MODELLING AND SIMULATION OF A TRAY DRYER USING MATLAB

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ABSTRACT

In this work, a low dimensional lumped parameter model describing the variation of moisture content and temperature of the potato chips undergoing drying in a batch tray dryer is developed using conservation of mass and energy. The model also captures the temperature and moisture content dynamics of the air draft in the dryer. Experimental data obtained were obtained using a computer controlled batch tray drier equipped with automatic data logging facility in the Chemical Engineering Laboratory of Afe Babalola University, Ado-Ekiti, Ekiti State, Nigeria. The differential equations derived were solved with the aid of MATLAB using ode45 function. There was close agreement between experimental data and simulation result. The variation of the potato temperature and moisture content obtained from the model followed the trend observed in the experiment. This simple model can thus be used to configure an appropriate controller to regulate the drying temperature, moisture content as well as the air draft temperature.

TABLE OF CONTENTS

CERTIFICATION…………………………………………………………………………………………………………….. ii

DEDICATION………………………………………………………………………………………………………………… iii

ACKNOWLEDGEMENT………………………………………………………………………………………………….. iv

ABSTRACT…………………………………………………………………………………………………………………….. v

LIST OF FIGURES…………………………………………………………………………………………………………. viii

NOMENCLATURE…………………………………………………………………………………………………………. ix

CHAPTER ONE………………………………………………………………………………………………………………. 1

  1. INTRODUCTION……………………………………………………………………………………………….. 1
    1. Background……………………………………………………………………………………………………… 1
    1. Statement of Problem………………………………………………………………………………………. 2
    1. Scope of Study………………………………………………………………………………………………… 3
    1. Aim of Study…………………………………………………………………………………………………… 3
    1. Objectives………………………………………………………………………………………………………… 3
    1. Justification……………………………………………………………………………………………………… 4

CHAPTER TWO………………………………………………………………………………………………………………. 5

CHAPTER THREE…………………………………………………………………………………………………………. 35

3.4 Equipment and Experimental Procedure…………………………………………………………………. 43

CHAPTER FOUR…………………………………………………………………………………………………………… 47

4.0 RESULT AND DISCUSSION………………………………………………………………………………….. 47

APPENDIX……………………………………………………………………………………………………………………. 54

Appendix A……………………………………………………………………………………………………………….. 54

Antoine Table…………………………………………………………………………………………………………….. 54

Appendix B……………………………………………………………………………………………………………….. 54

Simulation codes…………………………………………………………………………………………………………. 54

Appendix C……………………………………………………………………………………………………………….. 56

Experimental Data………………………………………………………………………………………………………. 56

LIST OF FIGURES

Figure 2. 1 Rate of drying of a granular material…………………………………………………………………. 9

Figure 2. 2 The use of a rate of drying curve in estimating the time for drying………………………. 11

Figure 2. 3:  2. 4 Rotary dryer, 0.75 m diameter × 4.5 m long for drying dessicated coconut….. 15

Figure 2. 4: Flow diagram for a typical continuous fluidized-bed dryer………………………………… 18

Figure 2. 5Air-lift dryer with an integral mill…………………………………………………………………….. 21

Figure 2. 6: Turbo-shelf dryer………………………………………………………………………………………….. 22

Figure 3. 2: Air system in a tray drier……………………………………………………………………………….. 39

Figure 3. 3: Schematic diagram of a tray dryer………………………………………………………………….. 43

NOMENCLATURE

SYMBOLSMEANINGUNITS
HsysEnthalpy of the systemkJ
HoutEnthalpykJ
WDRate of dryingkg m 2 s
hwEnthalpy of waterkJ/kg
MwMass of water of the systemKg
  Ms  Mass of solid  kg
QconvectionHeat due to convectionkJ
Dhv(water)Latent heat of vaporizationkg/kJ
TTemperature of the potatoK
TrefReference temperatureK
C psSpecific heat capacity of   potatokg/kJ
CpwSpecific heat capacity of waterkg/kJ
CpvSpecific heat capacity of vaporkg/kJ
WBFlow rate of airkg/s
CBSpecific heat capacity of airkg/kJ
TgoInlet temperature of the airK
TgOutlet temperature of the airK
aHeat transfer coefficientkW m2 K
AInterfacial Aream 2
YoHumidity of inlet airkg/kg
YHumidity of outlet airKg/kg
HHumidityKg/kg
%RHPercentage humidityNo unit
PwPartial pressure of waterN/ m2
PwoVapor pressureN/ m2
P*Vapor pressureN/ m2
NuNusselt numberNo unit
PrPrandtl numberNo unit
ReReynolds numberNo unit
ScSchmidt numberNo unit
PTotal pressureN / m2
Pbulk wPartial pressure/vapor pressure of componentkg ms 2
Psurface wPartial pressure of water vapor in the air at the solid interfacekg ms 2
Pair wPartial vapor of water vapor in   airkg ms 2
Symbol rMeaning   DensityUnits   kg m3
rairDensity of airkg m3
kMass transfer coefficientm s
kcMass transfer for a convective   driving forcem s
k pMass transfer coefficient for a   partial pressurekg m2s
LLength of drying Layerm
mairViscosity of airkg m.s
CpairSpecific capacity of airkJ/kg
kairThermal conductivity of airW mK
XMoisture contentNo unit

CHAPTER ONE

                                                                                                                                  INTRODUCTION

                      Background

The drying process is a complex process of heat and mass transfer resulting in a direct transfer of humidity from some substance into hot air. The heat transfer, necessary for that process, can be direct, convective from the drying agent which flows around the drying material, or indirect, by different procedure (Salemović et al., 2014). Drying process has long been used from the time of old to dry food. For example, foods like meat, fish and so on were dried using sun as the drying medium to preserve them and prevent growth of micro –organisms (Dagbe et al., 2014). Majorly, substances are/were dried for the following reasons:

  1. To remove moisture content which may otherwise lead to corrosion. One example is drying of gaseous fuels or benzene prior to chlorination.
    1. To reduce the cost of transportation.
  • To make material more suitable for handling, as for soap powders, dye stuffs and fertilizers.
    • To provide definite properties, such as for example maintaining free flowing of salt.
  • To mitigate the activities of the micro-organisms that can cause spoilage and decay in food products if moisture were present in the food.

Modeling of drying processes and kinetics is a tool for process control and necessary to choose suitable method of drying for a specific product. Developed models fall into three categories namely the theoretical, semi-theoretical and empirical. Semi-theoretical models offer a compromise between theory and ease of application (Khazaei and Daneshmandi, 2007). Semi-

theoretical models are Lewis, Page, Henderson and Pabis, logarithmic, two terms and two terms exponential, models are used widely for designing as well as selection of optimum drying conditions and for accurate prediction of simultaneous heat and mass transfer phenomena during drying process. It also leads to the production of high quality product and increase in the energy efficiency of drying system. Thin-layer drying models have been used to describe the drying process of several agricultural products.

In the Chemical Engineering Laboratory of Afe Babalola University the PID controller of our tray drier system has been giving unsatisfactory performances. It is envisaged to replace the controller in future with an advanced one-model predictive controller. In order to carry out this efficiently a low dimensional lumped parameter is sought. Some model in literature are too complex (PDE’s) to be used for control purposes or do not match the mechanics of the tray drier of interest. However, the greatest drawback of the tray dryer is uneven drying because of poor airflow distribution in the drying chamber that can be removed by implementing some modification in the dryer design. (Katiyar et al., 2013). Thin layer drying kinetics is needed for design, operation and optimization of food crops dryers (Olawale et al., 2012). Therefore this project is aimed at developing lumped parameter model that will be suitable for control, since most of the models developed are too emperical, strongly non linear, and too complex to characterize tuning parameters in a control system.

                          Statement of Problem

The PID controller in our laboratory tray dryer has been giving unsatisfactory performances. It is envisaged to replace the controller in future with a more advanced one – model predictive controller. To be able to do this easily and efficiently, a low dimensional lumped parameter

model is sought. Some available in literature are either too complex (PDEs) to be used for control purposes or do not match the mechanics of the tray dryer of interest.

                        Scope of Study

The scope of study covers the modelling and simulation of a convective drying process of a thin slice layers of potato, using a tray dryer as the drying medium and MATLAB software will be employed as the simulation tool for this project.

                      Aim of Study

The aim of this work is to derive a mathematical model suitable for control. Potato will be dried in a tray dryer in order to define the essential drying parameters of a static thin layer of potato and plantain of known magnitude of thickness which could be used subsequently for control of these agricultural products and similar natural products in a ‘Tray dryer’.

                    Objectives

The following objectives are expected to be carried out:

  1. Study and analyze existing mathematical models developed for tray dryer system drying some agricultural products
  2. Develop a mathematical model for a tray dryer using potato as the sample in the tray dryer.
  3. Simulation of the models using MATLAB software
  1. Compare the result with experimental data.

                      Justification

Since most of the models developed are too emperical, strongly non linear, and too complex complex to characterize tuning parameters in a control system. This project is aimed at developing lumped parameter model that will be suitable for control.