HEFAT2007
5
th
International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics
Sun City, South Africa
Paper number: K3
THERMAL DRYING TECHNOLOGIES: NEW DEVELOPMENTS AND FUTURE R&D
POTENTIAL
Mujumdar A.S.* and Wu Z.H.
*Author for correspondence
Department of Mechanical Engineering and Engineering Science Program,
National University of Singapore,
Singapore, 117575
E-mail: mepasm@nus.edu.sg
; website: http://serve.me.nus.edu.sg/arun
ABSTRACT
Thermal dehydration processes are highly energy-intensive
and are found in almost all industrial sectors, accounting for 10
to 20 percent on national industrial energy consumption in
developed countries. With escalating energy costs and need to
mitigate environmental pollution due to emissions from
combustion of fossil fuels, it is increasingly important to
develop innovative drying technologies. Furthermore, drying
also affects quality of the dried product due to physical and/or
chemical transformations that may occur during the heat and
mass transfer operation. With tens of thousands of products that
are dried in hundreds of dryer types, it is a formidable task
indeed to develop design and scale-up procedures of wide
applicability. Attempts have been made over the past three
decades to make fundamental and applied contributions to
transport phenomena and material science aspects in drying of
various forms of wet solids, pastes and liquids. This
presentation will attempt to summarize the state-of-the-art as
far as theoretical understanding of drying processes and provide
examples of some new technologies being developed.
Opportunities for challenging fundamental and modeling
studies to enhance drying technologies will be identified.
Illustrative results will be presented to show how mathematical
modeling of spray, spouted bed and heat pump dryers can be
utilized to develop new conceptual designs and to optimize
operating conditions as a cost-effective route to intensify
innovation in thermal dryer design.
INTRODUCTION
Almost all industrial sectors involve thermal dehydration
during one or several phases of their manufacturing processes.
Developed economies expend from 12-25% of their national
industrial energy for drying operations depending on the
product mixes they produce. This massive energy consumption
mainly using fossil fuels directly impacts CO
2
emission levels
which are being curtailed actively under the Kyoto Protocol. To
make matters worse, industrial dryers, most of which were
designed during the era of cheap and abundant energy, typically
operate at thermal efficiencies in the range 20 to 60 percent.
Clearly there is tremendous scope for improvement of
industrial drying technologies- a task that must logically begin
with R&D to enhance our knowledge base on drying as well as
dryers.
At the outset it is important to recognize that drying
involves heat and mass transfer but it is only a part of the
problem. It is important to be able to handle the wet material in
the dryer and be able to produce a dried product of prescribed
quality parameters- often not a simple task. In general what is
optimal for heat and mass transfer is not optimal for drying.
The latter is a coupled process involving transport phenomena
and material science. It may involve physical transformations
such as shrinkage, puffing, crystallization, cracking, glass
transitions along with potential chemical or biochemical
reactions. A mathematical model considering all these
phenomena- many unpredictable a priori- is still a distant dream
of drying researchers. A further complication arises from the
fact that some 50,000 materials with very diverse
physical/chemical properties need to be dried at different scales
of production and with very different product quality. No
wonder then that over 500 different types are reported in
technical literature and some 100 types of dryers are available
commercially. Contrast this with heat exchangers which can be
designed reasonably reliably using standard software packages.
No such luxury exists when it comes to heat and mass
exchangers involving wet solids. Indeed, the large body of
research literatures for dry solids becomes quite useless when
one is faced with a corresponding wet solid! It is obvious that
drying R&D presents numerous challenging problems some of
which are amenable to treatment with advanced computational
and analytical tools, but the actual scope of the problem is truly
of gigantic proportion.
The objective of this paper is to discuss some generic
problems encountered in the design and optimization of
industrial dryers, outline with some examples the nature of
problems that can be treated via mathematical modelling and
identify worthwhile R&D needs and opportunities for those
who wish to take up the challenge and make definitive and
useful contribution to the advancement of the science,
engineering and technology of thermal dehydration.
NOMENCLATURE
A [MPa] Elastic bulk modulus of dried materials
A [m
2
] The surface area of dried sample
B=KR/A [-] Coefficient of mass transfer (Biot Number)
c
1
,c
2
, …c
8
[-] Constants
D [m
2
/s] Coefficient of diffusion
f
[kg/m
2⋅
s]
Moisture flux
h [J/kg] Enthalpy
J
0
, J
1
[-] Bessel functions of first kind of zero and first order
k
[kg/m
2
⋅s]
Coefficient of convective vapour exchange
K [MPa] Elastic modulus due to shrinkage
M [MPa] Elastic shear modulus of dried sample
P [Pa] Pressure
r [m] Radial direction
R
[J/mol⋅K]
Universal gas constant
T [K] Temperature
t [s] Time
X [kg/kg] Moisture content, dry basis
Y [-] Vapour content in drying air
V [m
3
] Volume of dried sample
v [m/s] Velocity
Special characters
χ
[-] Depth scalar
ε
[-] Volume fraction
ε
[-] Volume strain
κ
(X)
[-] Coefficient of humid expansion
λ
1
, λ
n
[-] Enginvalue for Bessel functions
σ
[Pa] Stress
ρ
[kg/m
3
] Mass density
θ=X-X
r
[kg/kg] Relative moisture content
Α
[kg⋅s/m
3
]
Mass transport coefficient
Subscripts
a Air
b Bulk
e Equilibrium state
eff Effective
g Gas phase
l Liquid phase
s Saturated state
v Vapour
w Water
0 Initial state
INNOVATION IN DRYING
Innovation is the engine that drives R&D and advances in
technologies in general. As the world is getting “flatter”,
following Friedman’s terminology, at an accelerating pace,
global competition will provide the impetus for increased R&D
particularly in areas inevitably dependent on large consumption
of energy. Already developing economies are making more
than their share of drying R&D over the past decades as
reflected by publications on drying R&D. Energy crisis of the
early 70’s drove drying R&D, resulting in several conferences
devoted to drying and even a new journal focused on drying.
As energy costs dropped and levelled off drying R&D
continued but driven by need to reduce costs, improve quality
and meet global competition. Recent hikes in energy costs will
drive a second wave in drying R&D seeking to further improve
the energy efficiency of entire drying/dehydration systems and
potentially use renewable sources of energy where feasible.
With rapidly increasing cost of physical experimentation and
lack of talent, it is obvious that we need to turn to the almighty
computer for cost-effective solutions and even as a way to
intensity the innovation process. After all, we are facing the
Digital Big Bang resulting in explosive growth of computer-
assisted engineering solutions.
There is one major problem that is limiting general
utilization of mathematical models for innovation, design,
operation and optimization of dryers. We do not yet have a
reliable general theory of drying. In fact we do not have
generalized mathematical models for even a particular type of
dryer, for example for spray dryer for liquids or fluid bed dryer
for particles. We must depend on empirical data and lab or even
pilot scale tests to arrive at reliable full scale units; even then
knowhow is of overriding value relative to current knowledge
of these processes. Most models work well with specific
product-dryer type combinations and that too with a significant
amount of empiricism.
In this paper we will provide as examples modelling results
for several dryer types examined at NUS viz. spray dryer for
liquids, a spouted bed dryer of particles, pulse combustion
dryer for liquids or as impingement dryer for sheets and heat
pump dryer for heat-sensitive materials. The idea is to
demonstrate how one can utilize models, even if not general
and fully validated, can be used to innovate and examine new
conceptual designs of dryers. They also show the formidable
challenges ahead, leading to some ideas for future R&D.
MATHEMATICAL MODELS OF DRYING AND DRYERS
We cannot provide a general overview of the wide
assortment of modelling approaches, their relative merits and
limitations, within the limited scope of this presentation. Table
1 is a summary of some of the model types (along with some
references for the benefit of the interested reader). The type of
model clearly depends on the object of modelling, type of
product and drying equipment. Modelling of drying is a
microscopic level approach that ideally is independent of the
material. Even for the simplest well-defined porous material
this poses severe problems. Compared to what we find in the
literatures on porous media, the corresponding drying problem
is complicated by the fact that the porous material can undergo
physical deformation and even chemical reactions, change of
moisture transport mechanisms during drying, can involve glass
transitions, precipitation of solids, micro-crystallization etc.
Some phenomena can occur at the micro-scale while others
may occur at the macro-scale. The material being dried can be
non-homogeneous and anisotropic. There can be porosity
gradients within the product as it dries. Multiple modes of heat
transfer can be applied simultaneously or intermittently to
provide the heat of phase change. Indeed, the operating
temperature and pressure range can range from below the triple
point (freeze drying) to above the critical point (supercritical
CO
2
extraction of water form hydrogels). Drying times can
range form milliseconds (inkjet droplets) to several months (in
some drying kilns for wood). From this it is clear that it is
unrealistic to expect to develop a generalized theory drying
based only on fundamental properties of the material.
Table 1 Mathematical model for the drying process
Table 2 Mathematical models for dryers
Model Type Description Applications
Response
surface
methodology
A statistical technique that uses
regression analysis to develop a
relationship between input and
output parameters
Process
optimization[8],
finding significant
factors
Multivariate
analysis
A collection of statistical
procedures that involve
observation and analysis of
multiple measurements
Optimization,
finding significant
factors
Data mining Automatic searching of large
volumes of data to establish
relationships and identify
patterns
Statistical
techniques,
machine learning
Neural
networks
An artificial neural network
model is an interconnected
group of functions that can
represent complex input-output
relationships
Process control [9-
10], product
quality, wider
applications
Genetic
algorithms
Search algorithms in a
combinational optimization
problem
Parameters
optimization [11],
process control
method [12]
Fuzzy logic Fuzzy set theory that permits
the gradual assessment of the
membership of elements
Dryer selection
[13], control [14]
Indeed, mathematical models also help with scale-up and
optimization of operating conditions. Furthermore, model-
based control is becoming increasingly popular to ensure good
thermal efficiency, safe operation and product quality. Thus,
out thesis is that mathematical models of dryers are a valuable
prelude to arriving at innovative designs of dryers. Following
are a couple of recent examples from our laboratory.
It should be noted at the outset that modelling of dryers
basically requires two sub-models, viz. a drying model and an
equipment model. The former deals with the drying
characteristics of the material being dried and the latter deals
with the manner in which the material is handled in the
equipment which affects the heat and mass transfer rates and
residence times the material sees within the dryer. Both types of
models today need considerable amount of empirical data e.g.
drying kinetics over parameter ranges to be encountered in the
dryer, behaviour of the material in the equipment under a range
of parameters the dryer may be operated under etc. The need to
model solids and solids flow, that too when the solids are wet
and hence maybe sticky with tendency to form lumps or
agglomerates, presents unusually complex problem to
modellers. We will consider just a few examples in this
presentation.
Huang (2005) developed a CFD model to predict flow
patterns and overall drying performance of different spray dryer
designs [5]: the conventional cylinder-on-cone one; the dryer
with two pressure nozzles, rotating disk atomizer and ultrasonic
nozzle; the dryer with conical, hour-glass shape and lantern
shape chambers. Furthermore, the CFD model was used to
Model Descriptions Applications
Lattice
Boltzmann
Simulation
Complex fluid phenomena at the
mesoscopic scale systems;
Simplicity, powerful method for
simulating flow in porous media;
Efficient to parallel computing
Emulsification;
micro-filtration
process; few
application in drying
Population
balances
Modelling discrete or particulate
materials using a population density
function;
Accuracy and convenience in
description of particle properties
Expensive in computation
Particulates in
fluidized beds [1].
Particle formation ,
breakage , etc
Discrete
element
model
Tracking the motion of individual
particles.
Accuracy in description of
dynamics of particulate phase.
Expensive in computation cost
Particle mixing in a
drum[2], particle
dynamics in fluid,
spray bed, etc.
Pore
network
model
Simulating flow in porous bodies.
Influence of Pore- structures on
drying kinetics.
Microscopic description of transport
phenomena
Increased model performance.
Drying of Porous
materials [3]
Fractal
analysis
Powerful tool for characterizing
materials and processes.
Self-similarity theory.
Complex and chaotic problem.
Efficiency in predicting particle
properties
Difficulty in estimation of fractal
dimension
Particle diameter
distribution, material
properties[4]
Computati
onal fluid
dynamics
(CFD)
model
Comprehensive model for
engineering problem.
Governing equations + boundary
and initial equations.
Higher sophistication when coupled
with other models
Available in commercial software
packages.
Active in system design and process
optimization
Spray, fluid, spouted
bed drying[5-6],
wider applications
Finite
element
analysis
Modelling moisture transfer in wet
solid.
No need for additional equation to
assure continuity cross common
boundaries.
Easily handle complex geometries
and mesh gradation.
Easily handle mixed boundary
conditions
Easily programmed.
Grains, soybean, rice
drying, thin-layer
drying, etc [7]
evaluate an innovative one-stage and two-stage, two
dimensional horizontal spray dryer (HSD) concept. Figure 1
shows predicted particle trajectories inside various chamber
geometries design in one stage HSD dryer, where Figure1 (A)
show a basic rectangular box design similar to a commercial
horizontal spray dryer (Ceroges, 2004). From Figure 1, it can
be seen that the chamber volume is not fully used in Case A
and B. The particle deposit on bottom wall is reduced and the
chamber volume is fully utilized in Case C. However, a
recirculation zone near the outlet will lead to backflow of
ambient air. Condensation may occur and it may cause large
deposit and poor product quality. Case D and E can be
considered as good conceptual designs: high chamber volume
utilization ratio, reduced wall deposits, sufficient particle
residence time, etc. If the evaporation rate per unit volume is
considered, Case D gives better performance, about 25%, more
than case E. Thus, Case D is the best one among proposed
geometry designs
Figure 1 Predicted flow stream and particle trajectories for
various one stage HSD designs
A CFD two-fluid model was developed by Wu to describe
the gas-particle flow behaviours of a cylindrical spouted bed
under a steady spouting jet [6]. The typical flow pattern of the
spouted bed is shown in Figure2 (a), where a stable spout,
fountain and annulus regions were observed clearly. Calculated
particle velocities and concentrations agree well with the
published experimental data. The CFD model was also used to
evaluate the influence of operation parameters such as particle
size, density, and pulsating jet, etc on flow pattern of the bed.
Figure2 (b) show a bubble generate inside the bed under a
pulsating jet and is moving to the freeboard. The bubble size
and shape is related to the frequency of the pulsating jet and
bubbles will disappear when frequency exceeds a critical value.
Bubble formation and resulting flow instabilities were also
described. The drying kinetics of grains in the spouted bed
dryer was also investigated computationally. Figure 3(b) shows
the predicted mass fraction of vapour inside the bed after a
drying time of 1.2 second. Similar distributions can also
obtained for gas temperature, particle temperature, moisture,
density, water evaporation rate, etc at different drying times.
Such predictions can provide important information on the flow
field within the spouted beds for process design and scale-up.
Figure 2 Particle concentration distribution insider the
bed under steady (a) and unsteady spouting jet (b) and mass
fraction distribution of vapor at drying time of 1.2 s
(H=0.325m, ρ
s
= 2500 kg/m
3
, d
s
=1.41mm, U
ms
=0.54 m/s)
Thermo-Mechanical Models of Drying
When water is removed during drying processes, pressure
imbalance is produced between inner pressure of the material
and the external pressure, generating contracting stresses that
can lead to material shrinkage or collapse, changes in shape.
When rapid drying rate conditions are used and intense
moisture gradient through the materials are observed, shrinkage
is not uniform resulting in the formation of unbalanced stress.
In this condition, surface cracking may occur leading to
permanent deformation or even failure of the material. To avoid
such undesired effects, simulation tools that can handle
simultaneously the drying problem and the coupled mechanical
problem are necessary.
The thermo-mechanical models often comprise of simplified
drying models based on the diffusion equation with different
coefficients and boundary conditions for the first and second
periods of drying. The drying models enable estimation of
moisture content distribution in the dried sample. The
magnitude of stresses/shrinkage depends inter alia on the
moisture distribution gradient. Different models for drying-
induced stresses and shrinkages have been developed to
estimate these mechanical effects.
Distribution of moisture content
The distributions of moisture content are often evaluated
based on the diffusion model equations. Taking a pine-wood
disk as an example [15], the moisture transfer during the first
period of drying, also called the constant drying rate period, is
described by the following differential equation
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
∂
∂
+
∂
∂
=
∂
∂
rr
r
D
t
II
I
I )(
2
)(2
)(
)(
1
ϑϑϑ
(1)
The boundary and initial condition is given by:
0
0
)(
=
∂
∂
=r
I
t
ϑ
(2)
()
constYYk
t
A
an
I
Rr
I
I
=−=
∂
∂
−
=
)(
)(
)(
ϑ
(3)
const
t
I
==
=
0
0
)(
θϑ
(4)
where Y
n
and Y
a
are the vapour contents in the drying air close
to and far form the disk surface, and k
(
Ι
)
is the coefficient of
convective vapour exchange between the dried disk and the
ambient air, respectively.
The solution of the above initial-boundary value problem
was constructed by Kowalski (2005) with the help the
separation of variables method and its final form is described as
()
⎪
⎭
⎪
⎬
⎫
⎪
⎩
⎪
⎨
⎧
⎥
⎦
⎤
⎢
⎣
⎡
−+−=
∑
∞
=
−
0
0
2
0
)(
)(
0
,
)(
)(
2
)(
)/(
12
n
t
t
e
nn
n
I
I
tr
I
I
n
J
RrJ
t
t
CRB
λ
λλ
λ
θϑ
(5)
where
)()()(
/
III
ARkB =
,
()
RYYC
an
/−=
,
)(2)(
/
II
DRt =
and λn is the n-th eigenvalue calculated from the characteristic
equation
() {}{ }
.....,0
211
λ
λ
λ
λ
=→=
nn
J
,
(6)
Here J
0
and J
1
are Bessel functions of the first kind of zero and
first order, respectively.
Similarly, the moisture distribution in the disk during the
second period of drying reads
()
()
()
[]
()
⎟
⎠
⎞
⎜
⎝
⎛
−
−
+
×
⎪
⎭
⎪
⎬
⎫
⎪
⎩
⎪
⎨
⎧
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−−−+=
Π
Π
∞
=
ΠΠΠ
∑
)(
2
0
2
)(2
0
0
)(
2
)(
,
)(
exp
/
2
4
12
t
tt
a
aJBa
RraJ
B
a
aBb
s
n
nn
n
n
n
ee
tr
ϑθθ
(7)
Here a
n
is the nth enginvalue calculated from the characteristic
equation of the form
()
()
() {}{ }
.....,
2101
aaaaJ
a
B
aJ
nn
n
n
=→=
Π
Hence, equations (5) and (7) enable estimation of moisture
content distribution in the dried sample in several instants of
time. When temporal moisture content distribution is obtained,
the shrinkage of materials and stresses can be then determined.
Shrinkage
The moisture content of materials decreases during drying,
resulting in a decrease of its volume-shrinkage. Generally,
mathematical models for shrinkage can be classified as
empirical and fundamental ones. Empirical models are
relatively simple methods which develop an empirical
correlation between shrinkage and moisture content, including
occasionally the relevant process parameters like temperature
and humidity of air. The correlation can be linear: Lozano et al
(1980) used the equation
XccD
R 21
+= to model shrinkage
of the cylindered apple [16]. The reduced dimension D
R
refers
to volume; it can also be non-linear:
Vazquez, et al (1999)
applied the equation
)exp(
76
2/3
543
XccXcXccD
R
+++= to simulate
shrinkage of the slab garlic [17]. The reduced dimension is
thickness. These empirical models usually give good fit to
experimental data, but their use is limited because of their
dependence on the drying conditions and on the material
characteristics. They require extensive experimental testing and
should not be extrapolated.
Fundamental models, based on mass balances, density and
porosity definitions, assume in most cases additivity of the
volumes of the different phases of the system. That is,
shrinkage compensates for moisture loss. Suzuki, et al (1976)
used a linear equation to model the shrinkage of cube carrot,
potato, sweet potato, and radish:
1
7
0
+= Xc
V
V
where
e
XX
c
c
−
−
=
0
8
7
1
and
()
()
e
e
X
X
c
ρ
ρ
1
1
0
0
8
+
+
=
[18]. The reduced
dimension is area:
3/2
00
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
V
V
A
A
. Other types of
fundamental models for shrinkages were summarized in
Reference [19]. Compared with empirical models, it is not
usually necessary for fundamental models to obtain
experimental shrinkage values at every process condition. It
also allows the prediction of moisture content and/ or change in
volume to be obtained without complicated mathematical
calculations. However, the quality of the fundamental models
fitted to experimental data is relatively low.
Drying- induced stresses
Kowalski (2004, 2007) discussed the drying induced stress
during the wood drying process [15, 20]. The author assumed
that wood beyond the fibre saturation point (FSP) does not
shrink and has the lowest mechanical strength despite its
moisture content. Unsaturated wood, on the other hand, shrinks
when the moisture content decreases. The shrinkage is then
regarded as proportional primarily to the change of moisture
content; the volumetric strain due to shrinkage is
θε
)(
3
X
k=
.
The coefficient of humid expansion fulfils the following
criterion
⎩
⎨
⎧
≤≤
≤≤
=
se
X
s
X
k
k
θθθ
θθθ
)(
0
0
)(
0
(8)
![Table 3 Applications of thermo-mechanical models to drying [21]](/figures/table-3-applications-of-thermo-mechanical-models-to-drying-37cfho7i.webp)
