Numerical modeling of a co-current cascading rotary dryer

Accepted Manuscript Title: Numerical MODELING of a Co-Current Cascading Rotary Dryer Author: Yohann Rousselet Vijay K. Dhir PII: DOI: Reference:

S0960-3085(16)30033-5 http://dx.doi.org/doi:10.1016/j.fbp.2016.05.001 FBP 713

To appear in:

Food and Bioproducts Processing

Received date: Revised date: Accepted date:

3-7-2014 30-4-2016 5-5-2016

Please cite this article as: Rousselet, Y., Dhir, V.K.,Numerical MODELING of a Co-Current Cascading Rotary Dryer, Food and Bioproducts Processing (2016), http://dx.doi.org/10.1016/j.fbp.2016.05.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

*Research Highlights

HIGHLIGHTS

-

A steady state mathematical model was developed for combined heat and mass

ip t

processes in rotary dryers.

A general correlation for the volumetric heat transfer coefficient is presented.

-

A volumetric mass transfer coefficient was based on the volumetric heat transfer

cr

-

-

us

coefficient.

Moisture and temperature profiles along the dryer from the literature are

-

an

simulated accurately.

Dryer inlet parameters’ effect on dryer performance and energy consumption was

Ac ce p

te

d

M

investigated.

Page 1 of 48

NUMERICAL MODELING OF A CO-CURRENT CASCADING ROTARY DRYER

Yohann Rousselet and Vijay K. Dhir

ip t

Henry Samueli School of Engineering and Applied Science

University of California, Los Angeles

us

Los Angeles, CA-90095, USA

cr

Mechanical and Aerospace Engineering Department

Ph: (310) 825-9617, Fax: (310) 206-4830

an

E-mail: [email protected] ABSTRACT

M

A general mathematical model for co-current rotary dryers is presented. A novel approach is

d

taken in modeling of the mass transfer process in the dryer, in which a volumetric mass transfer

te

coefficient, obtained from a general correlation for the volumetric heat transfer coefficient through the Chilton-Colburn analogy, is used. This method does not require the determination of process-specific drying curves, and allows for this model to be easily applicable to a broad range

Ac ce p

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of conditions. The model presented in this work is shown to be able to simulate reliably drying process parameters for a wide range of dryer geometries, input conditions and product types. Dryer data obtained in the present study, as well as data found in the literature, are accurately calculated by the model developed in this work. Simulated moisture content and temperature profiles are in good agreement with data from the literature. A general correlation for the volumetric heat transfer coefficient was determined from the data presented in this study and that from the literature, and was used in this model. The effect of various dryer inlet parameters on the overall performance and energy consumption of the dryer was investigated.

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Page 2 of 48

NOMENCLATURE exponent, Eq. (13)

A

dryer cross sectional area, m2

C

constant, Eq. (13), in J K-1 kg-b sb-1 m2b-3.

cp

specific heat at constant pressure, J kg-1 K-1

D

dryer diameter, m

DH2O-air

diffusion coefficient for water vapor in air, m2 s-1

E

energy, J

E

rate of energy transport, W

hc

heat transfer coefficient, W m-2 K

hc/l

volumetric heat transfer coefficient, W m-3 K

hfg

latent heat of vaporization, J kg-1

hl

heat loss coefficient, W m-2 K

hm

mass transfer coefficient, kg m-2 s-1

hm/l

volumetric mass transfer coefficient, kg m-3 s-1

i j K l

te

d

M

an

us

cr

ip t

b

Ac ce p

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enthalpy, J kg-1

control volume index parameter drying constant, s-1

ratio of dryer volume to effective heat and mass transfer area, m3.m-2

L

dryer length, m

m

mass fraction, kgspecies kgmixture-1

ma

mass flow rate of dry air, kgdry air s-1

mevap

evaporation rate, kgwater s-1

2

Page 3 of 48

mass flow rate of dry product, kgdry product s-1

mwa

mass flow rate of moist air, kgmoist air s-1

mwp

mass flow rate of wet product, kgwet product s-1

M*

molecular weight, g mol-1

Ma

mass of dry air, kgdry air

Mp

mass of dry product, kgdry product

Mwa

mass of moist air, kgmoist air

Mwp

mass of wet product, kgwet product

n

number of control volumes

nf

number of flights

N

dryer rotational speed, rpm

P

pressure, Pa

Qburner

rate of heat transfer from the burner, W

Qloss

heat losses through the dryer shell, W

te

d

M

an

us

cr

ip t

mp

tr

Ac ce p

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T

temperature, oC

V

dryer volume, m3

W

ratio of mass flow rate of water in the product to mass flow rate of dry air

x

mole fraction, kgspecies kgmixture-1

Rw s

drying rate, kgwater kgproduct-1 s-1 slope of the dryer, %

ScH2O-air

Schmidt number for diffusion of water in air

t

time, s

residence time, s

3

Page 4 of 48

moisture content of the product on a dry basis, kgwater kgproduct-1

Y

absolute humidity of air on a dry basis, kgwater kgproduct-1

Xw

moisture content of the product on a wet basis, kgwater kgwet product-1

Yw

absolute humidity of air on a wet basis, kgwater kgmoist air-1

logarithmic mean temperature difference

μ

dynamic viscosity, Pa s-1

ρ

density, kg m-3

Ψ

fluid property, Eq. (25)

air

amb

ambient temperature

d

dry

H2O

te

a

f

an M

d

Subscripts and Superscripts

e

us

ΔTlm

cr

Greek Symbols

ip t

X

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equilibrium

at mean film temperature water

H2O-air

water vapor in air

in

inlet

out

outlet

p

product

ref

reference

4

Page 5 of 48

saturation

st

stored

v

water vapor

w

wet basis

ip t

sat

DRYING;

MATHEMATICAL

MODELING;

ROTARY

DRYING;

ENERGY

us

FOOD

cr

KEYWORDS

an

ANALYSIS, HEAT AND MASS TRANSFER.

INTRODUCTION

M

Rotary dryers are one of the most commonly used devices for drying purposes on an

d

industrial scale, typically in the chemical engineering and food processing industries. Rotary

te

drying is a complex process, involving simultaneous heat and mass transfers phenomena, coupled with the movement of solid particles and air within the dryer drum. The important operating costs of a rotary dryer, primarily due to the energy use, make it a priority for engineers

Ac ce p

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to be able to optimize the efficiency of their drying processes, which to date has to be done empirically, in most cases. The ability to model accurately the drying process would allow for faster and more reliable assessment of the performance of the dryer, and could help the design of new models or the scale up of existing ones. The most frequent approach taken in modeling rotary dryers is to develop a lumped parameter model, based on the establishment and solution of ordinary differential equations, which do not require extensive computational power and time, as opposed to more complex partial differential equations-based models. One of the earliest lumped parameter models was

5

Page 6 of 48

developed by Sharples et al. [1], in which the heat and mass balance were described by four ordinary differential equations solved simultaneously. Later, Thorpe [2] took a similar approach, but divided the dryer in a large number of stages on which were applied heat and mass balances.

ip t

By doing so, Thorpe [2] created a more efficient computer code than Sharples et al. [1], while obtaining similar results. In both studies, the simulations were not compared with any

cr

experimental data. In their models [1-2], a volumetric heat transfer coefficient (hc/l) to describe

us

the convective heat transfer between the moist particles and the drying gas was used. The concept of volumetric heat transfer coefficient was first introduced by Miller et al. [3], and used

an

industrial dryer data to determine other experimental parameters, such as the drying rate. Most of the studies that have followed, such as Thorne and Kelly [4] and Kamke and Wilson [5], have

M

used a similar approach, modifying the existing models and their parameters to fit specific drying

d

conditions (such as the type of moist solid or drying gas).

te

Douglas et al. [6], along with Wang et al. [7], improved the previous models by accounting for the spatial and temporal variations of solid and gas properties. More recently, various studies [8-11] have used dynamic models to study the transient response of a dryer to a step change in a

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governing parameter of the system, and improve the control of the drying process. While numerous mathematical models of rotary dryers have been presented in the literature, a large majority of them rely on a number of empirical parameters applicable only to a given dryer/solid combination, particularly the drying rate of the moist solid particles. The objective of this study is to develop a general model that could be applicable to a broad range of rotary drying processes. Also, to the best of the authors’ knowledge, few studies [11-13] have compared mathematical modeling and experimental data for widely different dryer sizes and product flow rates.

6

Page 7 of 48

NUMERICAL MODEL DEVELOPMENT Similar to the model developed by Thorpe [2], the co-current rotary dryer is axially divided into n fixed control volumes of length L/n, where L is the total length of the dryer. A schematic

ip t

of a control volume is shown in Fig. 1. In order to conduct steady state heat and mass balances on each section of the co-current dryer, the following assumptions were made:

Overall volumetric heat (hc/l) and mass (hm/l) transfer coefficients are adequate to

cr

(i)

us

model the convective heat and mass transfer processes, and are assumed constant throughout the dryer,

A heat loss coefficient (hl) is used to estimate the heat losses through the dryer shell,

an

(ii)

and is assumed constant throughout the dryer.

Particle surfaces are surrounded by a saturated water vapor – air mixture, at

M

(iii)

d

temperature T = Tp (product temperature),

dryer, (v) (vi)

te

The mass flow rates of dry air ( ma ) and dry product ( m p ) are uniform throughout the

(iv)

There is no back-mixing of the product inside the rotary dryer,

Ac ce p

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(vii)

No heat generation inside the dryer, The effect of radiation is negligible, as shown by Platin et al. [14],

A system of four ordinary differential equations was written to describe the one dimensional heat and mass transfer process in each section of the dryer, and to determine the four unknowns of the system, Xw,out, Yw,out, Tp,out, and Ta,out. The focus of the present study is the simulation of steady state dryer parameters and to develop a general model that can be easily applicable to a wide range of conditions.

7

Page 8 of 48

Mass and energy balances are written in terms of moisture content on a wet basis, Xw (kgwater kgwet product-1) and Yw (kgwater kgmoist air-1), for the product and the air, respectively, as well as wet

The moisture contents on a wet basis are given as M wp  M p M wp

Yw 

,

M wa  M a M wa

(1)

cr

Xw 

ip t

product and moist air mass flow rates, mwa (kgmoist air s-1) and mwp (kgwet product s-1), respectively.

us

where Mwp and Mwa are the masses of wet product and moist air, and Mp and Ma are the masses

an

of dry product and dry air in the control volume, respectively.

M

Mass balances: - Product moisture content:

te

Rearranging, at steady state,

(2)

d

dX  mwp ,in X w,in  mwp ,out X w,out  mevap dt

X w,out 

Ac ce p

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1

mwp ,out

m

wp ,in

X w,in  mevap 

(3)

where mwp ,in and mwp ,out are the mass flow rate of wet product coming in and out of the control volume, respectively, Xwp,in and Xwp,out are the moisture content of the product coming in and out of the control volume, respectively, and mevap is the mass flow rate of water evaporated from the product in the control volume. The mass flow rate of wet product coming in and out of the control volume are given as

mwp ,in 

m p ,in 1  X w,in

mwp ,out 

m p ,out

(4)

1  X w,out 8

Page 9 of 48

Since the model was developed for steady state analysis of co-current rotary dryer, and that the mass flow rate of dry product is uniform throughout the dryer and is a required inlet boundary condition, knowledge of total residence time (tr) of the product inside the dryer is not required.

ip t

As a result, no specific residence time model was selected for the development of the current approach. For the sake of completeness, tr from the present study and the literature were reported

us

cr

when available.

- Air moisture content:

an

dY  mwa ,inYw,in  mwa ,outYw,out  mevap dt

1 mwa,out

m

Y

wa,in w,in

 Yw,out  mevap 

(5)

(6)

d

Yw,out 

M

Rearranging, at steady state,

te

where mwa,in and mwa ,out are the mass flow rate of moist air coming in and out of the control volume, respectively, and where Yw,in and Yw,out are moisture content of the air coming in and out

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of the control volume, respectively. The air moisture content inside the control volume, Yw, is calculated as (Ywp,in + Ywp,out) / 2. The mass flow rate of moist air coming in and out of the control volume are given as

mwa ,in  mwa ,out

ma ,in 1  Yw,in

ma ,out  1  Yw,out

(7)

Note that in this study, ma is assumed as uniform throughout the dryer, and thus ma ,in = ma,out =

ma .

9

Page 10 of 48

Energy balances: - Product:

dt

  Ein 

wp

  Eout 

wp

 mwp ,in c p ,wp ,in Tp ,in  Tref   hcV Tlm  mwp ,out c p ,wp ,out Tp ,out  Tref

dt

is the rate of change of the thermal energy stored inside the wet product stream

us

d  Est wp

(8)

cr

 mevap h fg

where



ip t

d  Est  wp

of the control volume. Also,  Ein  and  Eout  are the rates of energy transport in and out of wp

an

wp

the wet product stream of the control volume, respectively. Rearranging, at steady state,

 mwp ,in c p ,wp ,in Tp ,in  Tref   mwp ,out c p ,wp ,out Tp ,out  Tref   1    Tref  mwp ,out c p ,wp ,out   hcV Tlm  mevap h fg  

M

Tp ,out 

(9)

d

where Tref is a reference temperature taken as Tref = 0 oC, and cp,wp,in and cp,wp,out are the specific

te

heats at constant pressure of the moist product coming in the control volume (at Tp,in and Xw,in), and the moist product leaving the control volume (at Tp,out and Xw,out), respectively. The

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logarithmic mean temperature difference ΔTlm used to determine the convective heat transfer term in the energy balances is defined for each control volume as

Tlm 

(Ta  Tp )out  (Ta  Tp )in

ln  (Ta  Tp )out (Ta  Tp )in 

(10)

10

Page 11 of 48

- Air:

  Ein    Eout  wa

wa

 mwa ,in c p ,wa ,in Ta ,in  Tref   mevap c p ,v  hcV Tlm  mevap c p ,v

d  Est  wa dt

Tp  mwa ,out c p ,wa ,out Ta ,out  Tref

Ta  Qloss



(11)

is the rate of change of the thermal energy stored inside the wet product stream

 

of the control volume. Also, Ein

wa



and Eout



cr

where

Ta

Tp

wa

us

dt

ip t

d  Est wa

are the rates of energy transport in and out of

 mwa ,in c p ,wa ,in Ta ,in  Tref   hcV Tlm  mevap c p ,v Tp  Tref Tp 1    mwa ,out c p ,wa ,out  mevap c p ,v Ta  Tref   Qloss Ta 

M

Ta ,out

an

the wet product stream of the control volume, respectively. Rearranging, at steady state,

    

 Tref

(12)

d

where Mwa is the mass of humid air contained in the dryer element, Qloss represents the heat lost

te

through the dryer shell, and cp,wa,in and cp,wa,out are the specific heat at constant pressure of the humid air coming in the control volume (at Ta,in and Yw,in), and the humid air leaving the control volume (at Ta,out and Yw,out), respectively. The specific heat at constant pressure of water vapor

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inside the control is given as cp,v and is calculated at both Tp and Ta, where Tp = (Tp,in + Tp,out) / 2 and Ta = (Ta,in + Ta,out) / 2.

For steady state analysis, which is the purpose of this study, Eq. (2) is solved in the limit of dX dY  0 . Similarly, Eq. (5) is solved in the limit of  0 . Finally, Eq. (8) is solved in the dt dt

limit of

d  Est  wp dt

 0 , while Eq. (11) is solved in the limit of

d  Est  wa dt

 0 . Also note that in

this study, m p is assumed as uniform throughout the dryer, and thus m p ,in = m p ,out = m p . In order to solve this system of four ordinary differential equations, knowledge of volumetric heat

11

Page 12 of 48

transfer coefficient, the evaporation rate, heat losses, and both wet product and moist air properties, is required. Equations for these key parameters are given in the following sections.

ip t

Volumetric heat transfer coefficient

The movement of solid particles within a rotary dryer is an extremely complicated process,

cr

as there is simultaneous motion of the particles due to the cascading motion resulting from the

us

lifting action of the flights, and the motion of the particles being lifted by the flights due to the slope of the dryer. This complex flow of the particles in the airborne and dense phases makes it

an

challenging to describe the particle surface area were the convective heat transfer process occurs. Numerous studies [8-11, 13, 15-22] have used the concept of overall heat transfer coefficient

M

introduced in [3] to describe the convective heat transfer process in the dryer. This simplifies the

d

modeling of the convection process since it does not require specifying the uncertain and hard to

te

quantify particle surface area where the heat transfer occurs, and allows for the treatment of rotary dryers as direct contact heat exchangers. Some authors [15-17] have chosen to develop hc/l correlations specific to their studies; by doing so, they limit the applicability of their models to

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their experimental conditions. On the other hands, various authors [18-21] have developed expressions of hc/l for a broad range of conditions that are commonly used in the literature [8-9, 11, 22]. In this work, the expression developed by McCormick [20] was used. The overall volumetric heat transfer coefficient is given as

 ma   A  hc l  C  D

b

(13)

where l represents the ratio of the volume of the dryer to the effective contact area between the solid and the gas in, A is the dryer cross sectional area, D is the dryer diameter, and ma is the dry

12

Page 13 of 48

air mass flow rate in . McCormick [20] recommends a value of 0.67 for the exponent b, while the constant C depends on experimental conditions and the exponent b, and typically varies between

ip t

100 and 200 J K-1 kg-b sb-1 m2b-3.

Evaporation rate

cr

Determining the evaporation rate is the most delicate aspect of modeling rotary dryers. To

us

quantify evaporation rate, the majority of studies available in the literature [5, 8-10, 13, 15-17, 22] have used Lewis’ thin film model [23] that assumes the drying phenomenon is controlled by

an

diffusion inside the solid. Lewis [23] formulated the following equation for the drying rate of the solid

dX  K  X  X e  dt

M

Rw 

(14)

d

where Rw is the drying rate, K is the drying constant, X is the product moisture content on a dry

te

basis (kgwater / kgdry product) defined as X = Xw / ( 1 – Xw ), and Xe is the equilibrium moisture content. The parameters K and Xe in Eq. (14) are calculated using empirical correlations. These

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correlations can be a function of air and product temperature, as well as air and product moisture content, and are often only applicable to a specific material. On the other hand, Duchesne et al. [24], García and Ragazzo [25], and LeGuen et al. [26], have used the analogy between heat and mass transfer to determine convective mass transfer coefficients (hm) based on existing correlations for convective heat transfer coefficients. The relationship between the heat and mass transfer coefficients for convective heat and mass transfers is given by the Chilton-Colburn analogy as

hc  Pr   cp   hm  Sc 



2 3

(15)

13

Page 14 of 48

where hc is the convective heat transfer coefficient and hm is the mass transfer coefficient. Other expressions of the mass transfer coefficient in rotary dryers available in the literature have been compiled by Krokida et al. [27]. In the current study, the choice was made to use a volumetric

ip t

mass transfer coefficient (hm/l), as introduced by Duchesne et al. [24] and later utilized by Rastikian et al. [28]. In this study, a general correlation for hc/l (Eq. (15)) specific to rotary

cr

dryers was used to calculate hm/l, which in theory should be applicable to any rotary drying

hc l  Prwa c p ,wa   ScH O  air 2 

  



2 3

(16)

an

hm l 

us

process. The volumetric mass transfer coefficient is given as

M

where cp and Pr are moist air properties evaluated at the mean film temperature Tf = (Tp + Ta) / 2. The Schmidt number ScH2O-air for water vapor in air (relevant to this study) is also evaluated at Tf,

te

d

and is defined as

ScH 2O air 

da

(17)

da DH O air 2

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where μ and ρ are properties of dry air. The diffusion coefficient for water in air DH2O-air is obtained using Marrero and Mason’s [29] formula, given as T 2.072 ; P T 1.632  2.75 109 ; P

DH 2O  air  1.87 1010 DH 2O  air

280 K  T  450 K

(18) 450 K  T  1070 K

for DH2O-air in m2 s-1, P in atmospheres, and T in K. The evaporation rate for a dryer element of volume V is obtained from the following equation



mevap   hm l V mH 2O ,sat Tp   Yw



(19)

14

Page 15 of 48

where V is the volume of a section of the dryer. The equilibrium mass fraction of water in air at product temperature, mH2O,sat(Tp), based on partial pressure for which vapor-gas mixture



PH 2O , sat Tp 

(20)

P

us

xH 2O , sat Tp  



xH 2O , sat Tp  M  H 2O  1  xH 2O , sat Tp  M air

cr

mH 2O , sat Tp  

xH 2O , sat Tp  M  H 2O

ip t

temperature is the saturation temperature, is given by

where PH2O,sat(Tp), is the saturation vapor pressure of steam at Tp, P is the total system pressure,

an

xH2O,sat(Tp) is the mole fraction of saturated steam in air, and M*H2O and M*air are the molecular

M

weights of water and air, taken as 18.00 g mol-1 and 28.97 g mol-1, respectively.

Heat losses

d

Heat losses through the dryer shell are determined for a section of the dryer of length L/n as

te

Qloss  hl D

L Ta  Tamb  n

(21)

where hl is the heat loss coefficient in W m-2 K-1. The ambient temperature was taken as 21.1 oC

Ac ce p

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

in this work. The heat loss coefficient is calculated using the correlation proposed by Arruda [15], as reported by Silva et al. [17]

m  hl  22  a   A

0.879

(22)

where A is the dryer cross sectional area and ma is the dry air mass flow rate. This correlation was developed for both co-current and counter-current non-insulated industrial-sized rotary dryers, for drying of fertilizer with hot air, and is applicable to a large range of dryer parameter.

15

Page 16 of 48

While a dryer specific correlation would yield more accurate results, Eq. (22) provides a satisfactory estimate of the heat loss coefficient.

ip t

Product specific heat at constant pressure

formula, from Christenson at al. [30]

us

c p,wp  X wc p,H2 0  1  X w  c p,dp

cr

The moist product specific heat at constant pressure cp,wp is obtained using the following

(23)

an

where Xw is the mass fraction of water in the product on a wet basis, cp,H2O is the specific heat at constant pressure of pure water, and cp,dp is the specific heat at constant pressure of the dry

M

product. The experimental data in the present study were obtained for drying of bread. The specific heat at constant pressure of dry bread, cp,dry bread, is given in [30] as (24)

d

c p ,dry bread  98.0  4.9  T

te

with T in K, and cp,dry bread in J kg-1 K-1.

Ac ce p

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

Moist air properties

The following expression is used to calculate the properties of moist air

 a  1  Yw  da +Yw v

(25)

where Ψda and Ψv are the properties of interest for dry air and water vapor, respectively. Dry air and water properties, as well as the latent heat of vaporization in Eq. (9), are calculated using the computer software REFPROP [31].

16

Page 17 of 48

NUMERICAL MODEL VALIDATION Solution procedure The equations were solved using Matlab. Each of the conservation equation was solved using

ip t

the variable-step method ode15s, with a maximum order set to 5 and an absolute tolerance of 10-6. The simulation time was set arbitrarily to 5000 seconds, to ensure that all the time

cr

derivative terms are equal to zero, and that the four output terms have reached steady state. To

us

verify that steady state is reached after 5000s, the absolute variation of each of the outputs of the solved equations was computed. If it is smaller than 0.0001% over the last 20 time steps, then

an

steady state is reached. The number of control volumes n was set to 200. A higher number of control volumes does not improve significantly the accuracy of the simulations, but increases

M

notably the computational time. Each control volume is referenced by an index number j that

d

varies from 1 to n, in increasing order from the inlet to the outlet of the dryer. The dryer inlet

te

conditions (Ta,in, Tp,in, mwa,in , mwp ,in , Yw,in, and Xw,in) were set as inlet boundary conditions for the first control volume. For the other control volumes, the outlet variables of the previous control volume (control volume j-1) were taken as the inlet boundary conditions for the current one

Ac ce p

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

(control volume j). Thermophysical properties for the air and the solid, as well as drying rate, are calculated in each section of the dryer. For each control volume, the four conservation equations, Eqs. (3), (6), (9), and (12), are solved to determine the four unknowns, Xw,out, Yw,out, Tp,out, and Ta,out.

Comparison between numerical results and experimental data from the present study The numerical model was validated using data obtained from an industrial-sized co-current rotary dryer used for drying of bread crumbs. The experimental data were obtained using a

17

Page 18 of 48

20.574 m long and 1.179 m in diameter dryer. The dryer is divided into 22 sections of equal sizes arranged in a staggered pattern, with 22 flights per section. The product fed to the dryer can be approximated as 1 cm to 2.5 cm thick bread cubes (refer to Eqs. (23) and (24) for the calculation

ip t

of moist product specific heat), and its average moisture content on a wet basis is 0.34 kgwater kgwet product-1. The average thickness of the product in the flights varied from one flight to another,

cr

along the circumference of the dryer. However, the average thickness of the product in the flights

us

along the dryer length was considered to be almost constant. It was measured to be 49.5 cm for typical dryer conditions, as summarized in Table 1. Table 1 also shows typical product and air

an

outlet conditions. The data reported in this study were provided by David Luskin of Reconserve, Inc., for standard operation of an industrial-sized rotary dryer. A comparison between the

M

calculated steady state outlet temperature values and the experimental data for various dryer

d

outlet parameters is shown in Table 2. The simulations in Table 2 were obtained with C = 270 J

te

K-1 kg-0.67 s-0.33 m-0.66 in Eq. (13). As can be seen in Table 2, the simulated outlet temperatures for the air and the product are within 7.5% of the experimental values. Similarly, the simulated moisture content for the air is accurately estimated. Finally, the outlet moisture content for the

Ac ce p

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

product is almost identical to the experimental value, due to the fact that the constant C was adjusted to yield the most accurate value possible. A simple mass balance on the air and product feeds for the entire dryer is used to determine if the total mass of water within the system is conserved. mH 2O ,in  X w,in  mwp ,in  Yw,in  mwa ,in  0.3400  9.57  0.010114.17  3.40 kg H2O s -1 mH 2O ,out  X w,out  mwp ,out  Yw,out  mwa ,out

(26)

 0.1075  7.09  0.1583 16.67  3.40 kg H2O s -1

18

Page 19 of 48

The dryer inlet and outlet water mass flow rates are identical. From the mass balance on the air flow, one can obtain the dryer overall evaporation rate, given as mevap ,total  Yw,out  mwa ,out  Yw,in  mwa ,in

(27)

ip t

 0.1583  16.67  0.0101 14.17  2.49 kg H2O s -1

A similar value is obtained by applying the same method on the product flow.

cr

The numerical model is used to evaluate the air and product temperature and moistures

us

contents in every control volume; therefore, it is possible to plot the temperature and moisture profiles along the dryer length. The simulated moisture content and temperature profiles along

an

the dryer are shown in Fig. 2. As can be seen in Fig. 2, the product temperature rises at first, then stagnates and decreases toward the dryer outlet. This is due to the fact that the heat transfer rate

M

is highest near the inlet of the dryer, were the temperature difference between the air and the

d

product is the largest. Then heat transfer rate decreases, and combined with the evaporation of

te

the moisture contained in the product, results in a decrease in product temperature. The rate of decrease in air temperature is important at the beginning of the dryer, and decreases along the dryer. The decrease in product moisture content is moderate near the inlet of the dryer, then

Ac ce p

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

increases sharply before diminishing again near the exit of the dryer. Similar moisture content profiles were obtained by Yliniemi [32] for drying of calcite in a rotary dryer.

Comparison between numerical results and experimental data from the literature In order to confirm the ability of the model to simulate accurately any co-current rotary drying process, numerical simulations were compared to experimental data available in the literature. A summary of the experimental conditions for the data reported in the literature is shown in Table 3, for co-current rotary dryers. Due to the lack of available product properties, the modeling of the data presented in Table 3 was achieved for cp,dp independent of temperature 19

Page 20 of 48

in Eq. (23). Note that the data from Zavala and Moya [34] was reported by Pérez-Correa et al. [42]. Some of the data presented in Table 3 does not feature values for tr, in which case tr values were determined using the residence time correlation suggested in each particular study. Some

ip t

studies did not report Yw,i; as a result, Yw,in was assumed to be equal to 0 kgwater kgmosit air-1 in these studies. Perry [38] did not report the type of product used, or the specific heat of the product. A

cr

cp,dp value of 1000 J kg-1 K-1 for the data from [38] was taken, as suggested by Pacheco and Stella

us

[43].

Comparisons between simulated Tp,out, and Ta,out¸ as well as correlated Xw,out, with data from

an

the literature can be seen in Fig. 3. Figure 3(a) shows that the agreement between calculated and

M

experimental values of Xw,out is very good. Almost all of the data are correlated within  5 %. The data from Yliniemi [32], on the other hand, is widely underestimated. This is most certainly due

d

to the fact that the outlet product is almost dry, and relative uncertainty is high. Further

te

adjustment of the C value is not possible, as it would yield non-physical temperature values. Also, the number of control volumes used in the simulations is finite; therefore the accuracy of the simulations is limited, particularly for outlet moisture contents close to 0 kgwater kgwet product-1.

Ac ce p

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

Indeed, even a small change in C could result in important relative change in Xw,out, for given control volume size. From Fig. 3(b), it can be seen that the calculated values of Tp,out are accurate to within  15 % of the experimental values. The results from Perry [38] are underestimated by the simulations, probably because cp,dp is unknown for these experiments and assumed to be equal to 1000 J kg-1 K-1, when in reality it might be higher. A higher cp,dp would results in a higher Tp,out. Finally, Fig. 3(c) shows the comparison between simulated and experimental values of Ta,out. Most of the experimental data is calculated to within  20 %. One can surmise that a better estimation of the heat losses through the dryer shell would allow for more accurate

20

Page 21 of 48

simulations. Overall, the model does a good job in simulating the steady state outlet conditions for the air and the product. The use of a volumetric mass transfer coefficient based on a volumetric heat transfer coefficient appears to be validated by the satisfactory simulations that

ip t

are obtained using the proposed model. Note that the constant C in Eq. (13) was adjusted for each test condition to obtain accurate Xw,out value, which is why the accuracy of the modeled

cr

Xw,out values is the highest. This choice was motivated by the fact that Xw,out is the most important

thus requires the highest possible level of accuracy.

us

output parameter to be calculated by the model when designing or optimizing a rotary dryer, and

an

In order to verify the accuracy of the model in simulating steady state temperature and moisture content profiles for the air and the product along the dryer, the simulations were

M

compared to the few moisture and temperature profiles available in the literature, for co-current

d

rotary dryers. Figure 4 shows the comparison between the simulations and the data obtained by

te

Zavala and Moya [34], as reported by Pérez-Correa et al. [42], for drying of soy meal. As can be seen in Fig. 4, the moisture content and temperature profiles simulations are in good agreement with the experimental data. Although the calculations are overall satisfactory, the air temperature

Ac ce p

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

for the second half of the dryer is underestimated. This is probably due to the fact that the volumetric heat transfer coefficient used in this model is assumed constant throughout the dryer, while in reality it certainly will decrease along the dryer. This results in an overestimation heat transfer between the air and the product and, as a consequence, an underestimation of air temperature. Most importantly, the heat losses through the dryer shell might be overestimated, since the heat loss coefficient is also assumed constant throughout the dryer, which results in overestimated heat transfer through the dryer shell, leading to underestimation of air temperature values. Kamke [36] reported product moisture content profiles, as well as air and product

21

Page 22 of 48

temperature profiles, for drying of sawdust for 6 different test runs. Comparison between the data from [36] and the simulated profiles is shown in Fig. 5. Figures 5(a) to 5(f) correspond to the conditions of runs 1 to 6 reported by Kamke [36]. The agreement between the data from [36] and

ip t

the simulated values shown in Fig. 5 is very good, with temperature and moisture content profiles being accurately modeled. The only important differences in what are found are seen in

cr

Fig. 5(f), in which all three measured parameters are consistently overestimated. The uncertainty

us

in the experimental data, combined with possible errors in reported experimental parameters, as well as the high entering air temperature, could explain these discrepancies, given the accurate

an

simulations of Runs 1 to 5.

The ability of the model developed in this study to simulate the steady state behavior of

M

rotary drying processes has been demonstrated. Data for various dryer geometries, input

d

parameters and product types were accurately calculated. The approach, taken in the study, of

te

determining a volumetric mass transfer coefficient based on an established volumetric heat transfer coefficient correlation, using the Chilton-Colburn analogy, has been proven reliable. The present model, however, relies on the determination of the constant C, in Eq. (13), that depends

Ac ce p

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

on experimental conditions. In order for this model to be a truly general one, an expression for C based on various input parameters, has to be determined. The constant C is plotted in Fig. 6 as a function of the ratio of the inlet mass flow rate of water in the product divided by the inlet mass flow rate of dry air, given as

Win 

X in m p ,in ma ,in

(28)

From Fig. 6, it can be seen that almost all of the experimental values of C can be correlated to within  20 % by the expression

22

Page 23 of 48

C  823Win0.606

(29)

Hence, from Eq. (13), the correlation for the volumetric heat transfer becomes 0.67

ip t

 ma   A  hc l  823Win0.606  D

(30)

cr

with Win as in Eq. (28). This correlation is valid for a large range of cylinder geometries (0.49m

us

≤ L ≤ 24 m and 0.18m ≤ D ≤ 4 m), inlet dry product and dry air mass flow rates (1.81x10-5 kg s-1 ≤ m p ≤ 13.766 kg s-1 and 0.013 kg s-1 ≤ ma ≤ 19.276 kg s-1), inlet wet product moisture content

an

(0.0061 kgwater kgwet product-1 ≤ Xw,in ≤ 0.7675 kgwater kgwet product-1), and product types.

M

OPTIMIZATION OF THE ROTARY DRYING PROCESS

Numerical simulations were performed to estimate the influence of various inlet parameters

te

d

on the outlet product conditions and energy consumption of the dryer, for the rotary drying process of bread crumbs investigated in this study. A gas burner is used to heat the air to the desired dryer inlet temperature. Assuming a 100 %

Ac ce p

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

efficient burner, the energy consumption of the burner is given as

Qburner  mwa,in  iwa,in  iwa,amb 

(31)

where Qburner is the rate of heat transfer from the burner to the air, iwa,in is the enthalpy of moist air at the inlet of the dryer and iwa,amb is the enthalpy of moist air at ambient temperature and relative humidity (taken as 21.1 oC and 50%, respectively). The effect of inlet product moisture content on the required inlet air temperature and burner power requirement to obtain a constant outlet product moisture content of 0.1075 kgwater kgwet product

-1

is shown in Table 4, for constant inlet product mass flow rate and temperature ( mwp ,in =

23

Page 24 of 48

9.58 kg s-1 and Tp,in = 23.9 oC), and constant inlet mass flow rate and moisture content of air ( mwa,in = 14.17 kg s-1, Yw,in = 0.0101 kgwater kgmoist air-1). In Table 4, Qburner / Qburner max is the ratio of the rate of heat transfer required to heat the gas to given inlet conditions to the rate of heat

and Ta,in = 496.2 oC). Table 4 shows that decrease in product inlet moisture content leads to a

cr

-1 air ,

ip t

transfer required to heat the gas to the experimental inlet conditions (Yw,in = 0.0101 kgwater kgmoist

decrease in the inlet air temperature required to maintain outlet product moisture content of

us

0.1075 kgwater kgwet product-1. A 26 % decrease in inlet product moisture content (from 0.34 kgwater kgwet product-1 to 0.25 kgwater kgwet product-1), results in a decrease in the required inlet air temperature

an

of 149.1 oC, which leads to a 23 % reduction in the energy consumption of the burner.

M

Table 5 shows the effect of inlet air temperature on outlet product moisture content and burner power requirement for a constant inlet product moisture content of 0.34 kgwater kgwet product-

C), and constant inlet mass flow rate and moisture content of air ( mwa,in = 14.17 kg s-1, Yw,in =

te

o

., for constant inlet product mass flow rate and temperature ( mwp ,in = 9.58 kg s-1 and Tp,in = 23.9

d

1

0.0101 kgwater kgmoist air-1). As can be seen in Table 5, outlet product moisture content increases

Ac ce p

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

with decrease in inlet air temperature. For example, a 169.3 oC decrease in inlet air temperature (similar to the 149.1 oC decrease presented in Table 4) results in a doubling of the outlet moisture content of the product, associated with a 26 % reduction in burner energy consumption. The most important parameter of typical industrial drying processes is the product outlet moisture content. The results presented in Tables 4 and 5 show that a reduction in the energy consumption of the dryer, without altering the quality of the dried product, could be achieved by lowering the inlet product moisture content. This solution would require the pre-drying of the moist product prior to feeding it to the dryer. Additionally, the results presented in Tables 4 and 5 highlight how the mathematical model presented in this study could be used to optimize an

24

Page 25 of 48

industrial drying process by studying the effect of various parameters on the overall dryer performance. The effect of inlet product moisture content on inlet moist product mass flow rate for a

ip t

constant outlet product moisture content of 0.1075 kgwater kgwet product-1, for constant inlet product temperature (Tp,in = 23.9 oC), and constant inlet mass flow rate, temperature and moisture content

cr

of air ( mwa,in = 14.17 kg s-1, Ta,in = 496.2 oC and Yw,in = 0.0101 kgwater kgmoist air-1), is shown in

us

Table 6. As can be seen in Table 6, in order to maintain a constant product outlet moisture content of 0.1075 kgwater kgwet product-1, the product inlet mass flow rate decreases with increase in

an

product inlet moisture content. This decrease is very large for small inlet product moisture

M

content, and is greatly reduced for large inlet product moisture content. As a consequence, the outlet mass flow rate of moist product decreases with increase in product inlet moisture content,

d

while maintaining outlet product moisture content.

te

Table 7 shows the effect of outlet product moisture content on inlet moist product mass flow rate for a constant inlet product moisture content of 0.34 kgwater kgwet product-1, for constant inlet product temperature (Tp,in = 23.9 oC), and constant inlet mass flow rate, temperature and moisture

Ac ce p

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

content of air ( mwa,in = 14.17 kg s-1, Ta,in = 496.2 oC and Yw,in = 0.0101 kgwater kgmoist air-1). From Table 7, it can be seen that there is a monotonous increase in inlet and outlet product mass flow rates with increase in outlet product moisture content. The dryer energy consumption is the same for each case presented in Table 6. However, a decrease in product inlet moisture content results in a much higher output of dried product. While the operating costs of the dryer associated with its energy use remains the same, the drying cost per kilogram of dried product decreases with decrease in inlet product moisture content. Similar conclusions can be drawn from the results presented in Table 7, which show that

25

Page 26 of 48

an increase in outlet product moisture content yields a larger dried product mass flow rate, for constant inlet product moisture content.

ip t

CONCLUSIONS

A general mathematical model was developed for combined heat and mass processes in co-

cr

current cascading rotary dryers. A system of four ordinary differential equations was obtained

us

and solved using Matlab. The mathematical model was validated by simulating rotary drying processes based on experimental data from the present study as well as data from the literature.

(i)

an

The main results are as follow:

A volumetric mass transfer coefficient was determined based on a general expression

M

of the volumetric heat transfer coefficient. Contrary to numerous models found in the

d

literature, this method does not require the determination of process-specific drying

(ii)

te

curves.

The ability of this model to simulate accurately the dryer outlet parameters was shown by comparing calculated values to data from the present study and the

Ac ce p

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

literature. The calculated outlet product moisture content is within  5 % of the experimental results. Almost all of the outlet product temperature data is simulated to within  15 %, and almost all of the outlet air temperature to within  20 %.

(iii)

Comparison of simulated moisture content and temperature profiles along the dryer length with data from the literature demonstrated the capacity of this model to simulate such profiles.

26

Page 27 of 48

(iv)

A general correlation for the volumetric heat transfer coefficient, appropriate to a large range of dryer geometries, input parameters and product types, was developed based on an existing correlation proposed by McCormick [20]. The mathematical model developed in this study was used to investigate the effect of

ip t

(v)

various dryer inlet parameters on the overall performance and energy consumption of

us

cr

the dryer, for the rotary drying process of bakery by-products presented in this study.

ACKNOWLEDGMENTS

an

The authors would like to thank David Luskin of ReConserve, Inc. for providing some of the

M

data presented in this study.

d

REFERENCES

te

[1] Sharples, K., Glikin, P. G., and Warne, R., 1964, “Computer Simulation of Rotary Dryers,” Transactions of the Institute of Chemical Engineers, vol. 42, pp. 275–284. [2] Thorpe, G. R., 1972, The Mathematical Modeling of Dryers. PhD thesis, University of

Ac ce p

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Nottingham, United Kingdom.

[3] Miller, C. O., Smith, B. A., and Schuette, W. H., 1942, “Factors Influencing the Operation of Rotary Dryers,” Transactions of the Institute of Chemical Engineers, vol. 38, pp. 841–844. [4] Thorne, B., and Kelly, J. J., 1980, “Mathematical Model for the Rotary Dryer,” in Drying’ 80, vol. 1, pp. 160-169, edited by Mujumdar, A. S., Hemisphere Publishing, Washington, USA. [5] Kamke, F. A., and Wilson, J. B., 1986, “Computer Simulation of a Rotary Dryer. Part II: Heat and Mass Transfer,” American Institute of Chemical Engineers Journal, vol. 32, pp. 269– 275.

27

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[6] Douglas, P. L., Kwade, A., Lee, P. L., and Mallick, S. K., 1993, “Simulation of a Rotary Dryer for Sugar Crystalline,” Drying Technology, vol. 11, issue 1, pp. 129–155. [7] Wang, F. Y., Cameron, I. T., Lister, J. D., and Douglas, P. L., 1993, “A Distributed

ip t

Parameter Approach to the Dynamics of Rotary Drying Processes,” Drying Technology, vol. 11, issue 7, pp. 1641–1656.

cr

[8] Iguaz, A., Budman, H., and Douglas, P. L., 2002, “Modelling and Control of an Alfalfa

us

Rotary Dryer,” Drying Technology, vol. 20, issue 9, pp. 1869-1887.

[9] Iguaz, A., Esnoz, A., Martínez, G., López, A., Vírseda, P., 2003, “Mathematical Modelling

an

and Simulation for the Drying Process of Vegetable Wholesale By-products in a Rotary Dryer,” Journal of Food Engineering, vol. 59, issues 2-3, pp. 151-160.

M

[10] Luz, G. R., dos Santos Conceicão, W. A., Matos Jorge, L. M., Paraíso, P. R.,

and

d

Goncalves Andrade, C. M., 2010, “Dynamic Modeling and Control of Soybean Meal Drying in a

te

Direct Rotary Dryer,” Food and Bioproducts Processing, vol. 88, issues 2–3, pp. 90–98. [11] Castaño, F., Rubio, F. R., and Ortega, M. G., 2012, “Modelling of a Cocurrent Rotary Dryer,” Drying Technology, vol. 30, issue 8, pp. 839-849.

Ac ce p

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

[12] Xu, Q., and Pang, S., 2008, “Mathematical Modeling of Rotary Drying of Woody Biomass,” Drying Technology, vol. 26, issue 11, pp. 1869-1887. [13] Abbasfard, H., Rafsanjani, H. H., Ghader, S., and Ghanbari, M., 2013, “Mathematical Modeling and Simulation of an Industrial Rotary Dryer: A Case Study of Ammonium Nitrate Plant,” Powder Technology, vol. 239, pp. 499-505. [14], Platin, B. E., Erden, A., and Gülder, Ö. L., 1982, “Modeling and Design of Rotary Dryers,” in Proceedings of the Third International Drying Symposium, vol. 2, pp. 466-477, edited by Ashworth, J. C., Drying Research Limited., Wolverhampton, England.

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[15] Arruda, E. B., 2006, Comparison of the Performance of the Roto-Fluidized Dryer and Conventional Rotary Dryer, PhD thesis, Federal University of Uberlândia, Uberlândia-Brazil. [16] Arruda, E. B., Lobato F. S., Assis, A. J., and Barrozo, M. A. S., 2009, “Modeling of

ip t

Fertilizer Drying in Roto-Aerated and Conventional Rotary Dryers,” Drying Technology, vol. 27 issue 11, pp. 1192-1198.

cr

[17] Silva, M. G., Lira, T. S., Arruda, E. B., Murata, V. V., and Barrozo, M. A. S., 2012,

us

“Modelling of Fertilizer Drying in a Rotary Dryer: Parametric Sensitivity Analysis,” Brazilian Journal of Chemical Engineering, vol. 29, number 2, pp. 359-369.

an

[18] Friedman, S. J., and Marshall, W. R., 1949, “Studies in Rotary Drying. Part II: Heat and Mass Transfer,” Chemical Engineering Progress, vol. 45, issue 9, pp. 573–588.

M

[19] Saeman, W. C., and Mitchell, T. R., 1954, “Analysis of Rotary Dryer and Cooler

d

Performance,” Chemical Engineering Progress, vol. 50, issue 9, pp. 417–475.

te

[20] McCormick, P.Y., 1962, “Gas Velocity Effects on Heat Transfer in Direct Heat Rotary Dryer,” Chemical Engineering Progress, vol. 58, number 6, pp. 57–61. [21] Myklestad, O., 1963, “Heat and Mass Transfer in Rotary Dryers,” Chemical Engineering

Ac ce p

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Progress Symposium Series, vol. 59, issue 41, pp. 129–137. [22] Fernandes, N. J., Ataíde, C. H., and Barrozo, M. A. S., 2009, “Modeling and Experimental Study of Hydrodynamic Characteristics of an Industrial Rotary Dryer,” Brazilian Journal of Chemical Engineering, vol. 26, number 2, pp. 331-341. [23] Lewis, W. K., 1921, “The Rate of Drying of Solid Materials,” Industrial and Engineering Chemistry, vol. 13, number 5, pp. 427-432.

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[24] Duchesne, C., Thibault, J., and Bazin, C., 1997, “Modelling and Dynamic Simulation of an Industrial Rotary Dryer,” Developments in Chemical Engineering and Mineral Processing, vol. 5, issues 3-4, pp. 155-182.

ip t

[25] García, M. A., and Ragazzo, A., 2000, “Mathematical Modeling of Continuous Dryers using the Heat and Mass Transfer Properties and Product-Air Equilibrium Relation,” Drying

cr

Technology, vol. 18, issues 1-2, pp. 67-80.

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[26] LeGuen, L., Huchet, F., and Tamagny, P., 2011, “Drying and Heating Modelling of Granular Flow: Application to the Mix-Asphalt Processes,” Journal of Applied Fluid Mechanics,

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vol. 4, number 2, special issue, pp. 71-80.

[27] Krokida, M. K., Maroulis, Z. B., and Marinos-Kouris, D., 2002, “Heat and mass Transfer

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Coefficients in Drying: Compilation of Literature Data,” Drying Technology, vol. 20, issue 1, pp.

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1-18.

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[28] Rastikian, K., Capart, R., and Benchimol, J., 1999, “Modelling of Sugar drying in a Countercurrent Cascading Rotary Dryer from Stationary Profiles of Temperature and Moisture,” Journal of Food Engineering, vol. 41, issues 3-4, pp. 193-201.

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[29] Marrero, T. R., and Mason, E. A., 1972, “Gaseous Diffusion Coefficients,” Journal of Physical Chemistry Reference Data, vol. 1, number 1, pp. 3-118. [30] Christenson, M. E., Tong, C. H., and Lund, D. B., 1989, “Physical Properties of Baked Products as Function of Moisture and Temperature,” Journal of Food Processing and Preservation, vol. 13, number 3, pp. 201-217. [31] REFPROP, Reference Fluid Thermodynamic and Transport Properties, NIST Standard Reference Database 23, version 8.0.

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[32] Yliniemi, L., 1999, Advanced control of a rotary dryer, PhD thesis, Faculty of Technology, Department of Process and Environmental Engineering, University of Oulu, Finland.

Rotary Sugar Dryer,” Control Engineering Practice, vol. 9, pp. 249-266.

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[33] Savaresi, S. M., Bitmead, R. R., and Peirce, R., 2001, “On Modelling and Control of a

Piloto de Contacto Directo, PhD thesis, USACH, Santiago, Chile.

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[34] Zavala, E., and Moya, A., 1994, Simulación Dinámica y Control de un Secador Rotatorio

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[35] Mani, S., Sokhansanj, S., and Bi, X., 2005, “Modeling of forage Drying in Single and triple Pass Rotary Drum Dryers,” ASAE Annual International Meeting, paper number 056082.

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[36] Kamke, F. A., 1984, Engineering Analysis of a Rotary Dryer: Drying of Wood Particles, PhD thesis, Forest Products Program, Oregon State University, USA.

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[37] Zabaniotou, A. A., 2000, “Simulation of Forestry Biomass Drying in a Rotary Dryer,”

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Drying Technology, vol. 18, issue 7, pp. 1415-1431.

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[38] Perry, R. H., Green, D.W., and Maloney, J.O., 2007, Perry's Chemical Engineers' Handbook, 8th Edition, McGraw-Hill, New-York. [39] Meza, J., Gil, A., Cortés, C., and González, A., 2008. “Drying Costs of Woody Biomass in a

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Semi-Industrial Experimental Rotary Dryer,” 16th European Conference and Exhibition on Biomass for Energy, Biomass Resources, Valencia, Spain. [40] Bacelos, M. S., Jesus, C. D. F., and Freire, J. T., 2009, “Modeling and Drying of Carton Packaging Waste in a Rotary Dryer,” Drying Technology, vol. 27, issue 1, pp. 927-937. [41] Renaud, M., Thibault, J., and Alvarez, P. I., 2001, “Influence of Solid Moisture Content on the Average Residence Time in a Rotary Dryer,” Drying Technology, vol. 19, issue 9, pp. 21312150.

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[42] Pérez-Correa, J. R., Cubillos, F., Zavala, E., Shene, C., and Alvarez, P. I., 1998, “Dynamic Simulation and Control of Direct Rotary Dryers,” Food Control, vol. 9, number 4, pp. 195-203. [43] Pacheco, C. R. F., and Stella, S. S., 1998, “Calculating Capacity Trends in Rotary Dryers,”

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Brazilian Journal of Chemical Engineering, vol. 15, number 3, pp. 235-245.

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TABLE CAPTIONS

Table 1 Co-current rotary dryer characteristics, and product and air input and output conditions

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- present study.

Table 2 Comparison between experimental data and simulated values of moisture content and

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temperature of air and product at the outlet of the dryer.

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Table 3 Experimental conditions for Figs. 3 to 6 - data from the literature.

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Table 4 Effect of inlet product moisture content on required inlet air temperature and burner power requirement for constant outlet product moisture content of 0.1075 kgwater kgwet product-1,

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for mwp ,in = 9.58 kg s-1, Tp,in = 23.9 oC, mwa,in = 14.17 kg s-1 and Yw,in = 0.0101 kgwater kgmoist air-1.

Table 5 Effect of inlet air temperature on outlet product moisture content and burner power

d

requirement for a constant inlet product moisture content of 0.34 kgwater kgwet product-1, for mwp ,in =

te

9.58 kg s-1, Tp,in = 23.9 oC, mwa,in = 14.17 kg s-1 and Yw,in = 0.0101 kgwater kgmoist air-1.

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

Table 6 Effect of inlet product moisture content on inlet moist product mass flow rate for a constant outlet product moisture content of 0.1075 kgwater kgwet product-1, for Tp,in = 23.9 oC, mwa,in = 14.17 kg s-1, Ta,in = 496.2 oC and Yw,in = 0.0101 kgwater kgmoist air-1. Table 7 Effect of outlet product moisture content on inlet moist product mass flow rate for a constant inlet product moisture content of 0.34 kgwater kgwet product-1, for Tp,in = 23.9 oC, mwa,in = 14.17 kg s-1, Ta,in = 496.2 oC and Yw,in = 0.0101 kgwater kgmoist air-1.

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Page 34 of 48

FIGURE CAPTIONS

Figure 1 Schematic of a control volume of the dryer.

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Figure 2 Simulated moisture content and temperature profiles along the dryer, for Ta,in = 496.2 o

C, Tp,in = 23.9 oC, mwa,in = 14.17 kgmoist air s-1, mwp ,in = 9.58 kgwet product s-1, Yw,in = 0.0101

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cr

kgwater kgmoist air-1, Xw,in = 0.34 kgwater kgwet product-1 and C = 270 J K-1 kg-0.67 s-0.33 m-0.66 (Eq. (13)). Figure 3 Comparison between experimental and correlated values of (a) Xw,out, and experimental

an

and simulated values of (b) Tp,out, and (c) Ta,out. Experimental conditions listed in Tables 1 and 3. Figure 4 Comparison between simulated moisture content and temperature profiles along the

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dryer and experimental data from [34], as reported in [42], for Ta,in = 250.0 oC, Tp,in = 24.0 oC,

ma ,in = 0.076 kg s-1, m p ,in = 0.0202 kg s-1, Yw,in = 0.05 kgwater kgmoist air-1, Xw,in = 0.323 kgwater kgwet -1

and C = 170 J K-1 kg-0.67 s-0.33 m-0.66 (Eq. (13)).

d

product

te

Figure 5 Comparison between simulated moisture content and temperature profiles along the dryer and experimental data from [36], for 156.7 oC ≤ Ta,in ≤ 267.3 oC, 17.7 oC ≤ Tp,in ≤ 24.1 oC, 1.598 kg s-1 ≤ ma ,in ≤ 1.968 kg s-1, 0.077 kg s-1 ≤ m p ,in ≤ 0.0202 kg s-1, Yw,in = 0 kgwater kgmoist air-1,

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

0.5748 kgwater kgwet product-1 ≤ Xw,in ≤ 0.5876 kgwater kgwet product-1 and C = 210 J K-1 kg-0.67 s-0.33 m-0.66 (Eq. (13)).

Figure 6 Constant C (Eq. (13) ) as a function of the ratio of inlet water mass flow rate in the product over inlet mass flow rate of dry air, for data from the present study and data from the literature. Experimental conditions listed in Tables 1 and 3.

34

Page 35 of 48

20.574 1.179 450 3.63 0 22

m wp,in (kg/s)

9.58

Ta,in (oC) Tp,in (oC) Xw,in (kgwater kgwet product-1) Yw,in ( kgwater kgmoist air-1) Ta,out (oC) Tp,out (oC) Xw,out (kgwater kgwet product-1) Yw,out (kgwater kgmoist air-1)

496.2 23.9 0.34 0.001 84.9 73.9 0.1075 0.16

Ac ce p

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14.17

cr

L (m) D (m) tr (s) N (rpm) s (%) nf m wa,in (kg/s)

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Table 1

Page 36 of 48

Table 2

o

o

Tp ( C) 73.9 68.4 -7.44 %

Outlet Conditions Yw (kgwater kgmoist air-1) Xw (kgwater kgwet product-1) 0.1583 0.1075 0.1583 0.1075 0.00 % 0.00 %

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Ta ( C) 84.9 Experimental 84.9 Predicted 0.00 % Difference

Tp ( C) 23.9

Inlet Conditions Yw (kgwater kgmoist air-1) Xw (kgwater kgwet product-1) 0.001 0.34

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Ta ( C) 496.2

o

cr

o

Page 37 of 48

Table 3

Iguaz et al. Yliniemi Savaresi Zavala and Mani et [9] [32] et al. [33] Moya [34] al. [35] Product

Vegetables Calcite

Sugar

Kamke [36]

Soy meal Sawdust Sawdust

Zabaniotou Meza et Bacelos et Renaud et Perry [38] [37] al. [39] al. [40] al. [41] Forestry biomass

n/a

Woody biomass

Carton waste

Sand

1382

840

1244

1760

900

900

2082

1000

2082

710

830

L (m)

9

3

9

3

24

5.5

0.49

7.62 – 16.767

4.5

0.8 – 2.7

3

D (m)

0.9

0.5

2.5

0.3

4

1.2

0.18

1.219 – 3.048

0.6

0.2 – 0.45

0.31

tr (s)

n/a

600

420

480

n/a

500 – 800

66 – 276

n/a

n/a

n/a

300 – 825

m p,in (kg/s)

0.015 – 0.026

0.042

8.645 – 13.766

0.0202

4.2

0.077 – 0.082

0.0002 – 0.0006

0.113 – 0.715

0.0155 – 1.81x10-5 – 0.01725 0.0183 5.37x10-3

ma,in (kg/s)

0.857 – 0.885

0.084

5.288 – 5.380

0.076

19.276

1.598 – 1.968

0.013 – 0.050

1.358 – 8.490

0.465 – 0.519

0.0328 – 0.1494

0.1186 – 0.1504

Tp,in (oC)

25.0

19.9

20.4 – 27.9

24.0

224.0

17.7 – 24.2

20.0

27.0

35.0 – 51.5

28.0

12.0

Ta,in (oC)

205.0 – 221.0

218.9

53.8 – 55.1

250.0

250.0

156.7 – 267.3

62.7 – 100.0

165.0

181.2 – 223.7

100.0 – 200.0

0.6815 – Xw,in (kgwater kgwet product-1) 0.7675

0.0240

0.0061 – 0.0089

0.323

0.2481

0.5748 – 0.5876

0.1166

0.25

0.46 – 0.55

65.0 – 68.3 0.13 – 0.627

n/a

0.0059 – 0.0084

0.0050

n/a

n/a

0.0654

n/a

n/a

n/a

n/a

cr

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d

n/a

0.08

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Yw,in (kgwater kgmoist air-1)

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cp,dp (J/kgK)

Page 38 of 48

Table 4

Ta,in (oC)

Xw,out (kgwater kgwet product-1)

Qburner (MW)

Qburner / Qburner max (-)

0.34*

496.2*

0.1075*

11.360

1.00*

0.33

472.1

0.1075

11.025

0.97

0.30

431.9

0.1075

10.286

0.28

390.4

0.1075

9.542

0.25

347.1

0.1075

8.784

cr

0.91 0.84 0.77

Ac ce p

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*experimental conditions

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Xw,in (kgwater kgwet product-1)

Page 39 of 48

Xw,out (kgwater kgwet product-1)

Qburner (MW)

Qburner / Qburner max (-)

496.2*

0.1075*

11.360

1.00*

427.0

0.1630

10.092

0.89

377.0

0.1976

9.210

0.81

327.0

0.2279

8.352

0.74

277.0

0.2537

7.518

227.0

0.2746

6.705

177.0

0.2900

5.912

127.0

0.3010

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Ta,in (oC)

cr

Table 5

0.66

an

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0.59

5.138

0.52 0.45

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te

d

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*experimental conditions

Page 40 of 48

mwp ,in

mwp ,out

(kg/s)

(kg/s)

0.15

28.42

27.08

0.20

18.31

16.42

0.25

13.81

11.58

0.30

11.08

8.69

0.34*

9.58*

7.08*

0.40

7.97

0.45

6.97

0.50

6.22

3.47

0.70

4.33

1.44

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an

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cr

Xw,in (kgwater kgwet product-1)

0.90

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Table 6

3.31

5.36 4.31

0.30

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te

d

*experimental conditions

Page 41 of 48

mwp ,in

mwp ,out

(kg/s)

(kg/s)

0.08

9.00

6.46

0.10

9.42

6.91

0.1075*

9.58*

7.08*

0.12

9.89

7.42

0.14

10.44

8.03

0.16

11.11

0.18

11.89

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cr

Xw,out (kgwater kgwet product-1)

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Table 7

8.72

an

9.58

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te

d

M

*experimental conditions

Page 42 of 48

Ac

ce

pt

ed

M

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cr

i

Figure 1

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pt

ed

M

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cr

i

Figure 2

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d

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cr

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Figure 3

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Ac

ce

pt

ed

M

an

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cr

i

Figure 4

Page 46 of 48

Ac ce p

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d

M

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cr

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Figure 5

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Ac

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pt

ed

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cr

i

Figure 6

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