ThesisPDF Available

HEAT TRANSFER MODEL FOR SUGAR BEET STORAGE PILE

August 2020

Thesis for: Masters
Advisor: Beaudry, Randolph

Authors:

Michigan State University

Harvested sugar beet (Beta vulgaris L.) are stored in cold regions in large piles exposed to ambient weather conditions and fluctuate temperatures during the winter storage period, which lasts for four months. To better understand the impact of air temperature on the pile temperature. A two-dimensional (2D) heat transfer steady-state model was designed to predict the temperature profile of the pile. To validate the model, temperatures obtained from the model were compared with the temperatures measured from onsite commercial piles during the storage seasons from the second season in Reese, MI. The model tended to underestimate the pile temperature (°C). The mean difference between measured and modeled temperature values was significant (P ≤ 0.05). Daily rate of sugar loss (kg/metric ton/day) based on measured and modeled temperatures were calculated and compared for model accuracy. The mean of the daily sugar loss based on the modeled pile temperature was significantly (P≤0.05). Additionally, three zones (upper, middle and lower) of the pile were studied for the model accuracy. There was a significant difference between the modeled and measured pile temperature between the three zones in the second season, whereas the first season didn't show difference between the temperatures of the upper and the middle zones (P≤ 0.05). Moreover, a comparison of predicted sugar loss as a function of pile geometry was conducted under 2012 air temperature and a 3°C increase in air temperature relative to 2012 data.

Photograph: Presents a cross section of the studied sugar beet pile showing the dimensions of the studied pile, which is located at Reese, Michigan for 2011-2012 and 2012-2013 seasons, to study the heat flux distribution inside the pile.

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Schematic design: Illustrates the sugar beet pile divided into three zones, lower (■), middle (•) and upper (♦) for the 2011 season. The colored symbols illustrate the thermocouple locations as distributed in each zone.

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Schematic design: Illustrates the sugar beet pile divided into three zones, lower (■), middle (•) and upper (♦) for the 2012 season. The colored symbols illustrate the thermocouple locations as distributed in each zone.

…

Heat transfer diagram: Illustrate the temperature profile of the Gera Road beet pile on December 5-10, 2011. The average air temperature is given in the thermometer to the right of each panel. A, B, C, D and SP indicate five thermocouple harnesses; harness D was embedded approximately 5 cm into the soil. White circles indicate locations of individual thermocouples.

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+21

Graph: Shows the measured (▲) and modeled (•) sugar beet whole pile temperatures for the 2012 season in relation to air temperature (■).

…

Figures - uploaded by Mona Shaaban

Content may be subject to copyright.

Content uploaded by Mona Shaaban

Content may be subject to copyright.

HEAT TRANSFER MODEL FOR SUGAR BEET STORAGE PILE

Mona Shaaban Mahmoud Shaaban

A THESIS

Submitted to

Michigan State University

in partial fulfillment of the requirements

for the degree of

Horticulture—Master of Science

2020

ABSTRACT

HEAT TRANSFER MODEL FOR SUGAR BEET STORAGE PILE

Mona Shaaban Mahmoud Shaaban

Harvested sugar beet (Beta vulgaris L.) are stored in cold regions in large piles exposed to

ambient weather conditions and fluctuate temperatures during the winter storage period, which

lasts for four months. To better understand the impact of air temperature on the pile temperature.

A two-dimensional (2D) heat transfer steady-state model was designed to predict the temperature

profile of the pile. To validate the model, temperatures obtained from the model were compared

with the temperatures measured from onsite commercial piles during the storage seasons from

November 2011 to January 2012 in the first season and from November 2012 to February 2013 in

the second season in Reese, MI.

The model tended to underestimate the pile temperature (°C). The mean difference between

measured and modeled temperature values was significant (P ≤ 0.05). Daily rate of sugar loss

(kg/metric ton/day) based on measured and modeled temperatures were calculated and compared

for model accuracy. The mean of the daily sugar loss based on the modeled pile temperature was

significantly (P≤0.05). Additionally, three zones (upper, middle and lower) of the pile were studied

for the model accuracy. There was a significant difference between the modeled and measured pile

temperature between the three zones in the second season, whereas the first season didn’t show

difference between the temperatures of the upper and the middle zones (P≤ 0.05). Moreover, a

comparison of predicted sugar loss as a function of pile geometry was conducted under 2012 air

temperature and a 3°C increase in air temperature relative to 2012 data.

iii

This thesis is dedicated to Dr. Sherine Awad and My Family.

Thank you for being who you are.

ACKNOWLEDGEMENTS

All the praises and thanks be to Allah, the Lord of the 'Alamin (mankind and all that exists).

I would also like to express my deepest appreciation to my major advisor Dr. Randolph Beaudry

for his enthusiasm, continuous help and persistent guidance that have a great effect in my life either

inside or outside the academic field. I would also like to sincerely thank Dr. Linda Hanson whose

guidance towards many authentication contributions to my study has lasting effect. I’m very

grateful to Dr. David Hodge for his valuable support and his welcoming attitude.

I would greatly thank Michigan Sugar Company for its funding and technical support

during my study. I would like to present my great thanks to the Department of Horticulture, the

Graduate School, CVIP, Office of International Students and Scholars and HOGS Club for

providing financial help during my study.

I would like to express my gratitude to my colleagues Safa Alzohairy, Shijian Zhuang, Pat

Murad, Khaled Yousef and Daniel Wyrembelski for their contribution to technical support. I

strongly express my thanks to my lab colleague Diep Tran for her lovely feelings and warm

thoughts. I would also like to thank my lab colleagues Dr. Sangeeta Dhingra, Dr. Sangram Dhumal,

Dr. Nihad Smairat, Dr. Mahmud Tengku Muda Mohamed, Patrick Abeli, Rossella Briano and

George Henrique for their big influence during my research.

The support before and during my master's study from my husband, Dr. Ahmed Rady was

crucial in completing my master's program and his sustained ambition inspiring me to continue in

my way. From the deep of my heart I want to thank my lovely children Yusuf, Jana and Omar

Rady for their patience for my absence from some of their important moments, but my wish that

one day they will give me an excuse and be proud of me as I’m always proud of them.

I also have so many feelings but cannot find words to express my love and appreciation to

my mother Nadia, I can only say to her that my life, happiness and success cannot be possible

without you. And to the spirit of my father Shaaban, I want to say to him that any time I write my

name I write yours to remember to pray for you even during my busy life, I will keep the last

promise that I gave you “keep learning” until the last day of my life whatever the responsibilities

I have and the way is hard until we meet in your beautiful place that you told me in my dreams

and you feel proud of me. To my only brother and my first friend Mahmoud, I know that we have

thousands of miles apart but you never stop thinking of me and I never do, please keep your praying

and warm thoughts for me and my family because we feel them in our life every day.

Dr. Sherine Awad, although I was like a tree whose brown leaves were falling and its dry

branches were fragile, you believed in me, stayed beside me, watered me and nourished me. Until

new buds revived, green leaves grew and cheerful flowers bloomed. I cannot thank you enough.

Last, and of big importance for me, I would like to give my unlimited thanks and

appreciation to my extended family in Egypt for their continues praying and encouragement and

to the Islamic community in East Lansing for being family and friends who occupied a special

place in my heart and for being a shelter and a shield for all my family in the hard days (Jazakom

Allah Khairan).

TABLE OF CONTENTS

LIST OF TABLES ................................................................................................................ vi

LIST OF FIGURES ............................................................................................................... vi

LIST OF ALGORITHMS ..................................................................................................... vi

KEY TO SYMBOLS ............................................................................................................ vi

INTRODUCTION .................................................................................................................. 1

ECONOMIC IMPORTANCE OF SUGAR ....................................................................... 1

SUGAR BEET PRODUCTION AND STORAGE ............................................................ 1

SUGAR BEET LOSS DURING STORAGE ..................................................................... 3

OPTIMIZING SUGAR BEET STORAGE CONDITIONS THROUGH

MATHEMATICAL MODELING ..................................................................................... 5

APPLICATION OF MODELING BIOLOGICAL SYSTEMS .......................................... 5

1. Models for Individual and Packed Products ........................................................... 6

2. Models for Bulk Stored Products ........................................................................... 6

3. Modeling Sugar Beet Storage ............................................................................... 10

MATERIALS AND METHODS ........................................................................................... 12

MODEL DESCRIPTION ................................................................................................ 13

MODEL PARAMETERS ................................................................................................ 14

1. Sugar Beet Thermal Properties ............................................................................. 14

2. Heat of Respiration of Sugar Beet ........................................................................ 14

3. Soil Thermal Properties ....................................................................................... 15

4. Air Thermal Properties ......................................................................................... 16

MODEL ASSUMPTIONS .............................................................................................. 16

GEOMETRY AND BOUNDARY CONDITIONS .......................................................... 17

MODEL EQUATIONS ................................................................................................... 18

1. Equations for Heat Transfer in the Sugar Beet Pile ............................................... 19

2. Equations for Heat Transfer in the Ground ........................................................... 20

3. Equations for Heat Transfer in the Air ................................................................. 20

MONITORING PILE TEMPERATURE .......................................................................... 21

CALCULATING SUGAR LOSS ..................................................................................... 22

PILE ZONE COMPARISONS ........................................................................................ 23

PILE DESIGN EVALUATION........................................................................................ 24

DATA HANDLING, STATISTICAL ANALYSIS AND EXPERIMENTAL DESIGN ... 26

RESULTS ............................................................................................................................. 28

MODEL ACCURACY BASED ON PILE TEMPERATURE ........................................... 30

MODEL ACCURACY BASED ON SUGAR LOSS ........................................................ 32

vii

1. Daily Sugar Loss ................................................................................................. 32

2. Cumulative Sugar Loss ........................................................................................ 35

PILE ZONE COMPARISON .......................................................................................... 38

1. Variation of the Measured Temperature Inside the Pile ........................................ 38

2. Daily Sugar Loss Comparison Between Pile Zones .............................................. 41

3. Cumulative Sugar Loss Comparison Between Pile Zones ...................................... 44

MODEL ACCURACY IN DIFFERENT ZONES ............................................................ 44

1. Temperature Comparison Between Pile Zones ..................................................... 44

EVALUATION OF PILE GEOMETRIES AND VENTILATION ON SUGAR LOSS ... 48

1. Daily Sugar Loss Comparison Between Pile Geometries and Ventilation ............. 48

2. Cumulative Sugar Loss Comparison Between Pile Geometries and Ventilation .... 51

DISCUSSION ....................................................................................................................... 53

SUMMARY AND CONCLUSIONS .................................................................................... 60

LITERATURE CITED .......................................................................................................... 63

viii

LIST OF TABLES

Table 1: Model parameters for sugar beet roots and soil used in developing the heat transfer

simulation of stored sugar beet pile in Reese, MI (Ochsner et al., 2001; Tabil et al., 2003a).

.............................................................................................................................................. 14

Table 2: Air parameters used in developing the heat transfer simulation of stored sugar beet

(Datta, 2002). ......................................................................................................................... 16

Table 3: Sugar beet pile geometry and boundary conditions used to develop the

mathematical model .............................................................................................................. 18

Table 4: Dimensions for different pile designs used for developing heat transfer models in

sugar beet storage piles .......................................................................................................... 24

Table 5: Measured and modeled beet pile temperatures (°C) for 2011 and 2012 averaged

across the storage campaign .................................................................................................. 32

Table 6: Sugar loss estimates based on measured and modeled beet pile temperatures for

2011 and 2012 (°C) averaged throughout the storage campaign .............................................. 35

Table 7: Calculated cumulative sugar loss (kg/metric ton) in field-stored sugar beets based

on measured and modeled pile temperature for 2011 and 2012 .............................................. 38

Table 8: Temperatures of the lower, middle and upper zones of the sugar beet pile in 2011

and 2012 averaged across the storage campaign. Means are the average of 37 d in 2011 and

97 d in 2012 ........................................................................................................................... 41

Table 9: Estimated rate of sugar loss (kg/metric ton/day) for field-stored sugar beets in the

upper, middle and lower zones of the beet pile based on measured temperature ..................... 44

Table 10: Estimated cumulative sugar loss (kg/metric ton) in the 2011 season (37 days)

and the 2012 season (95 days) calculated from the measured temperature of the lower,

middle and upper zones of the beet pile ................................................................................. 44

Table 11: Significance level, resulting from ANOVA analysis, assessing whether predicted

and measured pile temperatures differed in the upper, middle and lower zones over two

storage seasons ...................................................................................................................... 48

Table 12: Modeled prediction of the daily rate of sugar loss (kg/metric ton/day) for beet

piles having different heights or ventilation in a sugar beet pile based on the 2012 air

temperature ........................................................................................................................... 50

Table 13: Daily rate of sugar loss (kg/metric ton/day) for beet piles having different heights

or ventilation in a sugar beet pile based on 3°C increase in air temperature relative to 2012

data ....................................................................................................................................... 50

Table 14: Predicted total sugar loss (kg/metric ton) after 100 days of field storage based on

the temperatures obtained from models varying pile height, ventilation and average

temperature (+3 °C) for beet piles under the 2012 season ....................................................... 51

LIST OF FIGURES

Figure 1: Photograph: Presents a cross section of the studied sugar beet pile showing the

dimensions of the studied pile, which is located at Reese, Michigan for 2011-2012 and

2012-2013 seasons, to study the heat flux distribution inside the pile...................................... 13

Figure 2: Schematic design: Illustrates the sugar beet pile and pile’s boundaries included

in the model for the 2011season. The data used to predict pile temperature included inlet

air temperature, wind speed and ground temperature at 50 cm depth (5.5 °C (Schaetzl et

al., 2005)). The pile dimensions are 45.7 m, 4.9 m and 27.4 m for the base, height and top,

respectively. The black dots are the positions of the thermocouples in the middle of the.

The boundaries are assigned to be 9.75 m in height and 91.44 m in width. Arrows on the

left side show the direction of the inlet air .............................................................................. 18

Figure 3: Schematic design: Illustrates the sugar beet pile and pile’s boundaries included

in the model for the 2012 season. The data used to predict pile temperature included inlet

air temperature, wind speed and ground temperature at 50 cm depth (5.5 °C (Schaetzl et

al., 2005)). The pile dimensions are 45.7 m, 4.9 m and 27.4 m for the base, height and top,

respectively. The black dots are the positions of the thermocouples in the middle of the

pile. The boundaries are assigned to be 9.75 m in height and 91.44 m in width. Arrows on

the left side show the direction of the inlet air......................................................................... 18

Figure 4: Schematic design: Illustrates the sugar beet pile divided into three zones, lower

(■), middle (●) and upper (♦) for the 2011 season. The colored symbols illustrate the

thermocouple locations as distributed in each zone. ................................................................ 23

Figure 5: Schematic design: Illustrates the sugar beet pile divided into three zones, lower

(■), middle (●) and upper (♦) for the 2012 season. The colored symbols illustrate the

thermocouple locations as distributed in each zone. ................................................................ 23

Figure 6: Schematic design: Illustrates the suggested “decreased height” sugar beet pile.

The outer pile-shape describes the commercial pile, the insider pile-shape describes the

“decreased height” pile. Arrows show the air direction for the model. .................................... 24

Figure 7: Schematic design: Illustrates the suggested “increased height” sugar beet pile.

The outer pile-shape describes the “increased height” pile, the insider pile-shape describes

the commercial pile. Arrows show the air direction for the model. ......................................... 25

Figure 8: Schematic design: Illustrates the suggested “ventilated” sugar beet pile. The air

domain is surrounding the pile from all sides. Arrows show the air direction for the model.

.............................................................................................................................................. 25

Figure 9: Heat transfer diagram: Illustrate the temperature profile of the Gera Road beet

pile on December 5-10, 2011. The average air temperature is given in the thermometer to

the right of each panel. A, B, C, D and SP indicate five thermocouple harnesses; harness D

was embedded approximately 5 cm into the soil. White circles indicate locations of

individual thermocouples. ...................................................................................................... 29

Figure 10: Graph: Shows the measured (▲) and modeled (●) sugar beet whole pile

temperatures for the 2011 season in relation to air temperature (■). ........................................ 30

Figure 11: Graph: Shows the measured (▲) and modeled (●) sugar beet whole pile

temperatures for the 2012 season in relation to air temperature (■). ........................................ 31

Figure 12: Boxplot: Displays the distribution of the values of measured and modeled

temperatures for the beet pile temperature for the 2011 season. Diamonds (◊) represent the

mean values; circles (○) represent the outlier values. .............................................................. 31

Figure 13: Boxplot: Displays the distribution of the values of measured and modeled

temperatures for the beet pile temperature for the 2012 season. Diamonds (◊) represent the

mean values; circles (○) represent the outlier values. .............................................................. 32

Figure 14: Graph: Shows the daily sugar loss (kg/metric ton /day) from field-stored sugar

beets calculated from measured (▲) and modeled (●) pile temperatures for the 2011

season. ................................................................................................................................... 33

Figure 15: Graph: Shows the daily sugar loss (kg/metric ton /day) from field-stored sugar

beets calculated from measured (▲) and modeled (●) pile temperatures for the 2012

season. ................................................................................................................................... 33

Figure 16: Boxplot: Displays the distribution of the daily rate of sugar loss (kg/metric

ton/day) due to respiration as a function of measured or modeled sugar beet pile

temperature for the 2011 season. Diamonds (◊) represent the mean values; circles (○)

represent the outlier values. .................................................................................................... 34

Figure 17: Boxplot: Displays the distribution of the daily rate of sugar loss (kg/metric

ton/day) due to respiration as a function of measured or modeled sugar beet pile

temperature for the 2012 season. Diamonds (◊) represent the mean values; circles (○)

represent the outlier values. .................................................................................................... 34

Figure 18: Graph: Shows the cumulative sugar loss (kg/metric ton) from field-stored sugar

beets calculated from measured (▲, Lm) and modeled (●, Ld) pile temperatures for the

2011 season. ........................................................................................................................... 36

Figure 19: Graph: Shows cumulative sugar loss (kg/metric ton) from field-stored sugar

beets calculated from measured (▲, Lm) and modeled (●, Ld) pile temperatures for the

2012 season. ........................................................................................................................... 36

xii

Figure 20: Boxplot: Displays the distribution of measured or modeled Cumulative sugar

loss (kg/metric ton) for the 2011 season. Diamonds (◊) represent the mean values; circles

(○) represent the outlier values. .............................................................................................. 37

Figure 21: Boxplot: Displays the distribution of measured or modeled Cumulative sugar

loss (kg/metric ton) for the 2012 season. Diamonds (◊) represent the mean values; circles

(○) represent the outlier values. .............................................................................................. 37

Figure 22: Graph: Shows the temperatures (°C) of the lower (▲), middle (●) and upper (♦)

zones of the sugar beet pile and the average daily air temperature (■) for the 2011 season. ..... 39

Figure 23: Graph: Shows the temperatures (°C) of the lower (▲), middle (●) and upper (♦)

zones of the sugar beet pile and the average daily air temperature (■) for the 2012 season. ..... 40

Figure 24: Boxplot: Displays the average temperatures (°C) throughout the storage

campaign of lower, middle and upper zones of the sugar beet pile for the 2011 season.

Diamonds (◊) represent the mean values; circles (○) represent the outlier values. ................... 40

Figure 25: Boxplot: Displays the average temperatures (°C) throughout the storage

campaign of lower, middle and upper zones of the sugar beet pile for the 2012 season.

Diamonds (◊) represent the mean values; circles (○) represent the outlier values. ................... 41

Figure 26: Graph: Shows the calculated daily rate of sugar loss (kg/metric ton/day) based

on measurements of pile temperature (°C) for the lower (▲), middle (●) and upper (♦)

zones of the pile for the 2011 season. The secondary vertical axis is the average daily air

temperature (■). ..................................................................................................................... 42

Figure 27: Graph: Shows the calculated daily rate of sugar loss (kg/metric ton/day) based

on measurements of pile temperature (°C) for the lower (▲), middle (●) and upper (♦)

zones of the pile for the 2012 season. The secondary vertical axis is the average daily air

temperature (■). ..................................................................................................................... 42

Figure 28: Boxplot: Displays the average calculated daily sugar loss (kg/metric ton/day)

based on measured temperatures (°C) of lower, middle and upper zones of a sugar beet pile

for the 2011 season. Diamonds (◊) represent the mean values; circles (○) represent the

outlier values. ......................................................................................................................... 43

Figure 29: Boxplot: Displays the average calculated daily sugar loss (kg/metric ton/day)

based on measured temperatures (°C) of lower, middle and upper zones of a sugar beet pile

for the 2012 season. Diamonds (◊) represent the mean values; circles (○) represent the

outlier values. ......................................................................................................................... 43

Figure 30: Graph: Shows the measured (▲) and modeled (●) temperatures (°C) of the

upper zone of the sugar beet pile for the 2011 season in relation to air temperature (■)........... 45

xiii

Figure 31: Graph: Shows the measured (▲) and modeled (●) temperatures (°C) of the

upper zone of the sugar beet pile for the 2012 season in relation to air temperature (■)........... 46

Figure 32: Graph: Shows the measured (▲) and modeled (●) temperatures (°C) of the

middle zone of the sugar beet pile for the 2011 season in relation to air temperature (■). ........ 46

Figure 33: Graph: Shows the measured (▲) and modeled (●) temperatures (°C) of the

middle zone of the sugar beet pile for the 2012 season in relation to air temperature (■). ........ 47

Figure 34: Graph: Shows the measured (▲) and modeled (●) temperatures (°C) of the

lower zone of the sugar beet pile for the 2011 season in relation to air temperature (■)........... 47

Figure 35: Graph: Shows the measured (▲) and modeled (●) temperatures (°C) of the

lower zone of the sugar beet pile for the 2012 season in relation to air temperature (■)........... 48

Figure 36: Boxplot: Displays the distribution of the values for daily sugar loss rate

(kg/metric ton/day) of different designs of sugar beet storage piles based on 2012 air

temperatures. Diamonds (◊) represent the mean values; circles (○) represent the outlier

values. .................................................................................................................................... 49

Figure 37: Boxplot: Displays the distribution of the values for daily sugar loss rate

(kg/metric ton/day) of different designs of sugar beet storage piles based on predicted 3°C

increase in air temperatures relative to 2012 data. Diamonds (◊) represent the mean values;

circles (○) represent the outlier values. ................................................................................... 50

xiv

LIST OF ALGORITHMS

Equation 1: Respiration rate CO2 (mL·kg-1·hr-1) = (outlet CO2 (%) - inlet CO2 (%)) x flow

rate (mL·hr-1)/sample wt (kg) ................................................................................................. 15

Equation 2: Respiration rate = 0.97·T - 262.06 ....................................................................... 15

Equation 3: Q = exp (-6291 x (1/T) + 25.472)/182) ............................................................... 15

Equation 4: 𝜌𝐶𝑝𝑢 . ∇𝑇 + ∇ .𝑞 = 𝑄 ....................................................................................... 19

Equation 5: 𝑞 = − 𝑘𝑒𝑓𝑓∇𝑇 ................................................................................................... 19

Equation 6: keff = θpkp+ (1- θp) k + k disp ................................................................................ 19

Equation 7: 𝜌𝐶𝑝 𝑢 . ∇T + ∇ . q = 𝑄 ....................................................................................... 20

Equation 8: q = − kg∇T ....................................................................................................... 20

Equation 9: 𝜌𝐶𝑝 𝑢 . ∇T + ∇ . q = 𝑄 ....................................................................................... 20

Equation 10: q = − k∇T ....................................................................................................... 20

Equation 11: Ld= 0.7784 Lm – 0.021 ...................................................................................... 38

KEY TO SYMBOLS

T ambient temperature (K).

Q energy (W·m-3).

𝜌 density (kg·m-3).

Cp the specific heat at constant pressure (J·kg-1·K-1).

u the velocity (m·s-1).

∇T the temperature gradient (K·m-1).

q heat flux (W·m-2).

keff the effective thermal conductivity (W·m-1·K-1).

θ p porosity (%).

k thermal conductivity (W·m-1·K-1).

kdisp Dispersive thermal conductivity (W·m-1·K-1).

Lm= Estimated cumulative sugar loss (kg/metric ton) based on pile measured temperature.

Ld= Estimated cumulative sugar loss (kg/metric ton) based on pile modeled temperature.

INTRODUCTION

ECONOMIC IMPORTANCE OF SUGAR

Sugar (sucrose) is an important product around the world for home use and in numerous

industries (Asadi, 2005; FAOSTAT, 2014). Sugar is mainly produced from two sources, sugarcane

(Saccharum officinarum) and sugar beet (Beta vulgaris L.) (FAOSTAT, 1994).

In 2014, the world production of sugarcane and sugar beet were 2010.4 and 277.7 million

metric tons of raw product, respectively (FAOSTAT, 2014). The total crop values of production

in 2014 were about $224.9 and $14.8 billion for sugarcane and sugar beet, respectively (FAOSTAT,

2014).

SUGAR BEET PRODUCTION AND STORAGE

USA was ranked as the 11th largest producer of sugarcane in 2014 with 27.6 million metric

tons. The production of sugar beet in 2014 was 28.4 million metric tons, making the USA the 4th

largest sugar beet producer (FAOSTAT, 2014). Sugar beet accounted for 57% of the USA sugar

production in 2014, while sugarcane accounted for 43% (McConnell and Riche, 2015). This

represents a substantial increase of the sugar beet share from 25% in 1920 (Reference for Business,

2011).

Sugar beet was originally grown in temperate zones in winter and/or summer (Draycott,

1972). However, it is now cultivated all over the world in summer in cooler regions and with

supplemental irrigation in arid and semi-arid regions (Draycott, 1972). USA sugar beet production

is distributed over several regions; the Red River Valley (Minnesota and North Dakota), the far

west area (California, Idaho, Oregon and Washington), the Central High plain area (Colorado,

Montana, Nebraska and Wyoming) and the Great Lakes area (Michigan) with a contribution of

47.45%, 24.13%, 14.41% and 14.01% of the total USA sugar beet production, respectively (USDA,

2015).

In production areas with relatively cold temperatures, harvested roots are stored in large

piles and exposed to ambient environmental conditions during winter (Bugbee, 1993; Huijbregts

et al., 2013). A single hectare of sugar beet produces approximately 45 metric tons of roots, with

a volume of about 80 m3 (Campbell and Klotz, 2006; Draycott and Christenson, 2003). According

to McConnell (2015), approximately 538,000 ha of sugar beet is grown in the USA. The scale of

production prevents immediate processing, as the processing capacity of the beet extraction plant

can reach up to 17,000 metric tons per day (BMA, 2010), thus providing storage facilities is

required.

Beet harvest in Michigan begins at the end of September and continues until the middle of

November (Ruhlman, 2018). After harvest, the roots are transferred to the processing plant or

placed in specially built piling for storage grounds until processing (Bugbee, 1993; Huijbregts et

al., 2013). The storage period lasts for approximately 120 days (Van Eerd et al., 2012) and during

this period, the beet piles are exposed to the surrounding environment. During sugar beet storage

period in Michigan (October - April), the air temperature ranges from -28.7 °C to 29.8 °C

(according to the data obtained by our team from MSU extension station, located at the MSU

Saginaw Valley Beet and Bean Research Farm, Frankenmuth, MI. (Enviro-weather, 2011) for air

temperature in the piling areas for 2009-2014 storage seasons). In 2005, elevated ambient

temperatures during storage in the Great Lakes area contributed to increased respiration and

promoted many cases of microbial activity (Poindexter, 2012). Both phenomena were responsible

for a considerable amount of sugar loss that reached $25 million after such storage season in

Michigan alone (Beaudry and Loescher, 2008).

SUGAR BEET LOSS DURING STORAGE

Elevated storage temperature enhances the rate of root metabolism and thereby raises the

respiration rate (Vukov, 1977). During respiration, stored sugar is oxidized to CO2, converted to

needed metabolites and yields the energy for maintaining cell metabolic activities (Siedow and

Day, 2017). Over a storage campaign of 130 d, sugar losses are around 14 pounds per ton of roots,

about 4% of the total sucrose (Wyse and Dexter, 1971). Barr et al. (1940) estimated that 60% of

this sugar loss was attributable to respiratory losses and Wyse and Dexter (1971) calculated that

respiration accounted for roughly 80% of the sugar loss, with the remainder being lost due to the

interconversion of sucrose to invert sugars and other impurities. Wyse and Dexter (1971) also

noted that the respired CO2 exceeded that accounted for by sugar loss and that a significant

proportion (~38%) of the respired CO2 was derived from non-sucrose compounds.

Fluctuating temperatures during storage of bulk fresh crops can cause considerable loss

(Ullah et al., 2014; Wyse, 1978). Fluctuating storage temperatures increase the respiration rate and

encourage condensation (Hylmó et al., 1976). Free water, in combination with elevated

temperature, can promote virulence and root deterioration by some storage pathogens such as

Phoma betae (Cormack and Moffatt, 1961). Temperature fluctuation additionally reduces the root

quality when the temperature decreases sufficiently to cause freezing (Wyse, 1978). Upon freezing,

the root cell membranes rupture and cellular leakage occurs (Ullah et al., 2014; Wyse, 1978). Upon

thawing, the leaked sucrose-rich solution is available to bacteria, which form polysaccharide gums

that interfere with sugar extraction during the processing (Campbell and Klotz, 2006).

Storage rot of beet roots is another reason for sugar loss and varies in severity according to

storage temperature (Gaskill and Seliskar, 1952; Liebe and Varrelmann, 2016) and is an important

reason for understanding the temperature patterns inside the storage pile. Phoma betae Frank,

Botrytis cinerea L, Penicillium vulpinum (Cooke & Massee) Seifert & Samson (formerly

Penicillium claviforme Bainier) and Rhizopus stolonifera are storage rot pathogens (Bugbee, 1982;

Bugbee, 1986). Low storage temperature (<10 °C) slows the development of the rot by P. betae

and R. stolonifera (Cormack and Moffatt, 1961; Fugate and Campbell, 2009; Miles et al., 1977),

while B. cinerea and P. vulpinum can maintain their activity under a wider range of temperature

(Gaskill, 1952; Mumford and Wyse, 1976).

Respiratory sugar loss and fungal growth can be minimized by maintaining storage

temperature between 1.5 and 5 °C, relative humidity between 95% to 98% and oxygen and carbon

dioxide levels at 5% and 6%, respectively (Karnik et al., 1970). These conditions avoid cell rupture

and reduce dehydration and fungal growth (Bugbee, 1993; Campbell and Klotz, 2006; Wyse,

1978). In areas such as the Red River Valley region and parts of Canada where the winter

temperature is cold enough to 'deep freeze' beet piles (i.e., where weather temperatures remain

below -5 °C during the storage period), piles are kept frozen until processing (Bugbee, 1993;

Campbell and Klotz, 2006; Wyse, 1978). Deep freezing can be used for large 'super' piles with a

base equal to 66 m wide (Bugbee, 1993), but is also useful for smaller piles (e.g., 23 m width) if

an increased surface area for heat exchange is needed (Bugbee, 1993).

OPTIMIZING SUGAR BEET STORAGE CONDITIONS THROUGH MATHEMATICAL

MODELING

Empirical approaches have been employed to achieve optimal storage conditions. These

include covering the pile with straw (Akeson et al., 1974) or woven polypropylene (Perry, 1989),

forced air cooling or ventilation (currently applied in some locations in Michigan) (Clark, 2012),

deep-freezing (Bugbee, 1993) and storing in small piles or covered clamps (List, 2015). Although

empirical approaches help solve some of the storage problems to obtain uniformity and condition

optimization (Kumar and Kalita, 2017), they are not very useful for modifying storage techniques

or developing new approaches. On the other hand, mathematical models can test possible solutions

before practical implementation, with relatively low costs (Ambaw et al., 2013; Xie et al., 2006).

Therefore, mathematical models for optimizing post-harvest handling and storage conditions have

been of interest to researchers (Ambaw et al., 2013; Verboven et al., 2006) and numerical models

have been proposed to simulate and predict fluid flow and heat and mass transfer during

transportation and storage for agricultural commodities (Ambaw et al., 2013; Verboven et al.,

2006).

APPLICATION OF MODELING BIOLOGICAL SYSTEMS

Modeling approaches have been extensively applied to biological systems since the early

2000s (Rennie and Tavoularis, 2009a; Rennie and Tavoularis, 2009b; Verboven et al., 2006).

Many studies were recently performed to simulate and predict the cooling behavior and airflow

for individual products and packaged and bulk food or have simulated the effect of cooling and/or

airflow on the change in storage conditions and ventilation.

1. Models for Individual and Packed Products

Thorpe G. (2006) formulated a transient numerical model using individual products as

discrete entities to determine the efficiency of a hydrocooler for cooling spherical elements. The

model quantifies the time needed for a horticultural produce to reach a target temperature after

exposure to specific water temperatures. The study recommends the use of the mass-weighted

average temperature of the produce to calculate the time needed for cooling instead of using the

core temperature, because reaching the target temperature is significantly faster in the

recommended method.

A transient mathematical model for forced air cooling of apple was created by Arêdes

Martins et al. (2011) to describe the temperature of two apples as a function of the surrounding

airflow. The model explains the cooling in the tandem arrangements on apple trays. The results

demonstrated a delay of cooling in the downstream apple relative to the upstream apple.

Ferrua and Singh (2009a); Ferrua and Singh (2009b); Ferrua and Singh (2009c) developed

a mathematical model to predict the behavior of the airflow and temperature of the strawberry and

the clamshell packaging during the forced-air cooling of strawberry packages. Airflow calculations

were validated using a particle image velocimetry (PIV) approach as well as temperature

calculations. Later, Ferrua and Singh (2011) improved the commercial strawberry storage system

by improving the design of the clamshells and trays as well as the behavior of the airflow across

the cooling chambers, using the early designed model.

2. Models for Bulk Stored Products

To investigate the change of the airflow, temperature and moisture content in bulk stored

potatoes, Xu and Burfoot (1999) developed a transient three-dimensional (3D) computational fluid

dynamics (CFD) model for forced air cooling of potato. Temperature and weight loss were used

for model validation. The difference between simulated temperature and experimental temperature

of a potato bed with 2.4m height and 0.7m diameter reached 1.4 °C lower in the model than the

measured temperatures. There also were variation in weight loss between experimental and

simulated results reached 5%, due to excessive water evaporation of potato tubers and the possible

fluctuation of air speed and increase of the humidity near the inlet air.

As a further example, a transient 3D airflow heat and mass transfer model was designed

for bulk storage of chicory roots to study the commercial storage systems, and validate the ability

of the refrigerated store to maintain root quality (Hoang et al., 2003), by predicting airflow,

dehydration and temperature of chicory roots through a wind tunnel (a closed chamber that can

measure and/or control the parameters of the air passing through). Measured and predicted results

of temperature and moisture content were compared to validate the model. The simulated results

underestimated the actual root temperature. Also, the roots lost more moisture than predicted,

which was assumed to be due to the low relative humidity (RH) of the ambient air in the storage,

variation in the size of the voids between the roots, non-uniformity in the size of the roots and the

large size of the roots compared with the size of the voids between the roots.

Markarian et al. (2006) proposed a mathematical model that predicts potato temperature

and the surrounding relative humidity (RH) throughout cold storage. The model also described the

respiration and transpiration rate of the tubers during storage. The experiment was conducted in a

highly controlled condition and the findings were compared to measurements found in the

literature with a considerable agreement. The mean of absolute difference in temperature was 0.01

°C, the maximum absolute difference was 0.49 °C.

To study the airflow and energy transfer characteristics in ventilated layered and bulk apple

packages, Zou et al. (2006a) designed transient computational fluid dynamics CFD model based

on equations used for porous media. In a second study, Zou et al. (2006b) introduced user-friendly

software to solve the mathematical equations, then the model results were compared with

experimental temperature measurements for validation. The model underpredicted the product

temperature. This was thought to be due to errors in the positions of thermocouples, model input

values and/or model assumptions.

For potato, Chourasia and Goswami (2007a) examined the effect of several parameters,

such as rate of generated respiratory heat, void diameter in the medium, RH, tuber size and

temperature, on heat and mass transfer patterns in potato bulk storage. The study also included

steady-state and transient models and validated the models using experimental measurements of

temperature and moisture loss. In general, the simulation overestimated temperature and moisture

loss with an average error of 1.2 °C and 11.5%, respectively. Later, in another study by Chourasia

and Goswami (2007b), a 2D CFD-based model was developed to compute the change in airflow,

heat transfer and moisture content in potato bulk storage and they again examined the model

accuracy by comparing the modeled data with experimental data obtained from commercial potato

storage. The model was able to predict the potato temperature with an average error of

approximately to 0.5 °C, while the model over-predicted moisture loss by 61%. The difference

between simulated and experimental measurements was thought to be a result of changing storage

conditions for stored tubers due to the unloading of stored potatoes throughout three months of

storage.

Thorpe G.R. (2008) measured the change in temperature and moisture content of stored

grain and designed a CFD model. The model predicted the variation of temperature and moisture

content of the stored grains, but the results were not evaluated for accuracy by comparing the

modeled data with experimental measurements.

Xie et al. (2006) applied a CFD model to obtain the optimal flow and temperature

parameters for controlled cold storage of apples. The proposed 2D model was used to show the

behavior of airflow and temperature transport during forced air cooling. The model was also used

to evaluate the effect of several stacking patterns on the airflow and temperature of stored

foodstuffs. The model was reliable; the error range in temperature was ± 2 °C.

Airflow through a random arrangement of horticultural products in packages was modeled

by Delele et al. (2008), the model was developed based on measurements of low resistance

according to changes in a confinement ratio, void to product ratio and box vent ratio in random

stacking. Literature measurements were used for validation with good agreement.

The influence of product position and package vent arrangement on airflow and

temperature characteristics was studied by Tutar et al. (2009). A transient CFD model was used

for the simulation. The study showed a significant effect of the inflow rate compared with the vent

rate on airflow and product temperatures. However, model validation was not performed.

To investigate the change of spherical produce temperature according to a change of vent

area, Dehghannya et al. (2011) used solid polymer balls for simulation and developing a transient

2D airflow and energy transfer simulation model. The model results confirm the hypothesis that

improving ventilation by increasing the number of package vents from 1 to 5 (with area equal to

2.4% to 12.1% of the package area, respectively) can improve temperature uniformity inside the

package between the produce units as demonstrated by a reduced heterogeneity index from 61.5%

to 5.6%. Validation occurred by comparing the modeled core temperature by measured

temperature of the balls. Deviation from the modeled temperature was found due to some

inaccurate parameter inputs such as the velocity and temperature of airflow, the thermal properties

of the simulating balls and the failure of the numerical model to reach an iterative solution.

Tanaka et al. (2012) used a CFD modeling system to study the behavior of the airflow in a

semi-loaded truck and its influence on product temperature. The model was validated with

measurements of temperature and air velocity with a mean error of 1.4 °C and 0.36 m s-1,

respectively. Later the model was used to find the best loading configuration of the packages as

the results suggested arranging the packages flat with considerable gaps is optimal for

homogeneity of air cooling and temperature distribution. These findings were not validated with a

real experiment. However, the results were consistent with expectations, because this way of

arranging packages allows the cold air to consistently reach the commodities and achieve

temperature uniformity.

3. Modeling Sugar Beet Storage

There have been several attempts to model sugar beet storage. Bakker-Arkema and Bickert

(1966) designed a model to simulate the airflow and energy transfer of a ventilated deep-bed of

sugar beet. Significant differences between measured and modeled cooling rate were found and

thought to be from excluding mass transfer between beets and surrounding fluid. Later, Andales

et al. (1979) used the finite difference approach to develop a 2D model for the temperature and

weight loss of a ventilated sugar beet pile. They compared measured and modeled values for model

validation. Deviations between measured and modeled values were mainly attributed to the change

of porosity and heat loss at the pile walls. Holdredge and Wyse (1982) developed a relatively

simple model, comparing to that of Andales et al. (1979), the model was reduced to one dimension

as they found no significant variation of temperature in the horizontal plane. The model was

verified and tested using an insulated box simulating a section of the commercial pile. The model

validation showed good agreement between experimental and simulated values under the low and

moderate airflow 5.2 and 10.4 m3/ks-metric ton (10 to 20 cfm/ton), respectively. However, the fit

was poor under the high airflow rate applied (20.8 m3/ks-metric ton; 40 cfm/ton), which the authors

attributed to non-continuous fan operation by the company’s technicians trying to avoid blowing

hot air into the pile.

The previous studies focused on modeling a ventilated pile. No models exist to describe

the temperature profile inside unventilated beet piles. However, in Michigan about 50% of the

piles are currently unventilated (J. Stewart, Michigan Sugar Company, personal communication).

Further, there is a 2 to 4 °C increase in the average global temperature is predicted within this

century (New et al., 2011). Thus, more effective pile architectures could be of increasing value.

Therefore, the main objective of this project was to develop a two-dimensional mathematical

model using a finite-element approach to simulate heat transfer in commercial beet piles under

non-ventilated conditions. Such a model can be used to describe the temperature profile of an

unventilated sugar beet pile that directly affects sugar loss and microbial activity during storage.

Designing such a model can assist in decisions regarding pile management (size and duration).

The second objective was to study the effect of the spatial variation of the pile on temperature

distribution and sugar loss. Finally, we used the model to better understand how pile shape and

ventilation presence affects sugar loss during storage.

MATERIALS AND METHODS

Modeling a sugar beet pile’s temperature involved several steps. The first step contains

developing and solving model equations for beets, air and ground thermal properties and input

data (i.e. air temperature, air velocity and relative humidity (RH)) as stated in the model description

section. The second step was monitoring the pile temperature by measuring the temperature of

predefined points in a storage pile then comparing the collected temperatures with the temperatures

obtained from the model at the same points to test the accuracy of the model. The third step was

calculating sugar loss using the measured temperature and comparing it with the sugar loss

calculated using modeled temperature. The fourth step was to evaluate the pile as three horizontal

zones to help understand the model accuracy for each zone. The fifth step was to use the model to

predict how new systems of storage affect root storability then giving a recommendation for the

best storage system according to decreased predicted sugar loss.

The model design and simulations in this research were based on the pile structure and

conditions measured at a commercial sugar beet pile of the Michigan Sugar Company at the Gera

road piling ground, Reese, Michigan (43.409337° N, 83.739412° W). The dimensions of the

commercial pile were 45.7 m, 27.4 m and 4.9 m for the base, top and height, respectively as

illustrated in Fig. 1.

Figure 1: Photograph: Presents a cross section of the studied sugar beet pile showing the

dimensions of the studied pile, which is located at Reese, Michigan for 2011-2012 and 2012-2013

seasons, to study the heat flux distribution inside the pile.

Important input parameters were required for the model including: soil and sugar beet

thermal properties (described below) and heat of respiration generated by the sugar beet, in

addition to air temperature, air velocity and relative humidity (RH) were obtained from the weather

station located at the MSU Saginaw Valley Beet and Bean Research Farm, Frankenmuth, MI.,

(43.3995° N, 83,6980° W) (Enviro-weather, 2011).

MODEL DESCRIPTION

Input parameters underwent in a finite element analysis through a mathematical model to

calculate the rate of heat gain from the ground and respiratory activity and heat loss to the

environment. The model was built and integrated using finite element software COMSOL

(COMSOL Multiphysics ® 4.3b, COMSOL AB, Stockholm, Sweden). For simplification of the

calculations, the model was developed assuming a steady-state heat transfer condition in two

dimensions (2D) on a daily basis, which means the environmental conditions changed from day to

day but was considered constant during the day. However, this assumption might not be accurate

during the day especially with the fluctuating weather in the piling site based on observations. The

model included heat convection at the pile surface and heat conduction inside the pile between

beets and between the pile and the ground.

MODEL PARAMETERS

1. Sugar Beet Thermal Properties

Tabil et al. (2003a), measured the thermal properties of sugar beet roots including density

and specific heat (Table 1) which were used in the model. Root thermal conductivity (kp) was

calculated as a function of temperature (K) and was taken to equal 0.6 W.m-1.K-1. The thermal

conductivity for frozen roots on the other hand was taken as 1.16 W.m-1.K-1; freezing occurs at

temperatures equal to or lower than -5 to -2 °C (Campbell and Klotz, 2006).

Table 1: Model parameters for sugar beet roots and soil used in developing the heat transfer

simulation of stored sugar beet pile in Reese, MI (Ochsner et al., 2001; Tabil et al., 2003a).

Parameter

Value

Unit

Soil density

1700

kg·m-3

Soil thermal conductivity

0.525

W·m-1·K-1

Soil specific heat

1.615

kJ·kg-1·K-1

Root specific heat

3.5464

kJ·kg-1·K-1

Root density

1169.9

kg·m-3

2. Heat of Respiration of Sugar Beet

The respiration rate of sugar beet roots was calculated on the average rate measured for 38

cultivars. Three beet samples from each cultivar were stored in three different temperatures (3, 10

and 20 °C). Each sample was weighed then stored in 20-L high-density polyethylene pails. The

respiration rate was measured using the closed system method (Guevara et al., 2006; Hagger et al.,

1992; Lee, 1987; Song et al., 1992). To obtain accurate readings, respiration rate for each sample

was measured only after reaching system equilibrium. Each measurement took place by manually

injecting gas samples that were derived from the desired pail into a CO2 analyzer (Model ADC225-

MK3, Analytical Development Co., Hoddesdon, England) that uses N2 as the carrier gas (N2 flow

rate = 100 mL·min-1). Respiration rate was calculated using Eq.1

Equation 1: Respiration rate CO2 (mL·kg-1·hr-1) = (outlet CO2 (%) - inlet CO2 (%)) x flow rate

(mL·hr-1)/sample wt (kg)

A simple linear regression relationship was performed to obtain the best-fit line to predict

the respiration rate as a function of the ambient temperature. Eq. 2 shows the best-fit respiration

rate for CO2 production (mg·kg-1·h-1) as a function of ambient temperature T (K)

Equation 2: Respiration rate = 0.97·T - 262.06

where: T is ambient temperature (K).

To calculate the portion of heat released from the total energy of respiration, Siedow and

Day (2017) estimated that plant cells retain approximately 33% of the respiration energy for

metabolic processes. Therefore, 67% of the energy associated with respiration was assumed to be

released as heat, producing the exponential relationship between the energy of respiration (Q) per

unit volume (W·m-3) and the ambient temperature (T) as follows:

Equation 3: Q = exp (-6291 x (1/T) + 25.472)/182)

Where T is in units of K. Equation 3 can be applied in the case of unfrozen roots, while for frozen

roots respiration ceases (Campbell and Klotz, 2006).

3. Soil Thermal Properties

Reese, MI is characterized by its clay and loam soil type (Boring, 2009; Meyer, 2009) for

which thermal properties are known (Table 1) (Ochsner et al., 2001).

4. Air Thermal Properties

The thermal properties of moist air are built in the COMSOL software and were used to

develop the model. Table 2 shows the air thermal properties at 0°C.

Table 2: Air parameters used in developing the heat transfer simulation of stored sugar beet (Datta,

2002).

Parameter

Value

Units

Air density

1.225

kg·m-3

Air thermal conductivity

0.0243

W·m-1·K-1

Air specific heat

1.005

kJ·kg-1·K-1

MODEL ASSUMPTIONS

Several assumptions were required to simplify model development; these include:

• Heat energy transfers through the shortest two dimensions of the pile (width and height),

whereas the energy transfers through the length can be negligible due to the relatively long

dimension.

• Root density and specific heat do not vary significantly within the temperature range for

beet piles through the storage period.

• Ground density, specific heat and thermal conductivity do not vary significantly within the

temperature range throughout the storage period.

• The pile was considered as a porous material.

• Enthalpy due to the water vapor diffusion from beets was negligible.

• Inlet air conditions changed daily depending on the average temperature, RH and the

average wind velocity. However, the air direction will be assumed constant from south to

north based on prevailing wind conditions.

• COMSOL Multiphysics predicts the flow pattern of the air, either laminar or turbulent

according to Reynolds number as a function of the air velocity and pile dimensions, which

is provided as an input in the model.

• The ground temperature from November to April at 50 cm deep at Reese MI is 5.5 °C

(Schaetzl et al., 2005). Therefore, ground temperature was considered constant at that

temperature and depth.

• Root moisture content was considered constant at 70% to 80% (Tabil et al., 2003b) during

the experiment.

• Porosity is assumed to be constant during the experiment as 41.37% (Tabil et al., 2003b).

GEOMETRY AND BOUNDARY CONDITIONS

A geometric representation of the studied pile base, height and top, the dimensions of

which are 45.7 m, 4.9 m and 27.4 m, respectively, is constructed (Table 3, Fig. 2 for 2011 and Fig.

3 for 2012). We assumed that there are defined boundaries for the active air that interact with the

pile, beyond these limits there is no effect from the air on the pile. These boundaries are assigned

to be 9.75 m in height and 91.44 m in width, roughly 2x pile dimensions (Table 3). The assumed

boundaries were obtained based on our preliminary work and for simplicity.

Table 3: Sugar beet pile geometry and boundary conditions used to develop the mathematical

model.

Type

Base (m)

Height (m)

Top (m)

Pile geometry

45.7

4.9

27.4

Boundary dimensions

91.44

9.75

91.44

Figure 2: Schematic design: Illustrates the sugar beet pile and pile’s boundaries included in the

model for the 2011season. The data used to predict pile temperature included inlet air temperature,

wind speed and ground temperature at 50 cm depth (5.5 °C (Schaetzl et al., 2005)). The pile

dimensions are 45.7 m, 4.9 m and 27.4 m for the base, height and top, respectively. The black dots

are the positions of the thermocouples in the middle of the. The boundaries are assigned to be 9.75

m in height and 91.44 m in width. Arrows on the left side show the direction of the inlet air.

Figure 3: Schematic design: Illustrates the sugar beet pile and pile’s boundaries included in the

model for the 2012 season. The data used to predict pile temperature included inlet air temperature,

wind speed and ground temperature at 50 cm depth (5.5 °C (Schaetzl et al., 2005)). The pile

dimensions are 45.7 m, 4.9 m and 27.4 m for the base, height and top, respectively. The black dots

are the positions of the thermocouples in the middle of the pile. The boundaries are assigned to be

9.75 m in height and 91.44 m in width. Arrows on the left side show the direction of the inlet air.

MODEL EQUATIONS

For the numerical solution of the proposed problem, the heat transfer governing differential

equations were built in and calculated using COMSOL software (COMSOL_Multiphyics, 2013a;

COMSOL_Multiphyics, 2013b).

1. Equations for Heat Transfer in the Sugar Beet Pile

The beet pile was considered a porous medium with sugar beet roots as the solid phase and

moist air as the fluid phase as described by equations 4, 5 and 6 (COMSOL_Multiphyics, 2013a;

COMSOL_Multiphyics, 2013b).

Equation 4: 𝜌Cpu . ∇T + ∇ .q = Q

where:

Equation 5: q = − keff ∇T

and:

Equation 6: keff = θpkp+ (1- θp) k + k disp

where:

𝜌: is the density of the beet (kg·m-3),

Cp: is the specific heat of the beet at constant pressure (J·kg-1·K-1),

u: is the velocity of the moist air inside the pile (m·s-1),

∇T: is the temperature gradient (K·m-1),

q: is the conductive heat flux (W·m-2),

Q: is the respiration heat per unit volume (W·m-3),

keff: is the effective thermal conductivity (W·m-1·K-1),

θ p: porosity (%),

kp: beet thermal conductivity (W·m-1·K-1),

k: moist air thermal conductivity (W·m-1·K-1),

kdisp: Dispersive thermal conductivity (W·m-1·K-1).

2. Equations for Heat Transfer in the Ground

The ground was considered as a solid material and the following equations were used to

solve for the ground temperature (COMSOL_Multiphyics, 2013a; COMSOL_Multiphyics,

2013b):

Equation 7: 𝜌Cp u . ∇T + ∇ . q = Q

Equation 8: q = − kg∇T

where:

kg= ground thermal conductivity (W·m-1·K-1),

𝜌: is the density of the soil (kg·m-3),

Cp: is the specific heat of the soil at constant pressure (J·kg-1·K-1),

u: is the velocity field defined by the translational motion sub-node when parts of the model are

moving in the material frame (m·s-1),

∇T: is the temperature gradient (K·m-1),

q: is the conductive heat flux (W·m-2),

Q: is the heat flux (W·m-3).

3. Equations for Heat Transfer in the Air

Pile cooling occurs by natural convection (Beukema, 1980); therefore, moist air was

considered as a fluid material and relative humidity (RH) was used as an input quantity of

moisture. The following equations solve for air temperature (COMSOL_Multiphyics, 2013a;

COMSOL_Multiphyics, 2013b):

Equation 9: 𝜌𝐶𝑝 𝑢 . ∇T + ∇ . q = 𝑄

Equation 10: q = − k∇T

Where 𝜌: is the density of moist air (kg·m-3),

Cp: is the specific heat of the moist air at constant pressure (J·kg-1·K-1),

u: is the air velocity (m·s-1),

∇T: is the temperature gradient (K),

q: is the conductive heat flux (W·m-2),

Q: is the heat flux from the heat source (or sink) (W·m-3),

k: moist air thermal conductivity (W/m. ◦K).

MONITORING PILE TEMPERATURE

To monitor the pile temperature, wiring harnesses of T-type (copper/constantan)

thermocouples (OMEGA Engineering™, INC., Norwalk, CT, USA), encased in 6-mm i.d.

polypropylene tubing for protection, were installed in the middle of the beet piles in late October

in 2011 and in early November in 2012.

Harnesses were placed on the sloping face of the pile when the pile was partially

constructed. Following placement of the harnesses, pile construction was completed, burying the

thermocouples within the pile at predefined locations (Fig. 2 for 2011 and Fig. 3 for 2012). Each

harness had from 1 to 10 thermocouples, depending upon their position in the pile. One harness

was placed vertically down the face of the pile at the midpoint and another harness was placed

diagonally across the face of the pile from its outer shoulder to the base at its midpoint. A third

harness ran horizontally along the base of the pile to its midpoint and a fourth harness

(thermocouples only, no protective tubing used) was buried about 5 cm below the soil surface

along the base of the pile to its midpoint. One additional thermocouple was embedded in the pile

between the vertical harness and the diagonal harness and another two thermocouples were

embedded in the pile between the diagonal harness and the horizontal harness. A total of 26 (in

2011 season) and 25 (in 2012 season) locations were monitored. There was 1 failed thermocouple

in the 2012 season leading to a decrease in the number of locations in the later season.

Temperature measurements were collected every minute using digital dataloggers (CR-10,

Campbell Scientific, Inc., Logan, Utah, USA) and the average for each hour recorded. Temperature

data that was used for model validation was collected from November to January in 2011, and

from November to February in 2012. The 2011 storage season was dry and warm, limiting storage

to two months.

CALCULATING SUGAR LOSS

Evaluating the sugar loss and decrease in quality in the roots during storage are the main

ways to evaluate any storage system for sugar beet (Huijbregts et al., 2013). Thus, Cumulative

sugar loss (kg/metric ton) was estimated using measured and modeled temperatures to evaluate the

model accuracy and to study the effect of various modeled geometries and ventilation designs of

the pile which can be recommended sugar beet storage in the future.

Cumulative sugar loss was calculated as a function of the daily average of either the pile’s

measured temperature or modeled temperature. To calculate the daily sugar loss, Eq. 2 was used

to solve for the temperature to obtain the predicted CO2 respiration rate (mg kg-1 hr-1). Daily

sucrose loss (mg kg-1 hr-1) is equal to the daily CO2 respiration rate divided (mg kg-1 hr-1) by 1.55,

as the mass of CO2 is 1.55 times that of sucrose (Azcón-Bieto and Osmond, 1983; Siedow and

Day, 2017). To predict Cumulative sugar loss, calculated daily sugar loss was added for every day

of the period tested. Sugar loss was also used to compare between different pile zones, measured

and modeled temperatures and to test three designs of sugar beet storage systems (described in the

Pile design evaluation section later) compared to the actual sugar loss.

Three differing pile designs were developed to determine the effect of pile architecture on

beet root temperature, assuming a 3°C increase in air temperature relative to 2012 data. The

Cumulative sugar loss was calculated for the modeled scenarios.

PILE ZONE COMPARISONS

To simplify the interpretation of the results, the pile was divided into three zones. The

lower zone; from the base of the pile up to 1.6 m high, the middle zone; from the lower zone to

3.2 m high and the upper zone; from the middle zone to the top of the pile (4.9 m). Each zone

contained 6 to 14 collected temperature points (Fig. 4 for 2011 and Fig. 5 for 2012). The average

temperature of the points in each zone was used as the temperature of that zone. A comparison

between sugar loss was obtained based on average zone temperature.

Figure 4: Schematic design: Illustrates the sugar beet pile divided into three zones, lower (■),

middle (●) and upper (♦) for the 2011 season. The colored symbols illustrate the thermocouple

locations as distributed in each zone.

Figure 5: Schematic design: Illustrates the sugar beet pile divided into three zones, lower (■),

middle (●) and upper (♦) for the 2012 season. The colored symbols illustrate the thermocouple

locations as distributed in each zone.

PILE DESIGN EVALUATION

Three pile designs differing in height (50% decrease and 50% increase relative to a

commercial pile) and ventilation (by creating a pass underneath the pile that allows cold air to flow

under the pile to cool the base), were designed using the built model with some modifications in

each system to predict the effect of these design variables on temperature (Table 4). Modeled

temperature obtained from each design was used to estimate the daily and Cumulative sugar loss

during storage, which was used to compare the three designs.

Table 4: Dimensions for different pile designs used for developing heat transfer models in sugar

beet storage piles.

Pile shape

Pile height (m)

Pile width (m)

Commercial

4.8

45.7

50% Decrease

2.4

45.7

50% Increase

7.3

45.7

Ventilated

4.8

45.7

In the “decreased height” beet pile system (Fig. 6), the main pile height was decreased by

50%, while all other parameters were the same as the main pile.

Figure 6: Schematic design: Illustrates the suggested “decreased height” sugar beet pile. The outer

pile-shape describes the commercial pile, the insider pile-shape describes the “decreased height”

pile. Arrows show the air direction for the model.

In the “increased height’ beet pile system shown in Fig. 7, the main pile height was

increased` by 50%, while all other parameters were the same as in the main pile.

Figure 7: Schematic design: Illustrates the suggested “increased height” sugar beet pile. The outer

pile-shape describes the “increased height” pile, the insider pile-shape describes the commercial

pile. Arrows show the air direction for the model.

In the ventilated system (Fig. 8), the area of that system was kept the same as the

commercial pile area and natural convection ventilation was added below the pile to cool the base

while all other parameters were the same as the main pile.

Figure 8: Schematic design: Illustrates the suggested “ventilated” sugar beet pile. The air domain

is surrounding the pile from all sides. Arrows show the air direction for the model.

For validation, the calculated temperatures were compared with measured temperatures

obtained during 132 days total for both years from an actual commercial storage pile. In the first

year, the air temperature was higher than usual, leading to a short storage period, and we were able

to obtain data for only 37 days. In the second year, the temperature was at the normal range, so we

were able to obtain data for 95 days. The pile temperature was used to calculate the respiration rate

of stored beets and thereby estimate sugar loss during the storage campaign.

DATA HANDLING, STATISTICAL ANALYSIS AND EXPERIMENTAL DESIGN

In the current study, the model yielded one temperature value per day for each point among

the 26 (in the 2011 season) and 25 (in the 2012 season) predefined points in the pile. However,

each data logger recorded 24 temperature measurements (i.e. one value per hour) for each

thermocouple of the 26 or 25 thermocouples used in each pile. To achieve consistency between

the measured and modeled temperatures, the daily average of the 24 measurements from each

thermocouple was obtained. The average temperature of all the predefined points was calculated

to obtain the pile temperature for each day for the primary analysis.

Analysis of variance (ANOVA) was used to test the relationship between the measured and

modeled temperatures and estimated cumulative sugar loss. In this stage of analysis, only the

average daily temperature of the whole pile was calculated from the 26 daily temperature values

in 2011 and the 25 daily temperature values in 2012. Thus, the total number of analyzed points

was 37 and 95 for the 2011 and 2012 seasons, respectively. Additionally, another ANOVA was

conducted to study the effect of pile zones (lower, middle and upper) on the difference between

the measured and modeled temperatures. In this stage, the average daily temperature was

considered for each zone and each season, calculated from 14, 6 and 6 daily temperature values

for the lower, middle and upper zones, respectively for 2011, and 12, 7 and 6 daily temperature

values for the lower, middle and upper zones, respectively for 2012. Thus, the total number of

analyzed points for the 2011 season were 37 points for each zone. Whereas, the total number of

analyzed points for the 2012 season were 95 points for each zone. In each of the above tests, the

significance level was chosen to be 0.05.

If a significant effect of any of the studied independent variables was found according to

the ANOVA test, a mean comparison was carried out using the least significant difference (LSD)

T-test with a significance level of α ≤ 0.05. Besides, a correlation analysis was conducted to study

the relationship between cumulative sugar loss for measured and modeled temperatures with a

level of significance as (α ≤ 0.05) and the correlation coefficient (r) was used to estimate the

strength of this relationship. To predict Lm (the Cumulative sugar loss based on measured

temperature) as a function of Ld (the Cumulative sugar loss based on modeled temperature), a

simple linear regression analysis was conducted and the coefficient of determination (R2) was

calculated. The statistical analysis was performed using the PROC GLM procedure in SAS 9.4

(2014, SAS Institute Inc., Cary, NC, USA).

RESULTS

The pile temperature distribution changed throughout the day in response to changing air

temperature (Fig. 9). The temperature of the pile typically declined from the inside to the outside

of the pile. The center of the pile was usually the warmest region of the pile and of the three zones

chosen for analysis, the lower zone of the pile, near the ground surface, was usually warm

compared to the upper zone of the pile. The base of the pile typically ranged from 2.8 to 11 °C

warmer than the surface of the pile. During a warm period, when the air temperature was around

2 °C, large portions of the pile (>70%) had root temperatures above 7 °C. During a cool period,

when the air temperature was -7 °C, about 30% of the pile still had temperatures in the 4.5 °C

range, and almost half of the pile had temperatures below freezing.

Figure 9: Heat transfer diagram: Illustrate the temperature profile of the Gera Road beet pile on

December 5-10, 2011. The average air temperature is given in the thermometer to the right of each

panel. A, B, C, D and SP indicate five thermocouple harnesses; harness D was embedded

approximately 5 cm into the soil. White circles indicate locations of individual thermocouples.

MODEL ACCURACY BASED ON PILE TEMPERATURE

The modeled daily average temperatures for the whole pile were compared with measured

daily average temperatures for both storage seasons. The model tended to underestimate

temperature (Fig. 10 for 2011 and Fig. 11 for 2012). The mean difference between measured and

modeled temperature values was significant (P ≤ 0.05) (Table 5), and a boxplot shows the mean

of the modeled temperatures was lower than the mean of measured temperatures for both seasons

(Fig. 12 for 2011 and Fig. 13 for 2012). Due to some technical problems with dataloggers, some

measuring data was lost, resulting in gaps in temperature measurements in Fig. 10 and similar

subsequent figures.

Figure 10: Graph: Shows the measured (▲) and modeled (●) sugar beet whole pile temperatures

for the 2011 season in relation to air temperature (■).

Figure 11: Graph: Shows the measured (▲) and modeled (●) sugar beet whole pile temperatures

for the 2012 season in relation to air temperature (■).

Figure 12: Boxplot: Displays the distribution of the values of measured and modeled temperatures

for the beet pile temperature for the 2011 season. Diamonds (◊) represent the mean values; circles

(○) represent the outlier values.

Figure 13: Boxplot: Displays the distribution of the values of measured and modeled temperatures

for the beet pile temperature for the 2012 season. Diamonds (◊) represent the mean values; circles

(○) represent the outlier values.

Table 5: Measured and modeled beet pile temperatures (°C) for 2011 and 2012 averaged across

the storage campaign.

Pile temperature (°C)

Data source

2011a

2012b

Measured

6.21 A

5.68 A

Modeled

4.3 B

3.64 B

* Values followed by different letters within a column differ based on LSD test (α ≤ 0.05).

aLSD = 0.7714 for the 2011 season.

bLSD = 0.6222 for the 2012 season.

MODEL ACCURACY BASED ON SUGAR LOSS

1. Daily Sugar Loss

Daily rate of sugar loss (kg/metric ton/day) based on measured and modeled temperatures

were calculated (Fig. 14 for 2011 and Fig. 15 for 2012) and boxplot (Fig. 16 for 2011 and Fig. 17

for 2012) and mean different analysis (Table 6) were obtained. The mean of the daily sugar loss

based on the modeled pile temperature was significantly (P≤0.05) lower than the mean of the daily

sugar loss based on the measured pile temperature, which means that the calculations based on the

modeled pile temperature values underpredict the amount of sugar loss.

Figure 14: Graph: Shows the daily sugar loss (kg/metric ton /day) from field-stored sugar beets

calculated from measured (▲) and modeled (●) pile temperatures for the 2011 season.

Figure 15: Graph: Shows the daily sugar loss (kg/metric ton /day) from field-stored sugar beets

calculated from measured (▲) and modeled (●) pile temperatures for the 2012 season.

Figure 16: Boxplot: Displays the distribution of the daily rate of sugar loss (kg/metric ton/day) due

to respiration as a function of measured or modeled sugar beet pile temperature for the 2011

season. Diamonds (◊) represent the mean values; circles (○) represent the outlier values.

Figure 17: Boxplot: Displays the distribution of the daily rate of sugar loss (kg/metric ton/day) due

to respiration as a function of measured or modeled sugar beet pile temperature for the 2012

season. Diamonds (◊) represent the mean values; circles (○) represent the outlier values.

Table 6: Sugar loss estimates based on measured and modeled beet pile temperatures for 2011 and

2012 (°C) averaged throughout the storage campaign.

2011a

2012b

Rate of sugar loss

(kg/metric ton/day)

Type

Rate of sugar loss

(kg/metric ton/day)

Type

0.14 A

Measured

0.13 A

Measured

0.11 B

Modeled

0.10 B

Modeled

*Values followed by different letters within a column differ based on LSD test (α ≤ 0.05).

aLSD = 0.0116 for the 2011 season.

bLSD= 0.0094 for the 2012 season.

2. Cumulative Sugar Loss

There was a high correlation between Cumulative sugar loss (kg/metric ton) based on daily

average values of measured temperatures (Lm) and modeled temperatures (Ld) with a coefficient

of correlation (r) of 0.997 and 0.999 for the 2011 and 2012 seasons, respectively. The total number

of days in storage was 37 days in 2011, and 95 days in 2012 (Fig. 18 for 2011 and Fig. 19 for

2012). A mean comparison (Table 7) and a boxplot (Fig. 20 for 2011 and Fig. 21 for 2012) show

that there was a significant difference between the Lm and Ld (P≤0.05). The mean values of Ld

were significantly lower than the mean values of Lm by 1.06 (kg/metric ton) for the 2011 season

and 2.91 (kg/metric ton) for the 2012 season.

Figure 18: Graph: Shows the cumulative sugar loss (kg/metric ton) from field-stored sugar beets

calculated from measured (▲, Lm) and modeled (●, Ld) pile temperatures for the 2011 season.

Figure 19: Graph: Shows cumulative sugar loss (kg/metric ton) from field-stored sugar beets

calculated from measured (▲, Lm) and modeled (●, Ld) pile temperatures for the 2012 season.

Figure 20: Boxplot: Displays the distribution of measured or modeled Cumulative sugar loss

(kg/metric ton) for the 2011 season. Diamonds (◊) represent the mean values; circles (○) represent

the outlier values.

Figure 21: Boxplot: Displays the distribution of measured or modeled Cumulative sugar loss

(kg/metric ton) for the 2012 season. Diamonds (◊) represent the mean values; circles (○) represent

the outlier values.

Table 7: Calculated cumulative sugar loss (kg/metric ton) in field-stored sugar beets based on

measured and modeled pile temperature for 2011 and 2012.

2011a

2012b

Cumulative sugar

loss (kg/metric ton)

Type

Cumulative sugar

loss (kg/metric ton)

Type

2.91 A

Measured

6.97 A

Measured

2.18 B

Modeled

5.43 B

Modeled

* Values followed by different letters within a column differ based on LSD test (α ≤ 0.05).

aLSD = 0.6142 for the 2011 season.

bLSD= 0.943 for the 2012 season.

The cumulative sugar loss (kg/metric ton) for the 2011 and 2012 seasons were pooled

together to conduct simple linear regression analysis between sugar loss estimated from modeled

and actual temperatures. Cumulative sugar loss was estimated by the pile temperature based on the

model was used as an independent variable to predict Cumulative sugar loss based on the actual

temperature measured in the beet pile. The coefficient of determination (R2) was equal to 0.999.

The equation (Eq. 11) can be used to correct the modeled data using the cumulative sugar loss

based on measured temperatures. The equation can be used to obtain an estimate of the cumulative

sugar loss for models of different designs of the storage piles.

Equation 11: Ld= 0.7784 Lm – 0.021

Lm= Estimated cumulative sugar loss (kg/metric ton) based on pile measured temperature.

Ld= Estimated cumulative sugar loss (kg/metric ton) based on pile modeled temperature.

PILE ZONE COMPARISON

1. Variation of the Measured Temperature Inside the Pile

To study the spatial variation of temperatures inside the pile, the pile was virtually divided

into upper, middle and lower zones. The temperature in the upper zone was the lowest followed

by the temperature of the middle zone and finally the lower zone (Fig. 22 for 2011 and Fig. 23 for

2012). Boxplot analysis (Fig. 24 for 2011 and Fig. 25 for 2012) and mean comparison t-test

between measured temperatures of the different zones were conducted (Table 8). The average

temperature for the storage season of the three zones differed (p ≤ 0.05). The temperature of the

upper zone was significantly lower than the temperature of the middle and lower zones, and the

temperature of the middle zone was significantly higher than the temperature of the lower zone in

both seasons.

Figure 22: Graph: Shows the temperatures (°C) of the lower (▲), middle (●) and upper (♦) zones

of the sugar beet pile and the average daily air temperature (■) for the 2011 season.

Figure 23: Graph: Shows the temperatures (°C) of the lower (▲), middle (●) and upper (♦) zones

of the sugar beet pile and the average daily air temperature (■) for the 2012 season.

Figure 24: Boxplot: Displays the average temperatures (°C) throughout the storage campaign of

lower, middle and upper zones of the sugar beet pile for the 2011 season. Diamonds (◊) represent

the mean values; circles (○) represent the outlier values.

Figure 25: Boxplot: Displays the average temperatures (°C) throughout the storage campaign of

lower, middle and upper zones of the sugar beet pile for the 2012 season. Diamonds (◊) represent

the mean values; circles (○) represent the outlier values.

Table 8: Temperatures of the lower, middle and upper zones of the sugar beet pile in 2011 and

2012 averaged across the storage campaign. Means are the average of 37 d in 2011 and 97 d in

2012.

2011a

2012b

Zone

Temperature (°C)

Lower

7.65 A

6.45 A

Middle

5.05 B

Upper

2.75 C

3.85 C

*Values followed by different letters within a column differ based on LSD test (α ≤ 0.05).

aLSD = 0.9678 for the 2011 season.

bLSD= 0.6171 for the 2012 season.

2. Daily Sugar Loss Comparison Between Pile Zones

The calculated daily sugar losses (kg/ton/day), based on measured temperatures from each

of the three zones, were higher at the beginning of the storage season than the end of the season

(Fig. 26 for 2011 and Fig. 27 for 2012). The upper zone was predicted to have the lowest sugar

loss of the three zones and the lower zone had the highest (Fig. 28 for 2011 and Fig. 29 for 2012)

and (Table 9).

Figure 26: Graph: Shows the calculated daily rate of sugar loss (kg/metric ton/day) based on

measurements of pile temperature (°C) for the lower (▲), middle (●) and upper (♦) zones of the

pile for the 2011 season. The secondary vertical axis is the average daily air temperature (■).

Figure 27: Graph: Shows the calculated daily rate of sugar loss (kg/metric ton/day) based on

measurements of pile temperature (°C) for the lower (▲), middle (●) and upper (♦) zones of the

pile for the 2012 season. The secondary vertical axis is the average daily air temperature (■).

Figure 28: Boxplot: Displays the average calculated daily sugar loss (kg/metric ton/day) based on

measured temperatures (°C) of lower, middle and upper zones of a sugar beet pile for the 2011

season. Diamonds (◊) represent the mean values; circles (○) represent the outlier values.

Figure 29: Boxplot: Displays the average calculated daily sugar loss (kg/metric ton/day) based on

measured temperatures (°C) of lower, middle and upper zones of a sugar beet pile for the 2012

season. Diamonds (◊) represent the mean values; circles (○) represent the outlier values.

Table 9: Estimated rate of sugar loss (kg/metric ton/day) for field-stored sugar beets in the upper,

middle and lower zones of the beet pile based on measured temperature.

2011a

2012b

Zone

Rate of sugar loss

(kg/metric ton/day)

Rate of sugar loss

(kg/metric ton/day)

Lower

0.161 A

0.143 A

Middle

0.121 B

0.122 B

Upper

0.087 C

0.103 C

*Values followed by different letters within a column differ based on LSD test (α ≤ 0.05).

aLSD = 0.0145 for the 2011season.

bLSD= 0.0093 for the 2012 season.

3. Cumulative Sugar Loss Comparison Between Pile Zones

The amount of sugar loss was estimated to be highest in the lower zone and lowest in the

upper zone in both seasons (Table 10).

Table 10: Estimated cumulative sugar loss (kg/metric ton) in the 2011 season (37 days) and the

2012 season (95 days) calculated from the measured temperature of the lower, middle and upper

zones of the beet pile.

Zone

2011 (37 days)

2012 (95 days)

Upper

3.21

9.78

Middle

4.48

11.60

Lower

5.94

13.59

MODEL ACCURACY IN DIFFERENT ZONES

1. Temperature Comparison Between Pile Zones

Based on the measured and modeled data, the temperature values obtained from the model

were generally lower than the measured temperatures. However, in some days the modeled

temperatures in the upper (Fig. 30 for 2011 and Fig. 31 for 2012) and middle zones (Fig. 32 for

2011 and Fig. 33 for 2012) overestimated the measured temperatures, possibly due to the rapid

fluctuation in air temperatures. In the case of the lower zone, there was consistent temperature

underestimation by the model (Fig. 34 for 2011 and Fig. 35 for 2012).

According to ANOVA analysis (Table 11), there was no significant (P≤ 0.05) difference

between the measured and modeled temperatures in the upper and middle zones in the 2011 season.

This illustrates that the model has accuracy for predicting the pile temperatures in these zones.

This finding contrasts with the results for the lower zone. In the 2012 season, there was a

significant difference between the measured and modeled temperatures in all studied zones (P≤

0.05).

Figure 30: Graph: Shows the measured (▲) and modeled (●) temperatures (°C) of the upper zone

of the sugar beet pile for the 2011 season in relation to air temperature (■).

Figure 31: Graph: Shows the measured (▲) and modeled (●) temperatures (°C) of the upper zone

of the sugar beet pile for the 2012 season in relation to air temperature (■).

Figure 32: Graph: Shows the measured (▲) and modeled (●) temperatures (°C) of the middle zone

of the sugar beet pile for the 2011 season in relation to air temperature (■).

Figure 33: Graph: Shows the measured (▲) and modeled (●) temperatures (°C) of the middle zone

of the sugar beet pile for the 2012 season in relation to air temperature (■).

Figure 34: Graph: Shows the measured (▲) and modeled (●) temperatures (°C) of the lower zone

of the sugar beet pile for the 2011 season in relation to air temperature (■).

Figure 35: Graph: Shows the measured (▲) and modeled (●) temperatures (°C) of the lower zone

of the sugar beet pile for the 2012 season in relation to air temperature (■).

Table 11: Significance level, resulting from ANOVA analysis, assessing whether predicted and

measured pile temperatures differed in the upper, middle and lower zones over two storage

seasons.

Pile zone

2011

2012

Upper

0.34

< 0.0001

Middle

0.06

< 0.0001

Lower

< 0.0001

EVALUATION OF PILE GEOMETRIES AND VENTILATION ON SUGAR LOSS

1. Daily Sugar Loss Comparison Between Pile Geometries and Ventilation

Further analysis was conducted to study the effect of pile height (decreased, increased and

commercial) and the effect of ventilation using the model developed above. Pile shape was

predicted to affect temperature gradients and subsequently sugar loss. These models were

developed one time under actual air temperature according to the air temperature records from 1

November 2012 to 8 February 2013, and the second time with 3°C increase in the air temperature

relative to 2012 data every day to evaluate different designs in the case of warmer winters. The

ventilated pile yielded significantly (P≤0.05) lower daily sugar loss (kg/metric ton/day) while the

other designs did not vary significantly according to mean difference analysis under 2012 or

increased air temperatures (Table 12 for 2012 air temperature and Table 13 for 3°C increase in the

air temperature relative to 2012 data) and (Fig. 36 for 2012 air temperature and Fig. 37 for 3°C

increase in the air temperature relative to 2012 data).

Figure 36: Boxplot: Displays the distribution of the values for daily sugar loss rate (kg/metric

ton/day) of different designs of sugar beet storage piles based on 2012 air temperatures. Diamonds

(◊) represent the mean values; circles (○) represent the outlier values.

Figure 37: Boxplot: Displays the distribution of the values for daily sugar loss rate (kg/metric

ton/day) of different designs of sugar beet storage piles based on predicted 3°C increase in air

temperatures relative to 2012 data. Diamonds (◊) represent the mean values; circles (○) represent

the outlier values.

Table 12: Modeled prediction of the daily rate of sugar loss (kg/metric ton/day) for beet piles

having different heights or ventilation in a sugar beet pile based on the 2012 air temperature.

Treatment

Pile height

(m)

Rate of sugar loss

(kg/metric ton/day)a

Decreased height pile

2.4

0.083 A

Commercial pile

4.9

0.093 A

Increased height pile

7.3

0.096 A

Ventilated pile

4.9

0.04 B

*Values followed by different letters within a column differ based on the LSD test (α ≤ 0.05).

aLSD value = 0.0171

Table 13: Daily rate of sugar loss (kg/metric ton/day) for beet piles having different heights or

ventilation in a sugar beet pile based on 3°C increase in air temperature relative to 2012 data.

Treatment

Pile height

(m)

Rate of sugar loss

(kg/metric ton/day)a

Decreased height pile

2.4

0.105 A

Table 13 (cont’d)

Commercial pile

4.9

0.113 A

Increased height pile

7.3

0.105 A

Ventilated pile

4.9

0.085 B

*Values followed by different letters within a column differ based on the LSD test (α ≤ 0.05).

aLSD value = 0.0167

2. Cumulative Sugar Loss Comparison Between Pile Geometries and Ventilation

Table 14 represents the predicted amount of Cumulative sugar loss (kg/metric ton)

following 100 days of field storage in piles modeled with varying height or ventilated pile designs

under the 2012 actual air temperatures and 3°C higher air temperatures relative to 2012 data. The

amount of sugar loss was lower in the ventilated pile design than the other designs under both the

2012 and the increased pile temperatures according to the model.

Table 14: Predicted total sugar loss (kg/metric ton) after 100 days of field storage based on the

temperatures obtained from models varying pile height, ventilation and average temperature (+3

°C) for beet piles under the 2012 season.

Pile modification

Pile height (m)

Cumulative sugar loss over

100 days

(kg/metric ton)

Decreased height pile

2.4

8.37

Commercial pile

4.9

9.62

Increased height pile

7.3

9.33

Ventilated pile

4.9

6.03

Decreased height pile with

3°C increase in air

temperature relative to 2012

data

2.4

10.49

Commercial pile with 3°C

increase in air temperature

relative to 2012 data.

4.9

11.29

Table 14 (cont’d)

Increased height pile with

3°C increase in air

temperature relative to 2012

data.

7.3

12.09

Ventilated pile with 3°C

increase in air temperature

relative to 2012 data.

4.9

9.49

DISCUSSION

The model developed in the current study generally underestimated the measured

temperature as well as sugar loss in sugar beet pile during storage. The lack of fit between the

measured temperatures and modeled temperatures was possibly due to the steady-state heat

transfer condition of the model that was assumed for simplicity for model development instead of

accurately reflecting dynamic conditions. The steady-state condition refers to the situation when

the change of the internal energy does not vary with time (Datta, 2002), which we decided to be a

day. A steady-state condition may occur in a controlled system where the inputs (i.e., air

temperature and wind speed) do not change during the time. This was not the case in the studied

beet pile as the environmental conditions changed frequently. On the other hand, developing a

dynamic model for outdoor sugar beet pile storage would be highly challenging, because in the

most available transient models of storage systems, they have controlled environment with limited

variables, whereas in the case of this study we have the air temperature, wind speed, relative

humidity, precipitation, solar radiation, root temperature, respiration, desiccation, soil temperature,

soil moisture content, water evaporation, and condensation as variables that give the model so

much complexity. So that we found that considering the most important factors in a simple model

as a primary step, then modify that simple model in future studies working toward some

complexity.

Also employing a day to be the time for a steady-state was a relatively long time as we

found that the pile temperature was responsive to the air temperature that changes as much as 15

°C in one day. Also, neglecting the effect of moisture transfer and the change in the water content

inside the pile may have contributed to an inaccurate estimate of the thermal conductivity of the

pile material (beet, water and air). Results obtained by Xu and Burfoot (1999) confirm the

importance of accurately measuring or calculating the moisture content to develop heat transfer

models for biological materials. Although their model had a good fit in most parts of the pile, a

lack of fit occurred when the moisture content was incorrectly calculated. Hoang et al. (2003), also

attributed the underestimation of their model to desiccation on the surface of chicory roots during

storage, because the water heat transfer coefficient is 50 to 100 times higher than the air heat

transfer coefficient (Datta, 2002). Something similar could be a possible reason in the current

study, especially for the error found at the surface of the pile. Although lack of fit due to moisture

content miscalculations was expected, we adapted the idea of a simple, more easily applied and

less intensive model. For instance, moisture sensors to cover every part in a huge body like the

beet pile is very costly and time-consuming. Also, understanding the limitations of the current

model can help future researchers decide the important aspects to monitor or model to develop a

better model.

Non-uniform root size of the beet pile during storage, leading to varied sizes of voids

between roots, can also lead to inexact estimates of in thermal conductivity, water content and air

movement calculations (Hoang et al., 2003). In addition to the above, using the average of the

daily temperatures resulted in losing some model sensitivity to the change of temperature during

the day. As mentioned before, we used the daily average air temperature and wind speed as inputs

when we developed the model. At any time, these inputs change significantly during the day, using

the average of such inputs may have reduced the model’s sensitivity to changes in the

environmental condition. This likely affected accuracy, as the pile temperature was sensitive to the

changes in ambient conditions.

Lack of fit between measured and predicted temperatures often is found in models of

biological materials. For example, Zou et al. (2006b) explained the inaccuracy in their model by

errors in the position of thermocouples, model input values and/or model assumptions. Similarly,

Hoang et al. (2003) found underestimation of chicory temperature due to water loss and

condensation on the surface of the roots from evaporation due to low relative humidity in the

storage room as well as non-uniform porous, variation in the product sizes and the relatively small

voids compared to the size of the roots. On the other hand, Markarian et al. (2006) developed a

mathematical model with high accuracy, due to the controlled storage system, the model included

mass and heat transfer in three dimensions and for a limited storage time (1 hour). Their success

is likely a function of their control of conditions and highlights the difficulties in a complex,

uncontrolled system that contribute to lack of fit as in the case of our model.

The cumulative sugar loss depending on measured and modeled temperatures were highly

correlated. This means that the Cumulative sugar loss based on the modeled temperatures can be

helpful to roughly predict the cumulative sugar loss based on the measured temperatures. This can

be a helpful technique for storage managers to evaluate new pile designs.

According to the pile zone comparison, differences of measured temperatures between the

three pile zones described the existence of temperature variations inside the pile and show that the

upper zone was always colder than the middle and lower zones and the lower zone is always

warmer than the middle and the upper zone. The results for sugar loss are in good agreement with

the results for temperature. The results are expected because the upper zone is exposed to the

relatively cold air and removes the heat of the upper zone by convection. On the other hand, the

lowest zone gained heat from the ground by conduction, thereby increasing the temperature in that

zone.

Estimated daily sugar losses were higher early in the storage campaign. These results were

similar to the findings of Fox (1973) and Wyse (1975) that 50% of sugar loss in sugar beets occur

during the first two weeks of storage, and the majority of the sugar loss occurs during the first 40

days of storage.

Cumulative sugar loss calculations in different zones highlight an elevated sugar loss in

the lower zone compared with the middle and the upper zones. This indicates the importance of

reducing the temperature of this zone (Yang and Rao, 2006).

In the case of the effect of pile zones on modeled temperature accuracy, the modeled and

measured temperatures showed good agreement in the upper and middle zones during the 2011

season for these zones. This may be a function of the model making better predictions at higher

temperatures, this means that the model is accurate for predicting the pile temperatures in these

zones. However, the model underestimated the temperature of the lower zone for both storage

seasons.

It should be noted that the lower zone is mainly affected by the ground temperature and in

the model, as we used the semiannual average temperature of the ground obtained from Reese, MI

(Schaetzl et al., 2005) which resulted in losing part of the model sensitivity to the changes of

temperature in that zone. Moreover, in the pile base, the beet weight is relatively high and that

possibly caused damage to the roots and consequently increased respiration rate and thereby

increase temperature (Cole, 1977). The compressed damaged roots may have also caused blocking

of the voids which happened to potatoes (Pringle et al., 2009), which may have changed the

thermal conductivity of the pile material. Furthermore, beet roots in a field pile are often mixed

with topsoil and stones. (Flegenheimer, 2015) noted there were an estimated 136,000 metric tons

of topsoil and other debris are added to beet storage piles each year. The non-beet materials are

mainly accumulated at the base of the pile, filling the voids and altering the physical and thermal

properties of the pile material.

In the middle zone, differences between modeled and measured temperatures are possibly

from condensation in that zone. An increase in moisture content can subsequently affect porosity,

thermal conductivity and air movement. The middle zone is also likely to be warmer than

anticipated because of the heat gained from the lower zone. The warmer air stream that moves

from the lower zone to the middle zone holds moisture and can cause a condensation layer as

happened in a potato storage study by (Pringle et al., 2009). Consequently, an increase of the

moisture in the middle zone could lead to partially blocking the voids with water that change the

thermal conductivity of that zone and cause a decline in respiration (Lafta and Fugate, 2009). That

could be an explanation of the model agreement with measured temperature in 2011 with the

increase in air temperature and possibly increase in evaporation from the lower zone that causes

the formation of a condensation zone and reduces the respiration rate of the beets in that zone.

The upper pile zone is the most susceptible part of any changes in environmental

conditions, as it has the largest surface interacts with ambient conditions (e.g., sunlight, wind, rain,

snow, temperature, humidity). Fluctuations in air temperatures lead to an increase in respiration

rate and sucrose loss even if occur of storage temperatures of -1 °C or below (Wyse, 1978), which

was the case in the commercial pile especially in the upper zone. Therefore, evaluating the

respiration rate under a constant storage temperature and using that value in the model as a source

of heat possibly led to underestimation in temperature in this zone. Fluctuation can significantly

increase sucrose loss due to the accumulation of reducing sugars after respiration. Additionally,

the possibility of root dehydration in this zone is much higher than the other zones (Campbell and

Klotz, 2006; List, 2015). Dehydration damages the cells and can result in loss of permeability

control and electrolyte leakage, which significantly increase respiration (Lafta and Fugate, 2009;

Yang and Rao, 2006). Dehydration also occurs due to cell freezing, cells start to freeze (or damage)

at -2 °C and they are completely frozen at -5 °C (Campbell and Klotz, 2006; Wyse, 1978). Freezing

followed by thawing causes the cells to lose metabolic control and permeability, which causes

increased cell respiration, desiccation and root deterioration (Lafta and Fugate, 2009; Wyse, 1978).

Lafta and Fugate (2009); Wyse (1978) noted a temperature fluctuation and dehydration within 60

cm from the pile surface, which likely increases respiration, as dehydration causes more than 82%

increase in the respiration rate compared with the initial respiration rate

In the 2011 season, the air temperature was relatively higher than in the 2012 season and

that contributed to less freezing damage. The temperatures in that year were closer to those used

to calculate the respiration rate in the laboratory experiment, and may account for the increase in

the model accuracy (i.e., lack of significant difference between model and measured temperatures)

in the upper zone found that season.

The model predicted that pile height and ventilation at the base of the pile could make a

significant contribution to sugar loss. Through ventilation, the increase in the surface exposed to

cold air convection lead to a significant decrease in the rate of daily sugar loss compared to other

pile designs. The ventilated pile yielded lower daily and Cumulative sugar loss comparing with

the commercial, increased height and decreased height designs applying the 2012 air temperature

and 3°C increase in 2012 air temperature. The result is consistent with the results of the zone

comparison, which emphasized the significant increase in sugar loss found in the lower zone,

where heat is gained directly from the ground. Reducing the heat in the base of the pile, the sugar

loss significantly decreased from 9.3 kg/metric ton in the commercial pile to 3.95 kg/metric ton in

the ventilated pile, which is 68% decrease in sugar loss compared with the commercial pile. Thus,

after 100 days in the storage, a higher rate of sugar loss was found for the commercial pile (11.29

kg per metric ton per 100 days) compared to the ventilated pile (8.55 kg per metric ton per 100

days); a 3°C increase in air temperature would yield a 24% increase in sugar loss. On the other

hand, the change in the pile height (either increase or decrease) does not affect the sugar loss

significantly in comparison with the commercial beet pile based on the air temperature of 2012 or

3°C increase in 2012 air temperature. The results are similar to those for a study by Michigan

Sugar Company (List, 2015) in which they found that they needed to reduce the pile width by

83.9% and the pile height by 38.7% to reach 1% of the sugar loss from harvesting to December.

In addition to these findings, we recommend insertion of natural ventilation at the base of the pile

during the storage period.

SUMMARY AND CONCLUSIONS

The enormous production of sugar beet prevents the immediate processing of harvested

roots and is responsible for the need for vast storage facilities until processing. In Michigan, beets

are stored in huge piles exposed to the fluctuations in the surrounding environmental condition.

Approximately half of the storage piles are unventilated, thus, natural convection is the only

cooling technique for the top and sides of each of such piles. Fluctuating air temperatures enhance

respiration rate and microbial activity in the exposed piles, which results in a reduction in root

quality and increased sugar loss. In the current study, mathematical simulation methodology was

applied to solve for pile temperatures. Such simulation is intended to help storage managers not

only for predicting temperatures but also to improve management decisions regarding pile

structure (dimensions and shape), handling stored beet and installation of appropriate ventilation

systems.

A two-dimensional mathematical model was developed as a function of environmental

parameters (air temperature, air velocity, RH and an average ground temperature) to simulate the

heat transfer process during the storage period and to predict the temperature profile of an

unventilated sugar beet pile. The model was developed based on the finite element approach.

Model validation was obtained by comparing the modeled temperatures with measured

temperatures collected from a commercial beet pile using embedded thermocouples for two

seasons, 2011 and 2012, for 37 and 95 days, respectively.

The model that was developed generally underpredicted pile temperatures. This

underprediction is attributed to several factors including the assumption by the model of steady-

state conditions, meaning that pile temperature is assumed to be in equilibrium with its

environment, which is likely rarely true. Additionally, the model excluding moisture mass transfer

taking place in the pile, which can affect the heat loss and thermal conductivity and subsequently

alter heat transfer calculations.

The model accuracy was evaluated by comparing the modeled and measured temperatures

for three spatial zones in the pile upper, middle and lower zones. The modeled and measured

temperatures showed fair agreement in the upper and middle zones. However, the model

underestimated the temperature of the lower zone during the two storage seasons.

The measured and modeled temperatures were used to calculate the Cumulative sugar loss

(kg/metric ton). A strong relationship was obtained between modeled and calculated values with

a correlation coefficient of higher than 99%. As expected, based on differences in model and actual

temperatures, the Cumulative sugar loss calculated based on model temperature was lower than

the Cumulative sugar loss calculated based on the measured temperature. The effect of pile height

or use of ventilation compared to commercial piles was also tested by assessing two different pile

geometries, a 50% reduction of the height of the commercial pile or a 50% increase of the height

of the commercial pile, in addition to taking into account the ventilation at the base of the

commercial pile. The three models were evaluated relative to a commercial pile design under

normal and increased air temperature to examine the effects of the designs in the case of warmer

winters. The results showed that the ventilated pile yielded significantly lower sugar loss compared

with the commercial pile under actual (2012) and increased temperature scenarios. The increased

and decreased height-piles did not vary significantly from the commercial pile for sugar loss.

In future work, we recommend developing a model for a transient heat transfer condition,

including moisture mass transfer states and using hourly data instead of daily average values as

the air temperature for instant can change 15°C in one day during the storage period. The change

also occurs continuously in air velocity, RH and precipitation. A dynamic model (unsteady-state

conditions) will take into consideration the fluctuation in the environmental conditions which will

increase the model accuracy as a consequence. There is a need to include beet respiration rate

values for a wider range of temperatures and use various root sizes as it significantly affects

respiration (Wyse, 1978). Further, non-uniform root size can lead to varied sizes of voids between

roots which causes an inexact result in thermal conductivity, water content and air movement

calculations (Hoang et al., 2003). We can improve our model if we provide more precise

parameters for the designed model such as ground temperature measurements, porosity and airflow

inside the pile.

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Long-term post-harvest field storage of sugar beet

Thesis

Full-text available

May 2023

William English

The post-harvest storage of the sugar beet crop in Sweden occurs in the field. The harvest of roots generally ends along with the month of November, but the processing campaign can continue into February. The loss of quality of the stored roots during this period is economically important. This thesis groups the main mechanisms that results in loss of quality during post-harvest storage in two categories: plant health, and the storage environment. It focuses on the plant health dimension of mechanical properties, and the storage environment dimensions of moisture and temperature. The relationship between key agronomic inputs and mechanical properties and storability of sugar beet roots was investigated. Growing season available nitrogen and water were found to have little impact on mechanical properties. The storability of roots was found to decrease significantly when irrigation gave an optimal soil water availability throughout the season. This is likely a result of an interaction with an unspecified dimension of plant health. The quantification of sugar beet root mechanical properties with a traditional handheld penetrometer applied in-field was found to be reliable. It was also found that the methods used in the analysis of mechanical properties could be expanded to include the apparent modulus of elasticity and that fall-tests can be used to assess dynamic impacts. The use of a short, intense period of forced ventilation of a sugar beet bulk was found to lead to dehydration of sugar beet roots in a predictable manner. This resulted in increases to sucrose concentrations that would lead to greater gross income. Computational Fluid Dynamics modelling of the temperature within a clamp proved to be possible and insightful. The fluid dynamics within the clamp are important to include in such modelling.

Reducing Postharvest Losses during Storage of Grain Crops to Strengthen Food Security in Developing Countries

Article

Full-text available

Jan 2017

While fulfilling the food demand of an increasing population remains a major global concern, more than one-third of food is lost or wasted in postharvest operations. Reducing the postharvest losses, especially in developing countries, could be a sustainable solution to increase food availability, reduce pressure on natural resources, eliminate hunger and improve farmers’ livelihoods. Cereal grains are the basis of staple food in most of the developing nations, and account for the maximum postharvest losses on a calorific basis among all agricultural commodities. As much as 50%–60% cereal grains can be lost during the storage stage due only to the lack of technical inefficiency. Use of scientific storage methods can reduce these losses to as low as 1%–2%. This paper provides a comprehensive literature review of the grain postharvest losses in developing countries, the status and causes of storage losses and discusses the technological interventions to reduce these losses. The basics of hermetic storage, various technology options, and their effectiveness on several crops in different localities are discussed in detail

Biological and Bioenvironmental Heat and Mass Transfer

Book

Mar 2002

Ashim K. Datta

A Deep-Bed Computational Cooling Procedure for Biological Products

Article

Jan 1966
T ASABE

F. W. Bakker-Arkema and W. G. Bickert

Effects of ozone on several physiological indexes of postharvest peach (Prunus persica L. 'Shinvhong') under low temperature condition

Article

Dec 2006

The fruits of peach (Prunus persica L. 'Shinvhong') were stored at low temperature and treated with 8 mg·m-3 ozone. Several physiological indexes were measured during storage. The results showed that ozone treatment could delay fruit softing, respiration rate and the ethylene peak, inhibit the increase of malondialdehyde (MDA) content and electrolyte leakage, retain higher activity of catalase (CAT) and inhibit significantly the activities of peroxidase (POD), amylase and polyphenoloxidase (PPO), decaying rate decreased.

Effect of Fungus Infection on Respiration and Reducing Sugar Accumulation of Sugarbeet Roots and Use of Fungicides to Reduce Infection

Article

Oct 1976

Factors influencing storage decay of sugar beets by Phoma betae and other fungi

Article

Jan 1961
PHYTOPATHOLOGY

Potatoes postharvest

Article

Feb 2009

A wider understanding of potato postharvest practices is needed to improve working relations between growers, agronomists, pathologists and crop store managers. Providing a comprehensive examination of international potato production, this book identifies which storage systems suit particular climatic zones as well as considering interactions between crop microclimate, dehydration, crop cooling, condensation and disease development. Potatoes Postharvest will guide the reader through the activities following harvest from store loading, store management, and grading to packaging and dispatch.

Source of recoverable sugar losses in several sugarbeet varieties during storage

Article

Apr 1971

Effect of temperature on rate of rotting of sugarbeet tissue by two storage pathogens

Article

Jan 1952

Physio-chemical and micro-biological studies on controlled atmosphere storage of sugarbeets

Article

Jul 1970

HEAT TRANSFER MODEL FOR SUGAR BEET STORAGE PILE

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