventilation rate and the temperature of the supply air, the buffer zone temperature and the laboratory air temperature were measured during the experiments. A measurement and data collection unit (DATASCAN 7000, Measurement System Ltd.) with 192 channels was used for the data acquisition. The measurement frequency of the data logger can be programmed up to 400 readings per second.

This thesis is focusing on the 3D temperature distribution (bulk products and its surrounding air) in a ventilated process room filled up with obstacles. The hypothesis is that the 3D temperature distribution in airspace and products (defined in chapter 1) results mainly in an air mass flow through the obstacles and the interaction with the product temperature.

In the first step, the objective was to analyse whether the data based mechanistic model (DBM) method as developed for an empty room, could be applied in a ventilated room filled with obstacles. To have similar identical and well known obstacles, we used balls as obstacles in the first series of experiments. The second series of experiments potatoes in boxes were used.

29

Inlet

Ball Temperature sensor Outlet Heat generation element

Duct

Fig. 2-9 Room filled with balls The empty room was first filled with 480 plastic balls (Fig. 2.9), each with a diameter of 0.19 m and a weight of 0.12 kg to physically simulate uniform obstacles. These obstacles represented the physical presence of material in heating/cooling processes. The porosity, defined as airspace divides to total bulk volume in this experiment, was approximately 0.27. Later 144 boxes of potatoes (Fig. 2.10), each box (0.4 x 0.6 x 0.3 m) containing approximately 4.17 kg of potatoes (total 480 kg of potatoes), were used as biological products in heating/cooling applications. Product temperatures were monitored by an inserted thermocouple at the centre of a product (Figs. 2.11 and 2.12) with a Keithley 2700 data logger system. These measured potatoes were close to thermocouples that measured the temperature in the airspace.

30

Fig. 2-10 Room filled with boxes of potatoes

(a)

(a) Randomised balls in room

(b)

(b) Inserted thermocouple in the ball

Fig. 2-11 Position of balls in the test room and measuring air temperature inside the ball

(b)

(a)

(a) Potatoes in boxes

(b) Inserted thermocouple in the potato

Fig. 2-12 Product temperature measurements

31

To be able to modelling the heat exchange between airspace and products (in a large room was not enough energy to transfer to the products, therefore, the dynamic response is too low (See Fig. 2.17)), a uniform zone was selected in a small test installation (Fig. 2.13). This is a transparent mechanically ventilated room (located in the large test installation as described above) with 0.85 m (length) x 0.6 m (width) x 0.85 m height. It has a slot inlet (width 0.6 m and height 0.036 m). Ten T type thermocouples were installed in this test installation to measure inlet (one sensor), airspace (4 sensors), product (4 sensors) and buffer zone (one sensor) temperature. A Keithley 2700 data logger system was used for data recording. In this experiment, the air supply system used was the same as in the big room. The ventilation rate was adjusted by an air-extracted system (open and close system) to maintain the same ranges of ventilation rate through material in a big chamber (Fig. 2.14).

32

0.85m Air inlet

0.036m

0.4m 0.6m

Extracted air

0.85m

0.6m Sensor positions

Air extracted system

Air outlet

Fig. 2-13 Test installation for validating the obtained model

Fig. 2-14 Air extracted system To compare the obtained physically meaningful parameters (which related to heat transfer coefficient) by different methods and calculate the values of heat transfer coefficient based on the obtained physically meaningful parameters and the known physical characteristic of material. The room was filled with the table tennis balls (with pure water inside as known physical characteristic) was used and apples as an example for real biological products.

33

2.3

Materials and methods

2.3.1. Material In this research, two groups of material were used to develop and validate the models. Firstly, a group of non-biological products with known thermal characteristics were used, 480 plastic balls with diameter 0.19 m replaced the biological products to find a fitted model with physically meaningful parameters in a process (air inside the balls as a product temperature). Secondly, a room filled with 144 boxes of potatoes was used as a biological product. Finally, balls with diameter 0.04 m were filled with pure water as a well-known physical characteristic to validate the best-fitted model. Finally, biological products (apples) were used as an example for room filled with biological products.

The physical characteristics of materials are shown in Table 2.1 Table 2-1 Physical characteristics of materials used in this research Material

Number

Porosity

Experiments

0.2 per ball

480

0.27

(1), (2)

0.04

0.035

160

-

(4)

Potatoes

-

480 total

-

0.29

(3)

Apples

-

50 total

-

-

(4)

Plastic balls

Colour

Red,

Thickness

Diameter

Weight

(mm)

(m)

(kg)

1

0.19

0.45

yellow, blue, black (Fig. 2.9) Water filled

White

plastic balls

34

2.3.2. Methods 2.3.2.1 Research methods Data based mechanistic (DBM) modelling approach was applied to estimate the 3D temperature distributions in a room filled with biological products from the inlet air temperature.

Four steps of this study were conducted in this thesis (see Fig. 2.15.) (1) Adapting a data based mechanistic model approach from an empty room to a room filled with obstacles. In this test, air inside the ball was assumed as airspace in a test chamber and DBM was applied to model the dynamic response of airspace from inlet air temperature. If, it is able to model this process, the fitted model should be suggested. (2) Developing a data based mechanistic model for a room filled with plastic balls as obstacles, analysing the heat exchange from the environment to air inside the balls to find physically meaningful model parameters. (3) Developing a data base mechanistic model for a room filled with biological products, analysing the heat exchange from the environment to biological products (solid material) to find a physically meaningful parameter for online predicting the product temperature and real time control of 3D product bulk temperature in heating/cooling applications. (4) Evaluating the ability of the model can be used for cooling of biological products.

35

1

Testing a well mixed zone approach in ventilated room filled with non biological products

2

Data based mechanistic model development for room filled with non biological products

Order transfer function Physically meaningful parameters

3

Extending Data based mechanistic model for room filled with biological products

Physically meaningful parameters

4

Evaluating the ability of the model

Suggestion the order of the transfer function can be applied

Fig. 2-15 Researching methods to control 3D product bulk temperature in heating/cooling applications 2.3.2.2 Data collection To obtain dynamic data sets for dynamic modelling, dynamic step up (a) and step down (b) of air inlet temperature (Fig. 2.16) were conducted with different step changes depending on each experiment while maintaining the airflow rate constant. The inlet, airspace and product temperature profiles at a specific ventilation rate and certain position in test installation is

Temperature, oC

Temperature, oC

illustrated as an example in Fig. 2.17.

17

11

17

11

(a) 2000

Time, s

(b) 2000

10000

Time, s

Fig. 2-16 Step up (a) and step down (b) experiments: Inlet temperature setting; measured response

36

10000

o

Temperature ( C)

22 21 20 19

Inlet air temperature 0

100

200

300

400

500

600

700

500

600

700

500

600

700

Time (min)

o

Temperature ( C)

25 20 15

Airspace temperature 10

0

100

200

300

400

25

o

Temperature ( C)

Time (min)

20 15

Potato temperature 10

0

100

200

300

400

Time (min)

Fig. 2-17 Step up inlet air temperature and dynamic temperature changes in airspace and potatoes at ventilation rate 280 m3 h-1

2.3.2.3 Data Based Mechanistic (DBM) modelling approach In biological research, most of the time researchers use so-called mechanistic model to modelling processes. When scientists are observing the reality and developing a mechanistic mathematical model, they look though the glasses of their knowledge and education to decide what different model pair should be used to describe the complex reality. The disadvantage, however, is that in most cases, due to the complexity of the studied systems, this mostly results in very complex model structures with many parameters. For design purposes, this might be interesting since sensitivity analysis can be done. The disadvantage of this approach is that too many parameters are difficult to be given a correct value in real time modelling for control purposes. Another limitation is that the researcher is limited by his knowledge to discover new insight since he is projecting his existing knowledge in reality.

37

Another method for modelling process is “Data based mechanistic modelling”. This term was first used in Young & Lees (1993) but the basic concepts of this approach to model dynamic systems were developed over many years. This method was developed originally to analyse measured time-series data particularly in relation to signal processing, forecasting, and automatic control systems (Young & Chotai, 2001).

To determine the physical nature of an imperfectly mixed fluid based on experimental data. The Data Based Mechanistic (DBM) model approach has been shown to allow accurate modelling (e.g. De Moor and Berckmans, 1993; Janssens et al., 2000) which was applied to the problem of modelling imperfect mixing in the ventilated buildings (Janssens et al., 2004), cars (Quanten et al., 2004), etc. This DBM approach is unique for controlling imperfectly mixed fluids since it is a hybrid between the extremes of mechanistic and data based modelling and provides a physically meaningful description of the dominant internal dynamics of heat and mass transfer in the imperfectly mixed fluid (Berckmans and Goedseels, 1986; Berckmans, 1986; Berckmans et al., 1992).

Van Brecht (2004) listed the advantages of data based mechanistic modelling in Table 2.2

38

Table 2-2 Comparison between mechanistic, data based and data based mechanistic modelling Mechanistic approach (M) + Physical insight Suited for Design

High computational power Validation problem Not suited for control

Data based approach (DB)

+ Low No physical computational insight power Suited for Not suited for control design No validation problem

Many assumptions: turbulence model, boundary Conditions

Data based mechanistic approach (DBM) + Physical Not suited for insight design Suited for control Low computational power No validation problem

The main difference from data based ‘black box’ models and data based mechanistic models require a mechanistic interpretation. Data based mechanistic modelling is a model identification technique consisting of two phases (Fig. 2.18).

39

Dynamic Dynamic data data

Identification Identification experiments experiments

Identification Identification of of minimally minimally parameterised parameterised model model

Physical Physical knowledge knowledge

Physical Physical interpretation interpretation of of the the identified identified model model

No

1 Data Data based based phase phase

2 Mechanistic Mechanistic phase phase

Model Model physical physical meaningful? meaningful?

End End Fig. 2-18 Data-based mechanistic (DBM) modelling technique (Young et al., 2002) The first phase in DBM approach involves the objective identification and estimation of a minimally parameterised transfer function (TF) model from the experimental dynamic data (data based phase). The DBM principle only accepts this TF model, if the model gives not only a good identification of the dynamic data, but in the second phase also provides a physically meaningful description of the system under study (mechanistic phase).

In order to identify and model the temperature dynamics in a ventilated room, it would be preferable to perform experiments in which the inlet temperature is changed sharply in a ‘sufficiently exciting’ manner (Young, 1984). In other words, the input should be chosen to induce changes in the outlet temperature that are sufficiently informative to allow for the unambiguous estimation of the dominant dynamic characteristics. 40

The continuous-time SRIV algorithm (Young & Price, 1999) is used to identify the linear TF (ordinary differential equation) model between dynamic input and airspace temperature, with the coefficient of determination RT2 and the YIC identification criterion employed as model structure identification criteria (Young, 1989). A schematic overview of the general concept shows in Fig. 2.14. Input – output data

Use discrete time SRIV and convert parameters to their continuous time Equivalent for pre-filters

Generate auxiliary model

Update the pre-filters and auxiliary model

Generate filtered derivatives for input, output and auxiliary model

Instrumental variables

Algorithm converges ?

Return the model parameters

Fig. 2-19 Diagrammatic representation of the continuous time SRIVC algorithm (Young, 1989)

It is a logical extension of the more heuristically defined state variable filter (SVF) and follows from the optimal Refined Instrumental Variable (RIV) and SRIVC algorithms for discrete time identification (Garnier & Young, 2004), was selected. This method has been used for many years in a wide range of practical applications (e.g. De Moor & Berckmans, 1996; Price et al., 1999; Young et al., 2000; Janssens et al., 2004; Quanten et al., 2003, 2004; Desta et al., 2004, 2005; Van Buggenhout et al., 2006). A continuous-time transfer function model for a single-input single output (SISO) system has the following general form:

41

x (t ) =

B(s) u (t − τ ) and y(t ) = x(t ) + e(t ) A( s )

y (t ) =

B(s) u (t − τ ) + e (t ) A( s )

or

where A(s) and B(s) are the following polynomials in the derivative operator s =

d dt

A( s ) = s n + a1 s n −1 + ... + a n −1 s + a n B ( s ) = b0 s m + b1 s m −1 + ... + bm −1 s + a m

and τ is any pure time delay in time units. This transfer function model structure is denoted by the triad [n, m, τ]. u(t) is the input signal, x(t) is the ‘noise free’ output signal and y(t) is the noisy output signal. Initially, the noise e(t) is considered as zero mean, white noise with Gaussian amplitude distribution, it can also be written in the following differential equation form, which is often more familiar to physical scientists. d n y (t ) d n −1 y (t ) d m u (t ) + a + ... + a y ( t ) = b + ... + bm u (t − τ ) + μ (t ) 1 n 0 dt n dt n −1 dt m

where μ (t ) is defined as μ (t ) = A( s)e(t )

Note that s is used as the derivative operator in the transfer function model because of the very close relationship to the Laplace transform operator, which is often used for the incorporation of initial conditions of the variables and their derivatives. Initially, it is assumed that there are no major effects of any initial conditions remaining on the observed time series y(t) and u(t) that would complicate the estimation of the model parameters.

42

The SRIVC algorithm uses a recursive technique to analyze the data and to provide the best applicable model. The best-selected model is based on the coefficient of determination ( RT2 ) and on the Young Information Criterion (YIC). Particularly, the coefficient of determination ( RT2 ) is a widely applicable statistical index that represents the model fit by using the equation: ⎛δ 2 ⎞ RT2 = 1 − ⎜ 2 ⎟ ⎜δ ⎟ ⎝ y⎠

where δ 2 is the variance of the model residuals and δ y2 is the variance of the data. The Young Information Criterion (YIC) is a more complex index since it estimates the model fit and the efficiency of parameters by applying the following formula: ⎛δ 2 ⎞ YIC = ln⎜ 2 ⎟ + ln{NEVN } ⎜δ ⎟ ⎝ y⎠

where NEVN is the normalised error variance form (Young et al., 1980, Young et al., 1989, Young & Beven, 1994).

NEVN =

p 1 δ 2 ii ∑ p k αi

where p = m + n + 1 is the total number of parameters estimated, α i is the estimate of the ith parameter in the vector α for all the model parameters.

α= [a1 a2 ... an b0 b1 ... bm]T The first term of YIC is simply a relative logarithmic measure of how well the model explains the data: the smaller the model residuals the more negative the term becomes. The second logarithmic term, on the other hand, tends to become large (less negative) when the model is over-parameterized and the parameter estimates are poorly defined. Consequently, the criterion attempts to identify a model that explains the data well but with the minimum of statistically well-defined (low-variance) parameters. 43

44

3 Chapter 3 Modelling of Three-dimensional Air Temperature Distribution in Porous Media

45

46

Chapter 3 Modelling of Three-dimensional Air Temperature Distribution in Porous Media 3.1 Introduction The uniform quality of a product in a storage room has been greatly related to the air and

product temperature distribution (Ville & Smith, 1996, Chua et al., 2002; Verboven et al., 2004; Chao & Wan, 2004; Somkiat et al., 2005). It is now widely recognised that the air in a ventilated process is never perfectly mixed due to the existence of multiple airflow regions, the presence of stagnant zones and the occurrence of short-circuiting of air to the exhaust outlet. The spatially heterogeneous heat and mass transport phenomena in imperfectly mixed fluids are complex dynamic processes with considerable uncertainty about their nature (Janssens et al., 2004). In non-isothermal conditions, incomplete air mixing gives rise to three-dimensional (3D) temperature gradients (D’Alfonso et al., 1994; De Moor & Berckmans, 1993) that have a major impact on process quality, energy usage and process efficiency.

Although computational fluid dynamics (CFD) can be applied successfully to modelling velocity, temperature distributions to a detailed level (Campen & Bot, 2003); it must be used with care. One must be aware of the fact that a CFD model constitutes the culmination of a large number of assumptions and approximations resulting in models that lack the necessary accuracy to be appropriate for control purposes (Oltjen & Owens, 1987). The use of an insufficiently dense grid, the selection of an improper turbulence model and carelessly specified boundary conditions can lead to erroneous results.

When applied to the problem of active process control of the spatio-temporal heat and mass distribution in a ventilated air space or agricultural and industrial process rooms, such numerical CFD models are restrictive owing to their exceptional complexity. To overcome 47

this difficulty, a modelling approach was developed, which as a hybrid between the extremes of data based modelling, provides a physically meaningful description of the dominant internal dynamics of heat and mass transfer in the imperfectly mixed fluid (Berckmans & Goedseels, 1986; Berckmans et al., 1992a; Janssens et al., 2004). Data based mechanistic modelling (DBM) for 3D temperature distribution approach was developed for two reasons: (1) A DBM model is relatively compact, characterises the dominant modal behaviour of the dynamic system and is, therefore, an ideal basis for model based control system design (Camacho & Bordons, 1999; Maciejowski, 2002). (2) The model structure of a DBM model provides a physically meaningful description of the process dynamics and can, therefore, easily be applied to a wide range of imperfect mixing processes: in different fluids (air, water, etc.), on different scales (micro and macro scale) and in numerous application areas.

The objectives of this chapter is the quantification of the 3D spatial uniformity of air temperature in a ventilated room filled up with obstacles and tries to resolve the causes by using a DBM approach. 3.2

Materials and methods

3.2.1. Laboratory test room A mechanically ventilated laboratory test room described in Part 2.1, Chapter 2 (Fig. 2.1) was

used in this study. 3.2.2. Experiments Two configurations were used for the experiments: empty chamber (Figs. 2.1) and chamber

filled with obstacles (plastic balls) (Figs. 2.2). (Plastic balls were used as the well known obstacles which can be extended to heating/cooling processes)

48

For the room filled with balls as obstacles, the test installations were filled with 480 plastic balls (Fig 2.2), each with a diameter of 0.19 m and a weight of 0.12 kg to physically simulate uniform obstacles. These obstacles represented the physical presence of material in storage processes. The porosity, defined as airspace divides to total bulk volume, in this experiment was approximately 0.27.

To obtain dynamic data for modelling, experiments were carried out with step changes in inlet temperature from 11 to 17°C and 17 to 11°C (Fig 3.2) while maintaining a constant ventilation rate.

49

Temperature, oC

Temperature, oC

17

11

17

11

(a) 2000

Time, s

(b) 2000

10000

Time, s

10000

(a)

(c) Fig. 3-1 Step up (a) and step down (b) experiments (c) The measured dynamic response of airspace and buffer temperature from the inlet air temperature for a ventilation rate 280m-3 h1

, inlet temperature setting;

, measured response

The ventilation rate was varied between 120 and 280 m3 h−1 (13.3–31.1 volume changes per hour for empty room) in different experiments, while the internal heat production was maintained at 300 W in each experiment. The experimental design was in Table 3.1

50

Table 3-1 Overview of the dynamic experiments No. Experiments

Ventilation rates (m3 h-1)

1

120

2

120

3

140

4

140

5

160

6

160

7

180

8

180

9

240

10

240

11

250

12

250

13

260

14

260

15

270

16

270

17

280

18

280

Dynamic experiments Temperature (oC) Total time of experiment (s) 11 2000 17 10000 17 2000 11 10000 11 2000 17 10000 17 2000 11 10000 11 2000 17 10000 17 2000 11 10000 11 2000 17 10000 17 2000 11 10000 11 2000 17 10000 17 2000 11 10000 11 2000 17 10000 17 2000 11 10000 11 2000 17 10000 17 2000 11 10000 11 2000 17 10000 17 2000 11 10000 11 2000 17 10000 17 2000 11 10000

To be able to visualise the airflow pattern, the test installation was equipped with a smoke injection system, white smoke (3-ethylglycol (30% by weight), propylene glycol (30% by weight) in water) was injected at the air inlet. Four halogen lamps of 500 W each illuminated 51

the injected smoke, which was recorded by a black and white charge coupled device (CCD) camera (Hitachi KP-M1E/K) (Fig. 3.2). The camera was positioned in front of the test chamber. The back wall of the chamber was painted in black to ensure a good contrast with the white smoke pattern. Sixteen consecutive images of the recorded smoke pattern were digitised with a digitalisation card (Matrox Frame Grabber, PIP 1024 B) controlled by a personal computer. The time interval between the consecutive images was 0.7 seconds. The digitised images are 256 by 256 pixel matrices, resulting in a corresponding pixel size of 1.2 by 0.8 cm. The pixels have a grey value varying from 0 (black) to 255 (white). An algorithm was used to segment the smoke pattern out of the background of the test installation (Van Brecht et al., 2000). 4

1 3 2

y z

5 x

Fig. 3-2 Three-dimensional view of the test installation. (1) Air inlet, (2) Air outlet, (3)(4) Halogen lamp illumination, (5) Charge coupled device (CCD) camera. 3.2.3. Data-based mechanistic modelling approach Data based mechanistic modelling approach was applied to estimate the temperature

distributions in the obstacle room from inlet temperature. This approach is illustrated in Fig. 2.12. The most parametrically efficient model structure was first defined mathematically from the available dynamic data in an inductive manner, based on a generic class of black-box models (normally linear or non-linear differential equations or their difference equation equivalents). After this initial black-box modelling stage, the model is interpreted in a 52

physically meaningful, mechanistic manner based on the nature of the system under study and the physical laws that are most likely to control its behaviour (Young, 2002). 3.2.3.1 Mechanistic phase in the empty room

The DBM approach represents the imperfectly mixed fluid in a process room by a number of well-mixed zones (WMZs) in the room (Well mixed zone was defined as a zone around a temperature sensor in which there exists a good mixing and acceptably low temperature difference (Berckmans, 1986; Berckmans and Goedseeds, 1988; Berckmans et al., 1992a). The dynamic temperature response in the well mixed zone to the variation of air inlet temperature was considered for control purposes. Since the temperature within each well mixed zone has to be controlled by the control in puts (temperature of the in coming air, ventilation rate, etc.). The response of each well mixed zone temperature to the control inputs matter. The interaction between well mixed zones is considered as a disturbing factor taking into account in the real time model of each well mixed zone. These WMZs exist in every imperfectly mixed fluid. A schematic representation of a WMZ in a process room with ventilation rate Vin in m3 s−1) and with internal sensible heat production qc in J s−1 is given in Fig. 3.3.

53

Tlab Buffer zone

volbuff

Tbuff(t)

Air inlet T0(t-τ), V, γ0, Cp,0

Vin T0(t)

Ti(t)

WMZ

qc

Air outlet

voli V, Ti(t), γi, Cp,i

Fig. 3-3 Schematic representation of the well-mixed zone concept: Vin, air flow rate; V, part of the total ventilation rate entering the well-mixed zone i; voli , volume of well-mixed zone; vol buff , volume of the buffer zone; T0(t), supply air temperature at time t; Tbuff(t), temperature of air in the buffer zone at time t; Tlab, laboratory temperature; qc, part of the total heat production in the room entering the well-mixed zone i; t, time;τ, advective time delay; Cp,0, Cp,i, heat capacity of the air in the well-mixed zone i and the supply air; γi , γ0, densities of the air in the well-mixed zone i and supply air To describe the dynamic behaviour of temperature in each of the considered n WMZs, standard heat transfer theory was applied. In the case of a constant ventilation rate, this resulted in first-order differential equation of the form (Janssens et al., 2004) dTi ( t ).vol i .γ i .C p,i dt

= V .T0 ( t − τ )γ 0 .C p,0 − V .Ti (t )γ i .C p,i + qc + k1 .S1 (Tbuff ( t ) − Ti ( t ))

where: Ti(t) is the temperature in the well-mixed zone, °C. T0(t−τ) is the input temperature, oC. V is the part of the ventilation rate that enters the well-mixed zone, m3 h−1. voli is the volume of well mixed zone, m3. Tbuff(t) is the temperature in buffer zone, °C. k1 is the heat transfer coefficient between WMZ1 and WMZ2, J s−1 m−2 °C−1. S1 is the surface area of heat exchange between inside room and buffer zone, m2. 54

(3.1)

qc is a part of the internal heat entering the well-mixed zone in J s−1. Cp,0, Cp,i are the specific heats of air inlet and air in the well-mixed zone i, J kg−1 °C−1.

γ0, γi are the densities of the air supply and air in the well-mixed zone i in kg m−3.

The buffer zone consists of a volume of air between the central chamber walls and the envelope chamber walls. There is a heat exchange between the air in the buffer zone and the air in the central chamber. In contrast to the zonal and nodal models in the literature (Dalicieux et al., 1992; Li et al., 1992), the different WMZs here are considered as decoupled or non-interactive zones. Each WMZ is considered to be coupled with the control inputs Vin and T0. The reason for considering non-interactive 3D zones is that: (1) The resulting n models (the response of temperature in each WMZ to changes in the conditions of air temperature inlet is described by a single model, resulting in n first order models for n WMZs) that can be used for controlling the conditions in the n well-mixed zones each time only using the air inlet conditions. (2) Since the product in all positions within the ventilated process needs to be dried, the focus on the WMZ model concept is to model the movement of supplied air to a particular zone. Finally, all zones must be reached by using the process control inputs. This provides two major advantages: (1) it is not required to determine the interactions (air and heat flows) between the different zones that generate lots of inaccuracies in zoned and nodal modelling; (2) when considering non-interactive WMZs, the spatio-temporal model is also less complex and more appropriate for control purposes.

Under the assumption that γ0≈γi≈γ and Cp,0≈Cp,i≈Cp, differential Eqn (3.1) was rewritten by Janssens et al. (2004) as

55

⎛ V qc dTi (t ) k 1 . S1 k1 .S1 ⎞⎟ V = + T0 (t − τ ) + Tbuff (t ) − ⎜ Ti (t ) + ⎜ vol vol .γ .C ⎟ vol i .γ .C p dt voli voli .γ .C p i p ⎠ ⎝ i

(3.2) The associated steady state equations are as follows: ⎛ V qc k1 .S1 k1 .S1 ⎞⎟ V + =0 T0 + T buff − ⎜ Ti + ⎜ ⎟ voli .γ .C p voli voli .γ .C p ⎝ voli voli .γ .C p ⎠

(3.3)

with, T 0 , T i , T buff , input, room and buffer zone temperature at steady-state condition in °C. If only small temperature perturbations t0(t−τ), tbuff(t) and ti(t) are considered around steady state, then (Janssens et al., 2004) ⎛ V dt i ( t ) k1 .S1 k1 .S1 ⎞⎟ V t0 (t − τ ) + tbuff (t ) − ⎜ t (t ) = + ⎜ vol vol .γ .C ⎟ i dt voli voli .γ .C p i p ⎠ ⎝ i

(3.4)

dti (t ) = β1t0 (t − τ ) + K1tbuff (t ) − α1ti (t ) dt where the coefficient β1, K1 and α1 are given by ⎛ V

k .S

(3.5)

β1 =

V ; voli

K1 =

k1 .S1 ; voli .γ .C p

⎞

1 1 ⎟ = β 1 + K1 + α1 = ⎜⎜ ⎟ vol vol i .γ .C p ⎠ ⎝ i

Equation (3.5) can be expressed in a continuous-time transfer function form as

ti (t ) =

K1 β1 t0 (t − τ ) + tbuff (t ) s + α1 s + α1

(3.6)

It has already been shown that the spatio dynamic temperature response of 36 sensors in an imperfectly mixed ventilated empty room can be successfully modelled with the DBM concept [Eqn (3.6)] for a wide range of ventilation rates to variations of the supply air temperature. It has been demonstrated that the modelling approach is applicable to different fluids (air, water), to process rooms of different scale (macro-scale, micro-scale) and to

56

processes with different flow conditions (turbulent flow, laminar flow), (De Moor, 1996, Janssens et al., 2004).

It has been shown that the model parameters β1, K1 and α1 in Eqn (3.6) have a physical meaning (Berckmans et al., 1992a; Janssens et al., 2004). Parameter α1 in s−1 is the sum of β1 in s−1 and K1 in s−1. It is also the reciprocal of the time constant τ (s) of the first-order model. Parameter K1 is the local transmission coefficient of heat exchange between the WMZ and the buffer zone. Parameter β1 is the local volumetric concentration of fresh airflow rate (Berckmans et al., 1992a; Janssens et al., 2004) or the local outside air change rate (Li et al., 1994) in the WMZ. It is the amount in m3 of fresh supply air flowing into the considered WMZ per unit of time in second divided by the volume of the WMZ in m3.

A first order heat balance can be written for the buffer zone: dTbuff ( t ) vol buff .γ buff .C p,buff dt

= k1 .S1 (Ti ( t ) − Tbuff ( t )) + k 2 .S 2 (Tlab − Tbuff ( t ))

(3.7)

where: Tbuff(t) is the temperature in the buffer zone, °C. volbuff is the volume of buffer zone, m3. k2 is the heat transfer coefficient between buffer zone and environment, W m−2 °C−1; S2 is the surface of heat exchange between buffer zone and environment, m2. Tlab is the environment temperature, °C. γbuff is the density of air in buffer zone, kg m−3. Cp,buff is the specific heat of air in buffer zone, J kg−1 °C−1. with Cp,buff=Cp and γbuff=γ, Eqn (3.7) can be simplified analogous to dtbuff ( t ) dt

= K 3 .ti (t ) − ( K 3 + K 2 )tbuff (t )

57

(3.8)

where the coefficients K1, K2 and K3 are: K1 =

k1 .S1 k 2 .S 2 k1.S1 ; K2 = ; K3 = voli .γ .C p voli .γ .C p volbuff .γ .C p

These first orders of differential Eqns (3.5) and (3.8) can be converted to a transfer function (TF) form by using the Laplace operator. These yields

ti (t ) =

K1 β1 t 0 (t − τ ) + tbuff (t ) s + α1 s + α1 tbuff (t ) =

(3.9)

K3 ti ( t ) s + ( K2 + K3 )

(3.10)

The block diagram of Eqns (3.9) and (3.10) is given in Fig. 3.4. t0(t-τ)

β1

1 s + α1

+

ti(t)

K1 K3 s + (K 2 + K3 )

tbuff(t)

Fig. 3-4 Block diagram of the feedback connected the second order transfer function: s, Laplace operator; t0(t−τ), supply air temperature at time; tbuff(t), temperature of air in the buffer zone at time; ti(t), temperature of air in the well mixed zone; t, time; τ, advective time delay; β1, local volumetric concentration of fresh air rate; K1, K2, K3, α1, model parameters Combining transfer functions in Eqns (3.9) and (3.10), the second order continuous-time TF model for the central chamber-buffer zone system becomes (s is Laplace operator)

ti (t ) =

b0 s + b1 t0 (t − τ ) s + a1s + a2 2

where: b0=β1 ; b1 = β1 ( K 2 + K 3 )

a1 = α1 + K 2 + K 3 a2 = (K 2 + K 3 )α1 − K1 K 3 = (K 2 + K 3 )α1 − (α1 − β1 )K 3

58

(3.11)

3.2.3.2 Data-based phase in the empty room

The dynamic data obtained from dynamic experiments were used. In ‘data-based phase’, the modelling technique was used to fit data to several equations and evaluate each equation by statistical meaning. Although other techniques are available, the simplified refined instrumental variable (SRIV) approach was employed as a method for model identification, since it not only yields consistent estimates of the parameters but also exhibits close to optimum performance in the model order reduction context (Young, 1984). By combining the mechanistic and data based phase, a second-order fitting equation could be selected to estimate the heat exchange process in the empty room. 3.3 Results and discussions The uniformity of the air temperature distribution was calculated by the well mixed zone

approach with the acceptable temperature differences and the cause of the non uniformity was captured by applying the DBM approach both for the empty room and for the room filled with obstacles. 3.3.1. Uniformity of air temperature in the empty test installation A lot of applications require perfect mixing in certain regions (eg. storage of fruits and

vegetables, thermal processing, cooling, etc.). One of the control strategies in these applications can be the positioning of a specific well mixed zone. The well mixed zones were defined as the maximum 3D volume in which an acceptable temperature difference is measured. The well mixed zones were identified by visualizing the measured 3D temperature distribution (Fig. 3.5a).Then the average temperature is calculated at the considerate time and the position and volumes of well mixed zones were calculated with an acceptable temperature difference.

The temperature uniformity index Itemp is a useful index to quantify the spatial homogeneity of temperature in a ventilated airspace, and is defined as the volumetric part in % of airspace 59

with the temperature between the limiting value Tavg–ΔT and Tavg+ΔT, where Tavg is the average of air temperature in the chamber, and ΔT is the acceptable temperature difference .

ΔT is the range of temperature which hasn’t an effect on the quality and efficiency of the process, ΔT is defined by processes (Janssen, 1999). For example, in an oven for microchips the acceptable temperature difference is 0.02oC. In this thesis we used 0.2oC. n

I temp =

∑ vol i =1

i

(3.12)

VOL

where: voli is the volume of the well-mixed zone i in m3 ( voli =0 if temperature is not in Tavg±ΔT); VOL is a considerable volume in m3; ΔT is the acceptable temperature difference in °C; and Tavg is the average of air temperature in the chamber in °C.

As a representative example, Figs 3.5a and 3.5b visualise the measured 3D temperature distribution in the empty room under the following steady state condition (duration for steady state is 2 h). This figure illustrates that the empty room has an imperfectly mixed air volume with a non-uniform temperature distribution, and the volume part of airspace with acceptable temperature difference 0.2°C is 66.7%.

Air inlet

Air outlet

60

Outlet

Inlet

Width, m

0.8

2.0 1.6

0 1.2

1.6 0.8 0.8 Height, m 0 21.9

22.2

Length, m

0.4

22.4

0 22.6

22.8

23.1

23.3

Temperature scale, oC

23.5

23.7

23.9

24.2

(a)

Width, m

0.8

2.0 1.6

0 1.2

1.6 0.8 0.8

0.4

Height, m 0

Length, m

0

Fig. 3-5 (a) Visualisation of measured three-dimensional temperature distribution in the empty room under the following steady-state conditions: ventilation rate 120 m3 h−1, air supply temperature 17°C and internal heat production 300W; (b) visualisation of the 3D zone in the empty room with acceptable temperature difference 0.2°C and average temperature in a well mixed zone 23.1±0.2 oC 61

The measured temperature uniformity index is shown in Fig. 3.6 as a function of the acceptable temperature difference ΔT and the ventilation rate. The higher the acceptable temperature difference, the more volume of air in the test installation fulfils the condition of uniformity. The higher the ventilation rate, the better the air inside the room is mixed, resulting in a higher uniformity index. The temperature distribution in airspace is depend on airflow pattern (Berckmans and De Moor, 1993) and the relation between uniformity index to ventilation rates were non-linear (Özcan et al., 2005), but the high velocity in airspace is

Temperature uniformity index, %

resulted in the turbulent flow (high in the Reynol number) occurred in this experiment.

100 90 80 70 60 50 160 150 140 Ventilation rate, m3 h-1

0.6

130 120

0.2

0.8

1

0.4 o Acceptable C oC Acceptabletemperature temperaturegradient, difference,

Temperature uniformity index, %

(a)

100 90 80 70 60 50 280 270 260 3 -1

Ventilation rate, m h

250 240

0.2

0.4

0.6

0.8

1

Acceptable temperature gradient, oC Acceptable temperature difference, oC

(b)

Fig. 3-6 Temperature uniformity index (Itemp) of the empty room: (a) low ventilation rates (120–160 m3 h−1); (b) high ventilation rates (240–280 m3 h−1) with an acceptable temperature difference from 0.2 to 1°C

62

3.3.2. Data-based phase in the empty room Applying continuous time SRIV algorithm (Young, 1981) to estimate the parameters in the

first and second order transfer function is based on coefficient of determination RT2 and minimisation of the Young identification criterion (YIC) value. Positions (1) and (32) in the empty room were used as examples for calculating.

From Table 3.2, it is obvious that the first and the second-order transfer function can be applied in the empty room, but the second order has a higher value for RT2 than the first order. This result is in good agreement with previous research (Janssens et al., 2004). Table 3-2 The model parameter estimates with for sensor position (1) and (32) in the empty room with ventilation rate is 280 m3 h−1 Sensors

Order

[m ,n,τ]

of TF First

[0,1,10]

order 1

Second

[1,2,10]

order

First 32

[0,1,10]

order Second order

[1,2,10]

Parameter

Standard error

RSE,

estimates

of parameters

%

a1= 0.0297

0.00069

2.32

b0= 0.0155

0.00035

2.26

a1= 0.1135

0.00680

5.99

a2= 0.0004

0.00000

0.00

b0= 0.0427

0.00230

5.39

b1= 0.0003

0.00000

0.00

a1= 0.0723

0.00170

2.35

b0= 0.0481

0.00110

2.29

a1= 0.2458

0.01120

4.56

a2=0.0010

0.00010

10.00

b0= 0.1350

0.00590

4.37

b1= 0.0007

0.00010

14.29

RT2

YIC

0.0189

0.9759

-10.58

0.0076

0.9904

-8.23

0.0141

0.9886

-11.34

0.0035

0.9972

-10.06

SE

values

TF, transfer function; RSE, relative standard error of parameters (in %, it is the estimate's standard error (SE) divided by the estimate itself. The larger the RSE, the less precise the estimate); SE, standard error of equations; RT2 , coefficient of determination; YIC, Young identification criterion; m, n and τ, denominator, numerator and time delay; a1, a2, a3, b0, b1, parameters in the first and second order of transfer function. By modelling the temperature responses at each sensor location in the experimental chamber, physical meaningful model parameters were derived. The most important parameter in 63

relation to uniformity of air temperature is the local volumetric concentration of fresh airflow rate β1. In Fig. 3.7, the local volumetric distribution of the concentration of fresh airflow rate is shown on a vertical plane in the test installation as a function of the ventilation rate in the empty test installation. (At the low ventilation rate (120 m3 h−1) β1 changes in the range of 0.0013–0.0975 compared to 0.0042–0.135 at the high ventilation rate (280 m3 h−1)).

Fig. 3-7 Partial contours of parameter β1 in the empty chamber: (a) front plane at the ventilation rate is 120 m3 h−1; (b) front plane at the ventilation rate is 280 m3 h−1 Further, the contour plots calculated from the measured dynamic temperature distribution relate well to the airflow pattern (Fig. 3.7). The incoming air rapidly moves from the top to the bottom through holes on the duct system and coming out. Therefore, the air circulates 64

much more slowly at the top positions. The performance of β1 value (Fig. 3.7) is also in good agreement with the visualised airflow pattern in the smoke injection experiment (Fig. 3.8).

(a)

(b) Fig. 3-8 Visualisation of the airflow pattern with smoke: (a) 120 m3 h−1; (b) 280 m3 h−

65

3.3.3. Uniformity of air temperature in the test installation filled with obstacles Figures 3.9(a) and (b) visualise the measured 3D temperature distribution in the obstacle

room under the following steady-state condition. The volume part of airspace with acceptable temperature difference 0.2°C is 13.89 % of bulk volume.

Inlet

Outlet

(a)

66

Width, m

0.8

2.0 1.6

0 1.2

1.6 0.8 0.8 Height, m

0.4 0

Length, m

0

Fig. 3-9 (a) Visualization of measured three-dimensional airspace temperature distribution in obstacle room under the following steady state conditions: ventilation rate 120 m3 h−1, air supply temperature 17 °C and internal heat production 300 W; (b) Visualisation of the 3D zone in the obstacle room with acceptable temperature difference 0.2°C, a well mixed zone 23.6±0.2 oC The performance of these plots has the same form as the empty room (Fig. 3.10). At low ventilation rates and low acceptable temperature differences, the uniformity index is less. The lower the acceptable temperature difference, the less the volume of air in the test installation fulfils the condition of uniformity. The lower the ventilation rate, the less the air inside the room is mixed, resulting in a lower uniformity index. More detail of the comparison of the uniformity index in both cases is shown in Fig. 3.14.

67

Temperature uniformity index, %

100 80 60 40 20 160 150 140 3 -1

Ventilation rate, m h

130 120

0.4

0.2

0.6

0.8

1 o

Acceptable temperature gradient, C Acceptable temperature

difference, oC

Temperature uniformity index, %

(a)

100 80 60 40 20 280 270 260 3 -1

Ventilation rate, m h

250 240

0.2

0.4

0.6

0.8

1

o

Acceptable temperature gradient, C

Acceptable temperature difference, oC

(b) Fig. 3-10 Temperature uniformity index of airspace (Itemp) of the obstacle chamber at (a) low ventilation rates (120–160 m3 h−1); (b) high ventilation rates (240–280 m3 h−1)

3.3.4. Data-based mechanistic modelling approach in the obstacles room The continuous-time SRIV algorithm was used to identify and estimate the parameters in the

first, second and third order transfer function at 36 positions in the room. Positions 1 and 32 were used as examples in this chapter (Fig. 3.11).

68

21.5

20.5

o

Tem perature, C

21

20

19.5

19

18.5 0

1000

2000

3000

4000

5000 Time, s

6000

7000

8000

9000

10000

5000 Time, s

6000

7000

8000

9000

10000

(a) 20.5 20

o

Tem perature, C

19.5 19 18.5 18 17.5 17 16.5 0

1000

2000

3000

4000

(b)

Fig. 3-11 (a) The output of the first-order, second-order transfer function model compared with the measured airspace temperature response at the sensor position (1); (b) at the sensor position (32) in the obstacle chamber at ventilation rate 280 m3 s−1; , first order; , second order; noise line, experiment data

69

Table 3-3 The model parameter estimates with for sensor position (1) and (32) (in the obstacle room with ventilation rate is 280 m3 h−1) Sensors

Order of TF

[m, n,τ]

1

First order Second order

[0,1,10]

32

[1,2,10]

Third order

[2,3,10]

First order Second order

[0,1,10]

Third order

[2,3,10]

[1,2,10]

Parameter estimates a1= 0.0167 b0= 0.0085 a1= 0.0913 a2= 0.0003 b0= 0.0284 b1= 0.0002 a1= 0.1520 a2= 0.0022 a3= 0.0000 b0= 0.0373 b1= 0.0008 b2= 0.0000 a1= 0.1156 b0= 0.0936 a1= 0.3746 a2= 0.0024 b0= 0.2574 b1= 0.0002 a1= 0.9171 a2= 0.0224 a3= 0.0001 b0= 0.5666 b1= 0.017 b2= 0.000

Standard error of parameters 0.0032 0.0015 0.0028 0.0000 0.0011 0.0000 0.0176 0.0007 0.0000 0.0027 0.0002 0.0000 0.0026 0.0021 0.0024 0.0001 0.0093 0.0001 0.0317 0.0013 0.0000 0.0193 0.0009 0.0000

RSE, %

SE

RT 2

YIC values

1.92 1.18 4.49 0.00 3.87 0.00 11.5 31.8 0.0 7.42 2.5 0.00 2.25 2.24 3.71 4.17 3.61 5.00 3.46 5.80 0.00 3.41 5.29 0.00

0.0154

0.97

-10.84

0.0028

0.99

-9.60

0.0027

0.99

-5.61

0.008

0.99

-12.07

0.0015

0.99

-11.58

0.0013

0.99

-10.35

TF, transfer function; RSE, relative standard error of parameters; SE, standard error of equations; RT2 , coefficient of determination; YIC, Young identification criterion; m, n and τ, denominator, numerator and time delay; a1, a2, a3, b0, b1, b2, parameters in the first and second order of transfer function. Table 3.3 shows that the best identified transfer function model in terms of YIC identification criterion is a first order model. The best-fitting equation is the third-order model associated with the smallest standard error and highest value for the coefficient of determination ( RT2 ). The residuals plot of the first, second and third order models are shown in Fig. 3.13. From this figure, there is a significant difference between the first and second order model, but not between the second and third order model. Although, the third order model gives the best fitting equation, it is more complicated than the second order model (high in YIC values). So,

70

the second order of transfer function can be selected to estimate the air temperature distribution in the obstacle room with accuracy comparable to the third order model.

Fig. 3-12 Residual plots of the first, second and third order model at the sensor position (32) in the obstacle room with the ventilation rate 280 m3 h−1 The partial contour of β1 is equal to b0 parameter in a second-order transfer function of rear and front planes as presented in Fig. 3.13. β1 value at the position (32) is higher than the position (1). A high velocity in the obstacle room with the same ventilation rate is the cause of a high β1 in the position (32), but β1 in the obstacle room is not proportional to the air velocity. There is a significant relation with the heat transfer to objects and the airspace velocity distribution in the obstacle room.

The partial value of β1 for the front plane is presented in Fig. 3.13.

71

Fig. 3-13 Partial contours of parameter β1 in the obstacle chamber at the front plane with the ventilation rate 280 m3 h−1 3.3.5. Comparison between the empty test installation and the test installation filled with obstacles The same ventilation rate and acceptable temperature difference resulted in a different

temperature uniformity index of airspace with the empty room and room filled with obstacles (Fig. 3.14). With an acceptable temperature difference below 0.6°C there is a large difference between the two experiments. At an acceptable temperature difference above 0.8°C, however, there was not a significant difference. At higher ventilation rate, a higher temperature uniformity index was measured in the chamber due to the transport of internal heat production.

72

Temperature uniformity index, % Temperature uniformity index, %

100 80 60 40 20 0

120

140

150

160 240 250 Ventilation rate, m3 h-1 (a)

260

270

280

120

140

150

160 240 250 3 -1 Ventilation rate, m h (b)

260

270

280

100 80 60 40 20 0

Fig. 3-14 Comparison between the temperature uniformity index of airspace (Itemp) for two values of the acceptable temperature difference 0.2°C (a) and 1°C (b); †, empty room; „, obstacle room

The airspace (was defined as air surrounding the balls in Fig. 1.2) in the obstacle chamber was smaller than in the empty chamber (approximately 27% in comparison with the empty room), so the air velocity in the obstacle chamber was relatively higher in comparison with the empty chamber at the same ventilation rate of inlet air. The high velocity in the obstacle chamber means that there is more fresh air coming to each place in the chamber. It is clear that the value of β1 in the chamber with obstacle is high compared to that for β1 in the empty chamber but the value for β1 is not proportional to the air velocity in the obstacle room. A part of energy has been transferred to the air inside the obstacles so the β1 should be smaller than for the same air velocity in the empty room.

Acceptable temperature difference and local volumetric concentration of fresh air rate β1 have great relationship with uniformity index in both cases. Those are parameters to be considered to control the uniformity of temperature final products during thermal processing and storage processes. 73

3.4 Conclusions To control the uniformity of product quality in thermal processing and storage processes, in

this study, an earlier developed data-based mechanistic (DBM) approach was extended from an imperfect mixing process in an empty mechanically ventilated laboratory test chamber to a test installation filled with obstacles. The DBM model, with physically meaningful model parameters, could model the spatio-dynamic temperature response at 36 positions in the room to a variation of the supply air temperature with an accuracy of 0.1°C.

The local fresh air concentration in the empty test installation showed good qualitative agreement with the smoke visualisation experiments. This means that dynamic temperature experiment could be used to quantify the air temperature distribution inside the room.

Local fresh air rate in porous media was higher than in the empty room. For example, 0.028 and 0.247 compared to 0.042 and 0.135 at the positions (1) and (32), respectively, at the same rate of ventilation input (280 m3 h−1). This was explained by the fact that the local volumetric concentration of fresh air rate in the porous media is not only determined by air distribution but it also by the heat transfer to the objects.

A model from the second order and a coefficient of determination RT2 >0.99 was found to predict temperature distribution in the obstacle room with a very small error (0.99) and YIC value is low in the most estimations. The predicted values were shown in Fig. 4.5a, fit very well with the calculation of the third transfer functions, resulting in a mean prediction error of 0.1oC (Fig. 4.5b).

(b)

(a)

Fig. 4-5 Third order fitted model and residual plot for 280 m3 h-1 inlet air flow rate (63.6 volume changes per hour): (a) position 27; (b) position 30

4.3.2. Physical meanings of estimated parameters V Value β1 = b0 is equal to and is a local volumetric concentration of fresh airflow rate for voli a well mixed zone at a specific sensor position. The distribution of β 1 in a vertical plane 90

within the test installation can be shown as a partial contour plots for front and rear plane as in Fig. 4.6. From this figure, it is obvious that close to the air inlet position β 1 has a higher value than at other positions. The resistance of air movement in a room filled with obstacles resulted in the high of β1 at the air inlet positions.

Fig. 4-6 Two dimensional contours of parameter β1 in the obstacle chamber at the ventilation rate 280 m3 h-1 at positions of vertical planes: (a) rear plane; (b) front plane Also within the ventilated room, the airflow pattern of fresh air corresponds to zones with higher β 1 values. The difference between the rear and front plane in Fig. 4.6 can probably be explained by a non-symmetrical distribution of obstacles in the room.

At the same position (sensor 33), with a higher ventilation rate, a higher β 1 value was found (Fig. 4.7). This can be explained by the fact that β 1 is related to the air refreshment in the room. At other positions however (sensor 3), an increase in ventilation rate does not have a significant effect on β 1 . This means that β 1 not only depends on air replacement but also on the airflow pattern. 91

0.04 0.035

0.025

1

Parameter β , s

-1

0.03

0.02 0.015 0.01 0.005 0

160

180

200

220

240

260

280

Ventilation rate, m 3 h -1

Fig. 4-7 Comparison of parameter β1 at the different ventilation rates (160-280 m3 h-1) „, position 3; †, position 33

In ‘the data based phase’, the simplified refined instrumental variable (SRIV) technique was also used to identify parameters in Eqn (4.16) for modelling the temperature in the obstacles. Results are presented in Table 4.3. Table 4-3 First order model parameters in a relationship between temperature in WMZ1 ( ti (t ) ) and material temperature ( tm (t ) ) with associates statistics measure for step up experiment at 280 m3 h-1 Sensor positions

a0

a1

b0

RT 2

YIC values

3 6 15 18 27 30 33 36

1 1 1 1 1 1 1 1

0.0225 0.0121 0.0228 0.0112 0.0179 0.0226 0.0170 0.0264

0.0195 0.0115 0.0228 0.0108 0.0174 0.0212 0.0168 0.0263

0.9995 0.9994 0.9995 0.9987 0.9995 0.9998 0.9990 0.9997

-17.6490 -17.9800 -17.2940 -16.3210 -18.2790 -19.8300 -16.9460 -19.0890

92

Differences between a1 and b0 values, % 13.30 5.25 0.11 3.86 2.92 6.28 1.33 0.56

Table 4.3 shows a typical example of parameter estimates for eight sensor positions to model the temperature inside the obstacles with corresponding coefficient of determination RT2 and YIC values.

From Eqn (4.16), that has the same structure as a first order transfer function

y (t ) =

b0 u(t ) with y(t ) = tm (t ) ; u (t ) = ti (t ) , α2 values can be estimated from a1 or b0. a0 .s + a1

The estimated parameters a1 and b0 are not very different (maximum 13.3% at position (2) and minimum 0.11% at position (15)) in Table 4.3 and based on Eqn (4.18), these parameters are an estimate for α 2 .

At the same time, α 2 has a relationship with the heat transfer coefficient (km) and consequently, the heat transfer coefficient km can be calculated with known parameters α 2 , γ, d and Cp from equation α2 =

6.k m γ .d .C p

Otherwise, α 2 is the same structure with “cooling rate” in Newton’s law for cooling processes. The “cooling rate” value presents the change in product temperature for unit change of cooling time for each degree of temperature difference between the product and its surrounding. It depends on many factors including the rate of heat transfer, the difference in temperature between the product and the cooling medium, the nature of the cooling medium, the physical properties of the product, etc. (Brosnan & Sun, 2001).

The results of the α2 calculations for two-ventilation rates 160 and 280 m3 h-1 are presented in Fig. 4.8. The α 2 values are usually high in case of high ventilation rates due to increased 93

convection, but α 2 does not only depend on ventilation rate but also on the airflow pattern expressed by the β 1 value.

0.045 0.04

Parameter Cooling rate,αs2-1, s-1

0.035 0.03 0.025 0.02 0.015 0.01 0.005 0

3

6

15

18

27

Sensor positions

30

33

36

Fig. 4-8 Parameter α2 at several positions at ventilation rates 160 m3 h-1 and 280 m3 h-1 „, ventilation rate 160 m3 h-1; †, 280 m3 h-1

4.3.3. Calculating parameters from the third fitted model in the ventilated porous media It can be concluded that, the values in the set of transfer functions [Eqns (4.14), (4.15) and (4.16)] in this model for ventilated porous media, are based on estimated values from a third order transfer function in relationship between inlet temperature (t0(t)) and the temperature in WMZ1 (ti(t)) [Eqn (4.18)] combined with a the first order transfer function in a relationship between temperature inside the obstacles (tm(t)) and the temperature in WMZ1 (airspace) (ti(t)) [Eqn (4.16)].

The result of all estimated parameters at sensor position (33) at different ventilation rates is shown in Table 4.4. 94

Table 4-4 Calculated parameters at position (33) with ventilation rate from 220 to 280 m3 h-1 Ventilation rates, m3 h-1 220 240 260 280

β1

α1

α2

0.0279 0.0254 0.0363 0.0383

0.0814 0.0541 0.0891 0.0767

0.0143 0.0153 0.0164 0.0169

K1 0.0496 0.0247 0.0484 0.0338

Km 0.0039 0.0041 0.0044 0.0046

Comparison of local volumetric concentration of fresh air rate β1 and cooling rate α2 at the different ventilation rates is shown in Fig. 4.9. In general, higher values of β1 result in higher

α2 values. This can be explained by the fact that the heat transfer coefficient from the obstacles (expressed by α2) has a good relationship with air flow pattern and resulting air velocity in the media (expressed by β1), so estimated values from data based mechanistic model are in agreements with the heat transfer theory. The air flow pattern in a process room resulted from the convection and buoyancy effects. If buoyancy changes, the airflow pattern will change and heat transfer from airspace to products is also changed. But β1 in this research is the combination of convection and buoyancy effects which were obtained by online modelling. This technique could be used to control the 3D temperature distribution. 0.09

β

0.08

1

α

2

β1 and α2 (s -1)

0.07 0.06 0.05 0.04 0.03 0.02 0.01 0

220

240 260 3 -1 Ventilation rate (m h )

280

Fig. 4-9 Parameters β1 and α2 value at the difference of ventilation rates (position 33) 95

4.4 Conclusions A data-based mechanistic model was applied to model temperature distribution in the room filled with obstacles. A third-order transfer function was generated from heat transfer theories, to represent the dynamic response of heat exchange processes in the air within the ventilated porous media. By fitting the data from a dynamic experiments to a third-order transfer function, close agreement with local temperature measurements was obtained ( RT2 > 0.99), corresponding to an error of 99%), very low of YIC values (99.9) and very low YIC value (YIC