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Pneumatic drying of cassava starch: Numericalanalysis and guidelines for the design of efficientsmall-scale dryers

A. Chapuis, M. Precoppe, J. M. Méot, K. Sriroth & T. Tran

To cite this article: A. Chapuis, M. Precoppe, J. M. Méot, K. Sriroth & T. Tran (2017) Pneumaticdrying of cassava starch: Numerical analysis and guidelines for the design of efficient small-scaledryers, Drying Technology, 35:4, 393-408, DOI: 10.1080/07373937.2016.1177537

To link to this article: http://dx.doi.org/10.1080/07373937.2016.1177537

Accepted author version posted online: 05Jul 2016.Published online: 05 Jul 2016.

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DRYING TECHNOLOGY 2017, VOL. 35, NO. 4, 393–408 http://dx.doi.org/10.1080/07373937.2016.1177537

Pneumatic drying of cassava starch: Numerical analysis and guidelines for the design of efficient small-scale dryers A. Chapuisa,b,c, M. Precopped, J. M. Méota, K. Srirothc, and T. Trana,b,c

aCIRAD, UMR QualiSud, Montpellier, France; bCIRAD, UMR Qualisud, CGIAR Research Program on Roots, Tubers and Bananas (RTB), Bangkok, Thailand; cCassava Science and Technology Research Unit (CSTRU), Kasetsart University, Bangkok, Thailand; dInternational Institute of Tropical Agriculture (IITA), CGIAR Research Program on Roots, Tubers and Bananas (RTB), Dar es Salaam, Tanzania

ABSTRACT In a number of tropical countries, the expansion of cassava processing is tied to the development of small-scale, energy-efficient pneumatic dryers used to dry flour and starch. To facilitate this development, in this study a model of the pneumatic drying of starch particles was developed, to be fitted to measurements taken from large cassava processing factories. After that, numerical simulations were performed to analyze the effects of geometry and operating conditions on the energy efficiency and pipe length required to dry the product. The results clarified the influence of processing capacity, air inlet conditions, and starch particle size, emphasizing that air velocity as well as the dilution of the starch should be minimized. In light of the findings described here, we offer guidelines for the design of efficient small-capacity flash dryers.

KEYWORDS Cassava starch; design guidelines; energy efficiency; modeling; pneumatic dryer

Introduction

Development of the cassava starch industry

In a number of tropical countries, there is a growing interest in the development of the cassava processing industry. This is because such a sector is seen as essen-tial to increasing the economic benefits to be derived from existing cassava root production activities.[1,2] This trend has intensified since the food crisis of 2008, as there is a need to support local agricultural activities and reduce such countries’ reliance on imported staple foods, so as to limit their exposure to price fluctuations on international markets and improve food security at the national level. Traditionally, cassava roots are con-sumed fresh as food or processed into starch, flour, and other derived products. The crop’s main drawback is its short shelf-life, for after harvest the roots must be processed within 2 days, otherwise they spoil.[2] There-fore, the development of reliable technologies is a key factor in making cassava processing a profitable activity.

Thailand is the world’s premier exporter of cassava starch, thanks to a well-structured sector and modern factories that use state-of-the-art processing technolo-gies. In Thailand, cassava is grown by smallholders, mostly as a cash crop, and then sold to factories which produce starches used in a number of industrial sectors, such as paper and food manufacturing, pharmaceutical

products, and oil and gas. The production of cassava starch in Thailand is carried-out on a large scale, with the typical production capacity of factories being 200 tons of starch per day (at 0.14 kg kg� 1 moisture content dry basis) taken from 800 tons of roots, when running 24 h a day.[3] This sector uses a well-organized supply and distribution network which relies on a solid transport infrastructure. It is this which helps make the Thai starch industry so competitive.

For several decades, a number of countries have been processing cassava roots into starch, flour, and other products, then distributing and selling them to local markets.[4] However, the traditional processes used in these countries are rather limited in terms of their production capacity, and the quality of the products produced is highly variable. Therefore, the implemen-tation of more advanced processing technologies could be expected to increase the quantity and quality of cassava products on the local markets in Africa and potentially help to target the international market. This represents an opportunity to enhance the benefits generated from cassava, an already well-known and widespread crop on the continent.

As a consequence, local operators have tried to modernize their processing equipment, following the example of the large-scale factories. However, reducing the size of pneumatic dryers used at the end of the

CONTACT A. Chapuis arnaud.chapuis@mines-albi.fr CIRAD, UMR Qualisud, TA B95/16, 73 rue Jean-François Breton, 34398 Montpellier Cedex 5, France. Color versions of one or more of the figures in this article can be found online on at www.tandfonline.com/ldrt. © 2017 Taylor & Francis

production process remains a major problem. Drying is the most energy-demanding operation within the process, and its control is crucial for ensuring that the product produced is of a high quality. Thus, this study aims to contribute to the development of efficient drying equipment in response to the needs of small- scale cassava processing operations in developing countries, the challenge being to build small-capacity dryers of reasonable dimensions, yet which are energy efficient and able to deliver a product of high quality.

Pneumatic conveying dryers

The common process for producing cassava starch consists of a series of operations whose aim is to extract and separate the starch from the fibers contained in the roots. The roots are first finely crushed using raspers, to unbind the starch granules from the root matrix. Then, the resulting mash is dispersed in water and the starch separated from the fibers by centrifugal sieving. Finally, the water is mechanically removed by settling, centrifugation, or hydrocyclones, producing a crumbly starch cake with a moisture content of 0.55–0.60 kg kg� 1 dry starch particle (ds). This is then sent to the dryer.[3]

A pneumatic conveying dryer, also called a flash dryer, works on the principle of an entrained fluidized bed. The wet starch is introduced into a hot airstream using a feeding device such as a hammer mill, to break the sticky material into fine particles. Then, the particles are entrained in the hot air, dry as they travel along the pipe, and are finally separated using cyclones. The industrial dryers in operation in Thailand have daily capacities ranging from 100 to 400 tons of dry starch, using drying pipes with a diameter of about 1–2 m and a total length of 40–60 m. The drying air tempera-ture of such dryers is generally in the range 170–180°C at the inlet and the air velocity 15–25 m s� 1. Airflow through the pipe is generated based on suction, using a blower set at the air exhaust. This setting provides a slightly negative operating pressure, and this prevents starch dust being blown out in the case of damage.

The target moisture content for the product ranges from 0.13 to 0.15 kg kg� 1 ds. A major constraint on pre-serving the quality of the product during drying is the potential gelatinization of the starch, a phase change which can occur when the temperature goes above 60°C and the moisture content rises above 0.35 kg kg� 1

ds. To ensure homogeneity of the product’s quality, and despite fluctuations in input parameters such as air and starch moisture contents, the process requires continu-ous control. In most cases, the blower and boiler are operated at a fixed load, while the outlet air temperature

is maintained at around 50–55°C by controlling the starch feed rate.

In contrast, smaller starch producers in other countries aim for daily capacities of 2–10 tons of starch and use dryers with pipes 10–15 m long. These produ-cers tend to use similar operating conditions as the large factories, though with slightly lower air velocities. However, common problems faced by such operators are insufficient drying and—when the target moisture content level is achieved—high energy consumption levels and product quality issues due to gelatinization. Actually, a range of factors affects the performance of a flash dryer, from the drying pipe design (dimensions) to the operating conditions used, including the air temperature, velocity, and feed rate.

Modeling and numerical analysis of flash drying

The modeling of heat and mass transfer in a dryer can provide a better understanding of the drying process and allows one to identify those parameters governing performance. The modeling of flash drying has been widely covered in the scientific literature, since such drying is used for a range of powder materials, including PVC, silica,[5] alumina,[6,7] limestone,[8] and sawdust[9] as well as food products such as rice powder and other starchy products.[10–12] However, no specific work has been published on the design of flash dryers for use with cassava starch.

In this paper, therefore, we propose to use modeling to help understand the influence of design and operating parameters on the performance of flash dryers, and to analyze the possibilities for scaling down the process. First, we built a mathematical model to describe and simulate the drying of starch par-ticles. This model was based on previously published articles about the drying of potato starch and rice powder,[10,11] although with major differences in terms of the assumptions used. While the previous authors considered the drying to be convection driven, we considered it to be diffusion driven. The model was then fitted to processing data taken from five industrial producers of cassava starch in Thailand and Paraguay.

A new approach taken in this work was the use of numerical analysis to determine guidelines for the design of small-scale flash dryers with high energy efficiency levels, yet with reasonable dimensions. To this end, we performed a series of simulations to analyze the trade-off between pipe length and specific energy- efficient consumption under various operating con-ditions. The results described here clarify the effects of design and operating parameters on dryer performance,

394 A. CHAPUIS ET AL.

leading to the development of guidelines for the design of energy-efficient dryers.

Description of the drying model

Drying mechanism and modeling assumptions

A one-dimensional incremental model was applied to describe the changes in moisture content, temperature, and velocity of the air and particles that took place within the dryer. This type of model has already proved successful in simulating the pneumatic drying of particles.[7,9–11,13] Moreover, it provides an appropriate level of detail and accuracy for dryer design purposes, yet requires far less computing time than CFD models.[14]

Pelegrina and Crapiste[10] proposed a mathematical model for the pneumatic drying of food particles that was later improved and used by Tanaka et al.,[11] who studied the drying of rice powder. In this study, the same overall balance equations were used but with different assumptions made concerning the physical mechanisms driving the drying process at the particle level.

The drying of a particle in a flash dryer occurs through two mass transfer mechanisms in series: the diffusion of water from the inside to the surface of the particle, and the convective transfer of water from the surface to the air. The slowest mechanism determines the maximum drying rate. The Biot number compares the relative resistance to water transport of diffusion and convection processes.[15] In the case of starch particle drying, the Biot number is of the order of magnitude of 105, which indi-cates that the drying rate is entirely governed by the kinetics of water diffusion. Practically, it means that when a starch particle enters the drying pipe, its surface dries almost instantaneously to the equilibrium moisture level of the surrounding air. In turn, the moisture gradient created within the particle causes the water to migrate from the centre to the surface.

Eventually, the size of starch particles is heteroge-neously distributed, with diameters ranging from 50 to 450 µm. The diameter reached is highly variable, and depends on the moisture content and feeding system used, plus continually changes as particles agglomerate or split during drying.[16] To describe these phenomena within the drying model here would be prohibitive due to the complexity involved. Moreover, as the measure-ment of this property is very difficult, almost no experi-mental data are available in the literature.

Thus, as a simplifying assumption for the model used here, the particles were considered spherical and homogeneous in size, meaning that during drying, they would maintain a constant volume while their porosity

increases (see “Starch particle properties” section). This meant that drying could be modeled identically for all particles, though in reality not all particles dry at the same rate; the moisture equilibrates afterward. The consequence of this assumption was that the particle diameter in the model was considered as a parameter equivalent to the actual particle size distribution. In practice, however, its value may vary from one dryer to another as the result of different feeding systems. The main drawback of this method is that the possible effects of operating conditions on particle size are not modeled.

In total, five industrial starch dryers were simulated within the model, to evaluate the particle diameter range. Based on the simulations, the particle diameter was chosen so that the model output would match the manufacturers’ data in terms of starch outlet moisture, which is the most sensitive output variable. This is further detailed in the “Model fitting using field data from large-scale dryers” section.

Overall balance equations

The method used for modeling such drying operations consisted of balancing the exchanges between the starch and the drying air in terms of mass, momentum, and heat.[17] The resolution of balance equations allows one to calculate the moisture, velocity, and temperature profiles of air and starch particles along the drying tube. This section presents the one-dimensional balance equations originally proposed by Pelegrina and Crapiste.[10] The physical and thermodynamic properties of the moist air were retrieved from Bimbenet et al.,[15] Conde,[18] Green and Perry,[19] and Kreith et al.[20].

Momentum balance The momentum balance for a single particle is given by Eq. (1), while Eq. (2) refers to the drying air present within a control volume (portion of the drying pipe defined as ua · S · dt).

dup

dt¼ _up ¼

A0p2Vp� CD �

qaqp� ua � up� �

� ua � up��

��

� 1 �qaqp

!

� g �fp � u2

p

2D

ð1Þ

dua

dt¼ _ua ¼ �

1qa � ua

�dPdt� g �

4 � fa � u2a

2D

�A0p

2Vp� CD �

1 � e

e� ua � up� �

� ua � up��

��

ð2Þ

DRYING TECHNOLOGY 395

The drag coefficient was calculated using the correlation proposed by Schiller and Naumann.[21] In the model, the pipe was made of drawn stainless steel, so the air–wall friction coefficient was calculated using the Blasius correlation for smooth pipes.[17] The particle–wall friction coefficient was calculated using the experimental correlation taken from Capes and Nakamura.[22]

The void fraction e of the bed of particles—defined as the ratio of the air volume to the total volume of air and starch particles in a given section of pipe—was used to couple the solid-phase and gas-phase balance equations. It can be expressed using the mass balance equations for air and particles, as in Eq. (3)

_mda � 1þ Yð Þ

qa¼ ua � S � e ð3Þ

To solve the momentum and mass balance equations, the dry air and dry starch mass flow rates were set as a constant. The initial particle velocity could not be set to zero, because this would have been inconsistent with the one-dimensional model (if velocity ¼ 0, flow rate ¼ 0). Instead, the initial particle velocity was set to a slightly positive value; small compared to the air velocity, e.g., 0.5 m s� 1.

Heat balance Equations (4) and (5) give the heat balance related to a particle and to the drying air, respectively.

dTp

dt¼

Ap

Vp�

1qp � C

pp� _q � _w � Lsð Þ ð4Þ

dTa

dt¼�

1Ca

p�

�Ap

qa �Vp�

1 � e

e� _qþ _w � Cv

p � Ta � Tp� �� �

þ_Qloss �ua

_mda � ð1þYÞ

�

ð5Þ

The temperatures of air and particles were con-sidered homogeneous and were set to Ti

a and Tip at

the initial state, respectively. Heat losses to the environment occur by heat transfer

through the pipe wall and were estimated here by calculating the heat flux through the pipe wall, which includes internal and external convection and conduc-tion through the pipe’s insulation. Based on the infor-mation provided by the starch factories, the study dryers’ pipes were generally made of 2-mm-thick stain-less steel with a conductivity of 16.3 W m� 1 K� 1, insu-lated with a layer of rock wool which had a conductivity of 0.04 W m� 1 K� 1. The internal convective transfer coefficient was calculated using the

Sieder–Tate correlation,[15] and the free convection coefficient to the ambient was set to an average value of 15 W m� 2 K� 1.[23]

Water mass balance The water mass balance is expressed by Eqs. (6) and (7), giving the variations in moisture content over time of starch and air, respectively.

dXdt¼ _X ¼ �

Ap � _wVp � qp

� 1þ Xð Þ ð6Þ

_Y ¼ � _X �_mds

_mdað7Þ

The air moisture content was considered homo-geneous, while the moisture profile within the particle was calculated by solving the diffusion equation to be discussed in the following section.

Water and heat transfer at the particle level

In addition to the overall balance equations, local models were required to evaluate the heat and mass exchanges at the particle level. The resolution of these local models provided the heat and mass flux terms _q and _w, which were required in the overall balance.

Diffusion-driven water mass transfer According to the assumption made on diffusion-driven drying, the drying rate _w is governed by the dynamics of diffusion at the particle level. The transport of water from the centre to the surface of starch particles com-bines several mechanisms, including vapor and liquid diffusion, capillary flow, and surface diffusion. This was modeled here using the second Fick’s law with an effective diffusivity coefficient,[24] and this included the effects of all the mechanisms involved. The effective diffusivity of water in starch was evaluated as a function of temperature and water concentration, as proposed by Karathanos et al.[25] Therefore, the diffusivity was con-sidered to be temporally and spatially dependent. Assuming that the diffusion properties of water in starch are isotropic, the diffusion has a spherical sym-metry and thus was expressed in a spherical coordinate system, using Eq. (8).

@C@t¼

1r2 �

@

@r� r2 � DwsðC;TpÞ �

@C@r

� �

ð8Þ

Initially, moisture is homogeneously distributed within the particle. After the introduction of the particle to the drying pipe, the particle surface is instantaneously in equilibrium with the surrounding air, i.e., the water vapor pressure at the particle surface is equal to

396 A. CHAPUIS ET AL.

the vapor pressure in the surrounding air. Knowing the vapor pressure and the particle surface temperature, the water activity aw can be deduced using Eq. (9).

aw ¼pv Yð Þ

psat Tp� � ð9Þ

where pv(Y) and psat(Tp) are the vapor pressure in air and the saturation vapor pressure at the particle surface temperature, respectively.

Water activity at the surface of a product can be related to its moisture content at a given temperature using sorption isotherms. No specific sorption data were found in the literature for cassava starch at the tempera-ture range used during this process. Therefore, we used the sorption isotherm of high-amylopectin starch being processed at 45°C, as proposed by Al-Muhtaseb et al.[26]

This assumption was justified by the fact that cassava starch is mostly composed of high amylopectin. More-over, according to Al-Muhtaseb et al.,[26] the sorption properties of high-amylopectin and high-amylose starch are very similar.

The sorption isotherm was described using a GAB model, i.e., Xp ¼ f(aw). Knowing the water activity at the particle surface, the GAB relation was used to calcu-late the starch moisture content at the particle surface, providing the boundary conditions required to solve the diffusion equation. The resolution of water diffusion in the particles allowed us to calculate the drying rate; represented by the water mass flux density at the surface of the particle.

Convection-driven heat transfer As for the water mass transfer, the transfer of heat between the air and the particle occurs through convec-tion and conduction working in series. To identify the governing transfer mechanism, the Biot number for heat transfer was evaluated at several positions along the drying pipe, using data on the thermal conductivity of granular starch provided by Drouzas and Saravacos.[27] As the conductivity of starch strongly increases with bulk density and moisture content levels, the Biot number remains relatively low (�0.1) through-out the drying pipe, indicating that heat conduction within a particle is relatively fast and that the transfer is mostly controlled by convection at the interface.[15,28]

Therefore, in this model, the temperature of the particles could be considered homogeneous.

The convective heat flux is calculated according to Eq. (10) and using the convective heat exchange coefficient h. A modified version of the common Ranz–Marshall correlation, specifically developed for drying particles, was used to evaluate h, as

recommended in previous studies.[13,14,29]

_q ¼ h � Ta � Tp� �

ð10Þ

Starch particle properties

Owing to their structure (agglomerated granules), starch particles are porous materials and their bulk density should be expressed as a function of porosity:[30]

qb ¼ 1 � ep� �

� qs

where ep is the porosity of the particle, and ρs (kg m� 3) is the solid density.

Marousis and Saravacos,[31] and Karathanos and Saravacos[30] studied the density and porosity of starch materials during drying and observed that the porosity of starch increases linearly during drying. Following Marousis and Saravacos,[31] the solid density of starch granules was expressed here as a function of moisture content, using Eq. (11).

qs Xð Þ ¼ 1442 þ 837 � X � 3646 � X2 þ 4481 � X3

� 1850 � X4

ð11Þ

Based on the same work, the porosity of cassava starch at the dryer inlet, i.e., moisture content within 0.5–0.6 kg kg� 1 ds, was estimated to be 0.175 by analogy, with results obtained for Amioca starch.

Then, assuming no shrinkage occurred during drying, it was also assumed that the water evaporated during drying would be replaced with air. As a result, the bulk density of particles could be calculated as a function of initial porosity and moisture content, as shown in Eq. (12)

qp ¼ 1 � epi� �

� qs Xð Þ �1þ X1þ Xi

ð12Þ

where epi (–) and Xi (kg kg� 1) are the porosity and moisture content of the particle at its initial state, respectively.

The heat capacity of dry starch is 1,500 J kg� 1 K� 1,[32]

while the heat capacity of humid starch particles is calcu-lated as the mass fraction average of pure starch and pure water heat capacities. In the absence of specific data for granular cassava starch, the heat of sorption was cal-culated here based on highly amylopectin and highly amylose starches data provided by Al-Muhtaseb et al.,[33]

for temperatures ranging from 30 to 60°C, and moisture content levels ranging from 0.02 to 0.2 kg kg� 1 ds.

DRYING TECHNOLOGY 397

Implementation of the model

The model was implemented using Matlab® (MathWorks, Natick, MA). The mass, momentum, and energy balance equations we resolved using a fourth-order Runge–Kutta integration method. At each time step, the partial differential equation of diffusion (8) was solved using the finite element explicit method, providing the water concentration profile within the particles, as proposed by Pakowski and Mujumdar.[28]

The discretization scheme used for Eq. (8) was recom-mended by Ford Versypt and Braatz,[34] who conducted a detailed analysis of the precision and stability of different discretization schemes for diffusion problems in spheres, with variable diffusivity.

The stability of such a resolution method depends on the time and spatial steps chosen. In the present case, the relation

N <R0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 � D � dtp

where N is the number of grid points, D is the diffusiv-ity, and R0 is the radius of the sphere should be verified.

As an indication, with dt ¼ 10� 4 s, R0 ¼ 200 µm, and D ¼ 10� 9 m2 s� 1, the maximum number of grid points is N ¼ 224. Using more grid points would require using a shorter time step; hence increasing the computing time is required.

The precision of the resolution method used here was tested by comparing the results for various spatial and time steps. To consider the least favorable case, the data from dryer TH-2 (see the “Model fitting using field data from large-scale dryers” section) was used, since it had the longest pipe and was thus more prone to the accumulation of errors. The time step was varied between 10� 5 and 10� 4 s, while the number of spatial grid points ranged from 50 to 250. Over this domain, the model output in terms of starch moisture content varied by less than 1.5%. For the range N ¼ 100–250, this variation was reduced to less than 0.5%, which was precise enough for the purpose of this study. There-fore, to ensure a good precision level while keeping reasonable computing time, the number of grid points was set to N ¼ 100, and the time step to dt ¼ 10� 4 s.

Dryer efficiency: Specific energy consumption

An efficient dryer is a dryer that maximizes the use of the sensible heat present in the drying air to evaporate the water from the product. Ideally, the outlet air should be saturated with moisture and its temperature is as low as possible. In the case of isenthalpic drying (free water removal at a constant temperature), the minimum

outlet air temperature corresponds to the adiabatic satu-ration temperature.[35] A common indicator used to characterize the performance of a dryer is its specific energy consumption, defined as the energy required to evaporate 1 kg of water from the product.[36] Its expression is given in Eq. (13). Its value can be com-pared to the latent heat of the vaporization of water at the inlet temperature of the product

Qs ¼_mda � ð1þ YiÞ � ðhin � hextÞ

_mds � ðXi � XfÞð13Þ

where hext (kJ kg� 1) and hin (kJ kg� 1) are the specific enthalpy of the drying air at ambient and dryer inlet conditions, respectively.

Numerical analysis method

The model was used to assess the potential to improve the design of small-capacity flash dryers when wishing to maximize their energy efficiency, while retaining reasonable dimensions. The analysis method was based on a series of numerical simulations; it allowed us to quantify the trade-off between pipe length and energy consumption while assessing the effects of various fac-tors, including inlet air conditions and processing capacity.

Design problem description and method of analysis

The basic functional specifications for the construction of a flash dryer are the capacity (starch feed rate), the moisture content of the feed, and the target moisture content of the product, which are fixed. Then, the objec-tive is to create a design that minimizes the specific energy consumption and the length of the drying pipe. The design used in this study included two aspects: the geometry of the drying pipe and the operating con-ditions. Constant diameter pipes were used to limit the range of possible geometries, meaning pipe geometry was defined using two variables: the diameter and the length. The operating conditions were also defined using two variables: the velocity and tempera-ture of the drying air at the inlet, right before the feed point. Overall, four variables were required to define the system and, since there was a constraint; this being that the starch outlet moisture content had to meet the target level, only three variables were independent (i.e., three degrees of freedom).

Accordingly, when operating conditions are fixed (air velocity and temperature), two variables remain; the pipe diameter and length, with only one degree of

398 A. CHAPUIS ET AL.

freedom. Thus, in the model, the pipe diameter was set as the independent variable and the model used to cal-culate the pipe length required to dry the starch to the target moisture content level. This was achieved using a “while” loop that exited the time iterations when the starch moisture content met the target.

Note that when the inlet air velocity and temperature are fixed, pipe diameter directly controls the air mass flow rate, and; thus, the dilution of the starch, i.e., the ratio _mda= _mds.

Obviously, to meet the target moisture content level, first one must ensure that the air mass flow has the capacity to absorb the moisture released by the starch. The lower bound can be calculated by assuming that the drying air undergoes an adiabatic humidification during the process, up to saturation point, so giving the adiabatic air mass flow rate. Then, the second condition is that the pipe length provides a residence time long enough to allow the transfer of the moisture in the starch to the air. Under fixed operating conditions, the residence time—and so the pipe length—required to meet the target moisture content is controlled by the dilution of starch, i.e., by the diameter of the pipe. This is explained by the fact that dilution actually affects the gradient of vapor pressure (or humidity) between the air and the particles, which is the driving force behind the drying that takes place. Therefore, high dilution (a large diameter) will result in a shorter pipe length and vice versa.

A second objective is to minimize the dryer’s energy consumption. This is achieved when all the sensible heat in the drying air is used to evaporate the product’s moisture, or in other words, the exhaust air is saturated with moisture (although, in practice, condensation should be avoided). Following this theory, maximizing the energy efficiency would lead to a maximization of the drying pipe’s length, meaning that under fixed oper-ating conditions, there has to be a trade-off between pipe length and energy efficiency.

To analyze this trade-off, the drying model program was tuned so that it considered both the pipe length required to reach the target moisture content, and the energy consumption of the dryer as a function of pipe diameter ([Qs, Lpipe] ¼ f[D]). This method provided all the pipe diameter and length combinations needed to dry a given flow rate of wet starch to the desired moisture content level, under given inlet conditions. By performing simulations for various inlet conditions, the effects of air velocity and air temperature were able to be assessed. Moreover, the influence of other para-meters such as the processing capacity of the dryer and particle diameters were also studied. In all simula-tions, the pipe was assumed to be set in a vertical position, with an upward air flow, since the length was unknown beforehand.

Default values for input parameters

For the simulations, it was necessary to define default values for all input parameters, and these are presented in Table 1. As one of the key drivers of this work was to investigate the possibility of using flash dryers in small- and medium-scale starch factories, the default proces-sing capacity was set at 2 tons of starch per day, which corresponds to a dry starch mass flow rate of 0.02 kg s� 1. The default particle diameter was set to 230 µm, corresponding to the average of fitted dia-meters (see the “Model fitting: Determination of particle size” section). For the other parameters, midrange values were chosen as the defaults.

The default air velocity was varied between 10 and 20 m s� 1. In practice, the lower bound for air velocity is the minimum required to entrain the largest particles. According to previous research studies,[37,38] the mini-mum entrainment velocity for starch particles with a diameter in the order of 230 µm is below 1 m s� 1. Therefore, even though starch particles may

Table 1. Input parameter values used in the sensitivity analyses (the pipe diameter value ranges are only valid for the default starch flow rate).

Variable name Unit Default value Min Max

Fixed parameters Maximum pipe length Lmax

pipe m 40

Rock wool insulation mm 75 Initial starch moisture content Xi kg kg� 1 ds 0.58 Target starch moisture content Xf kg kg� 1 ds 0.149 Initial air moisture content Yi kg kg� 1 da 0.016 Ambient temperature Text °C 30 Initial starch temperature T i

p °C 35

Variable parameters Pipe diameter D m (0.13) (0.28) Starch particle diameter Dp µm 230 210 270 Initial air velocity ui

a m s� 1 15 10 20 Dry starch mass flow rate _mds kg s� 1 0.02 0.02 2 Initial air temperature T i

a °C 170 140 180

DRYING TECHNOLOGY 399

agglomerate, an air velocity of 10 m s� 1 should be fast enough to entrain the largest particles. Experimental trials would be necessary to identify the lower bound.

Eventually, the range of the simulations (realized using the function [Qs, Lpipe] ¼ f[D]) was bounded according to the output values. Only those dryers fea-turing a pipe length below 40 m and a specific energy consumption lower than 10,000 kJ kg� 1 were considered here.

Results and discussion

Model fitting using field data from large-scale dryers

In order to compare the model’s predictions to the actual performance of cassava starch flash dryers, data were collected from five industrial production plants; three in Thailand (referred to as TH-#) and two in Paraguay (referred to as PA-#). Details for these plants are summarized in Table 2. In practice, several factors that influence the drying process can vary, and especially the inlet air moisture content and the wet starch moisture content. This problem is overcome by continuously adjusting the starch feed rate to keep the air outlet temperature constant, using automatic con-trols. Therefore, the information provided by the starch manufacturers for this study in terms of air and starch input and output conditions was in the form of value ranges rather than accurate values. Thus, average values were considered for the simulations.

In Thailand, the starch factories have, on average, larger processing capacities than in Paraguay. The dryers in Thai factories, therefore, have larger dimen-sions, both in terms of diameter and length. They also use higher air temperatures than the dryers in Paraguay (on average 173 vs. 143°C). Another significant differ-ence between the two countries is the climate, as it is dryer in Paraguay, resulting in lower air inlet moisture content levels.

Among the five dryers, the air inlet velocity ranged from 9.8 to 23.8 m s� 1. In terms of pipe geometry, all five dryers included an upward followed by a downward section. Three dryers (TH-1, TH-3, and PA-1) used constant pipe diameters, while in the two others (TH-2 and PA-2), the diameter of the pipe varied in some places. In TH-2, there was a pipe enlargement in the downward section, which was installed to increase the particles’ residence time by reducing air velocity. On the other hand, PA-2 had a pipe restriction just before the loop at the top of the upward section. This was presumably done to raise the air velocity, as it may have been too low at this point to entrain the

particles. Indeed, the air velocity was already relatively low at the inlet (9.8 m s� 1) and decreased to 8 m s� 1

in the first section of the pipe, due to the important temperature decrease caused by the drying (according to the simulation results).

Model fitting: Determination of particle size As mentioned in the section “Drying mechanism and modeling assumptions,” the particle diameter was used as a fitting parameter for the model. To this end, five industrial dryers were simulated using the model, based on the data provided by the manufacturers and taking

Table 2. Study flash dryers characteristics, including geometry, operating conditions, and model-predicted values (in all cases, particle diameter is as defined in Table 3).

Unit Inlet Outlet Outlet

(model)

TH-1 Pipe diameter m 1.16 Id. Pipe length m 46 — Rock wool insulation mm 50 Air velocity m s� 1 16.3 — 12.7 Air temperature °C 173 52 51.4 Air moisture content kg kg� 1 of da 0.0186 — 0.0667 Starch feeding rate kg of ds · s� 1 1.800 — Starch temperature °C 35 — 50.3 Starch moisture kg kg� 1 of ds 0.515 0.163 0.163

TH-2 Pipe diameter m 1.5 1.94 Pipe length m 57.7 — Rock wool insulation mm 75 Air velocity m s� 1 23.8 — 11.2 Air temperature °C 175 54.5 54.0 Air moisture content kg kg� 1 of da 0.0208 0.068 0.0688 Starch feeding rate kg of ds · s� 1 3.615 — Starch temperature °C 35 — 52.0 Starch moisture content kg kg� 1 of ds 0.563 0.149 0.149

TH-3 Pipe diameter m 1.14 Id. Pipe length m 45 — Rock wool insulation mm 50 Air velocity m s� 1 22.5 — 17.8 Air temperature °C 170 54.5 54.2 Air moisture content kg kg� 1 of da 0.0191 — 0.0642 Starch feeding rate kg of ds · s� 1 2.006 — Starch temperature °C 30 — 51.6 Starch moisture content kg kg� 1 of ds 0.506 0.149 0.149

PA-1 Pipe diameter m 1.2 Id. Pipe length m 33 — Rock wool insulation mm 50 Air velocity m s� 1 12.0 — 10.0 Air temperature °C 130 45 46.0 Air moisture content kg kg� 1 of da 0.01285 — 0.0459 Starch feeding rate kg of ds · s� 1 1.110 — Starch temperature °C 30 — 44.4 Starch moisture content kg kg� 1 of ds 0.493 0.149 0.149

PA-2 Pipe diameter m 1.5 0.95 Pipe length m 20.7 — Rock wool insulation mm 0 Air velocity m s� 1 9.8 — 20.4 Air temperature °C 155 62 64.8 Air moisture content kg kg� 1 of da 0.01189 — 0.0454 Starch feeding rate kg of ds · s� 1 1.010 — Starch temperature °C 30 — 55.2 Starch moisture content kg kg� 1 of ds 0.667 0.204 0.204

400 A. CHAPUIS ET AL.

into account the pipe geometry, including upward and downward sections and diameter changes. For each of the five dryers, simulations were run to analyze the effects of particle diameter on process output variables. Then, based on the results of these simulations, the particle diameter was fitted so that the model output matched the real data in terms of product moisture content. Product moisture content was used as the reference, because it was the most reliable measurement available at the dryer outlet. Indeed, for the starch to be marketable, its moisture content must be within a cer-tain range, e.g., the standard in Thailand is 12–13%. The air outlet temperature is also a reliable measure-ment to use, since it is commonly used to control the drying process.

Figure 1 illustrates the variation in starch outlet moisture content levels seen, as a function of particle diameter, varying from 180 to 280 µm for the five industrial dryers. The fitted particle diameters, as indi-cated by the square markers in Fig. 1 and reported in Table 3, ranged from 210 to 245 µm with an average of 227 µm. This shows that the approach used here, using an average particle diameter to fit the model to the field data, provided consistent results. The fitted particle diameters were in the same range as actual starch particle diameters (50–450 µm) and; moreover, among the five industrial dryers, the variation in fitted diameters was limited, only �8% from the average value. To go further in the validation of this approach, experimental tests would be required to verify if the fitted diameter varies with the drying conditions.

As expected, the particle size had a significant effect on the diffusion kinetics at fixed geometry and inlet

conditions. So, reducing the particle size resulted in lower outlet starch moisture content levels. The conse-quences of this are further analyzed in the “Effects of particle diameter” section. It should be noted that dryer PA-2 was particularly sensitive to variations in particle diameter, due to the short length of this dryer’s pipe, which resulted in a short residence time. This phenom-enon should be taken into account when designing dryers, since it might have an impact on how the equipment can be used.

Simulation results: Drying profiles and energy consumption For the five dryers, simulations were run using the fitted particle diameters, to illustrate the air and starch pro-perty profiles along the length of the drying pipe, and to compare the model’s outputs with the data provided by the manufacturers. The results are presented in Table 2. The model outputs could only be compared to the actual data in terms of air temperature and moist-ure levels, as the manufacturers do not provide the other outlet parameters.

In all cases, the model output closely matched the manufacturers’ data in terms of air temperature. Since the particle diameter was calibrated to match the outlet starch moisture content, the evaporated mass flow rate calculated by the model was equal to the actual value. Consequently, as outlet air temperature depends mostly on the evaporation rate, the model outputs were close to the measured values. The thermodynamic properties of moist air are well known, so the observed variations may have been the result of errors in the evaluation of heat loss, heat of sorption, or starch heat capacity. As an indication, the calculated heat loss for dryer TH-2 amounted to 6.7 kW, while the power required to heat the inlet air was about 4.6 MW. Without the 2-inch rock wool insulation in place, the heat loss would have been 10 times higher.

Figure 2 gives details of the air and starch properties found along the pipe in the case of dryer TH-2. When the particle entered the drying pipe, it underwent a rapid acceleration and about 5 m after the inlet, it reached a velocity close to that of air. The difference between air and particle velocity, termed slip velocity,

Figure 1. Results of the numerical simulation used to fit the model to the field data. The figure illustrates the outlet product moisture content as a function of particle diameter, for each dryer. The particle diameter is determined by fitting the product moisture to the actual value, represented by square markers on the graph.

Table 3. Fitted diameters, residence times, and specific energy consumption levels for the five study dryers.

Dryer Fitted particle diameter (µm)

Residence time (s)

Specific energy consumption (kJ kg� 1)

TH-1 245 3.52 3,117 TH-2 241 3.38 3,116 TH-3 210 2.46 3,257 PA-1 216 3.38 3,058 PA-2 222 1.80 3,798

DRYING TECHNOLOGY 401

was about 0.75 m s� 1. At 37 m, the particle velocity became higher than air velocity, which corresponded to the top of the drying pipe and the beginning of the downward section. This sudden drop in both air and particle velocities, at 45 m from the pipe inlet, corre-sponded to an increase in pipe diameter of 0.44 m, or

from 1.5 m to 1.94 m. The velocity decreased from 19 to 11 m s� 1, which increased the residence time of the particles.

The moisture profile shows that the drying was very fast at the beginning of the pipe, because of a strong moisture and temperature gradient. This high drying rate was accompanied by a dramatic decrease in air tem-perature, which dropped from 175 to 100°C over the first 10 m. Alongside this, the starch temperature increased progressively, rising from 35 to 62°C over the first 10 m, and then decreasing progressively up to the outlet. Thus, the starch remained right at the limit of gelatinization conditions[25] (which occur around 60–70°C), which is crucial to avoid if one wishes to preserve product quality. It should be noted that the temperature of the starch particles during drying might have been slightly overestimated, due to the assumption made over the homogeneous temperature.

The specific heat consumption and the particle residence time of the dryers were calculated, with the results presented in Table 3. The values for specific heat consumption ranged from 3,060 to 3,800 kJ kg� 1, which may be compared to the latent heat of vaporiza-tion of water at ambient temperature, which was 2,425 kJ kg� 1—the theoretical minimum energy requirement for drying. Dryers TH-1, TH-2, and PA-1 were the most energy efficient, with an average con-sumption of 3,100 kJ kg� 1. This performance may be explained by the long residence time of the particles in these dryers; 3.4 s on average, which resulted from the combination of air velocity and pipe length. TH-2 had a very long pipe (57 m) with a relatively high velocity (24 m s� 1), while PA-1 used a short pipe (33 m) with a low velocity (12 m s� 1). Meanwhile, TH-1 used a midrange pipe length and an average air velocity. PA-2 was the least efficient dryer of the group and also the one with the shortest residence time. These issues are further discussed in the next section, based on the results of the numerical analysis carried out.

Results of the numerical analyses, and the design guidelines

This section describes the results obtained using the numerical analysis method presented in the section “Design problem description and method of analysis.” In all simulations, all parameters were set to their default values, as listed in Table 1, except the parameter for which the effect was being analyzed. The effects of pipe geometry, processing capacity, and air inlet con-ditions are successively presented, followed by the prop-osition of guidelines for the design of efficient pneumatic dryers.

Figure 2. Profiles of air and starch properties along the drying pipe in the case of dryer TH-2. Solid and dashed lines refer to starch and air, respectively. (a), (b), and (c) illustrate the profiles of velocity, moisture content, and temperature, respectively.

402 A. CHAPUIS ET AL.

Effects of pipe geometry, dilution ratio, and proces-sing capacity The first result presented is the influence of pipe geometry, being as it is one of the main interests of this paper. The model was used to simulate variations in pipe diameter and assess the effect of this on the pipe length required to reach the target moisture content level and on the specific energy consumption of the dryer (using [Qs, Lpipe] ¼ f[D]). Under the default set-ting, the pipe diameter was varied from 0.145 to 0.23 m, which resulted in a variation of the starch dilution ratio ( _mda= _mds) from 9.6 to 24.2. The results are presented in Fig. 3. Figure 3a meanwhile gives the energy consumption and the pipe length as a function of the dilution ratio, and Fig. 3b gives the particle resi-dence time as a function of pipe length.

As expected, when increasing starch dilution, the pipe length required for drying decreased, while the energy consumption increased linearly. The lowest

energy consumption achieved was 3,250 kJ kg� 1 using a pipe length of 36 m (providing a residence time of 3.2 s) and a dilution ratio of 9.6. A long pipe provided for a longer residence time, allowing the starch to dry with a limited air mass flow. In such conditions, the air reached the dryer outlet close to adiabatic saturation, so the energy available in the form of sensible heat was fully utilized. This clearly highlights the trade-off between pipe length and energy consumption. Accord-ing to Fig. 3a, under default settings, the pipe should be at least 25 m long (together with a dilution ratio of 11 or less) to ensure a specific energy consumption lower than 4,000 kJ kg� 1. This length corresponds to a residence time of 2.2 s. For shorter pipes, the energy consumption increases sharply. Note that this trade-off partly deter-mines the economic compromise between capital and operating costs; nevertheless, as it also depends on sev-eral local factors, such as the prices of energy and raw materials, it was not included in the present study.

This result explains the difficulties faced by starch manufacturers trying to set up small capacity dryers. In most attempts here, the pipe length used was shorter than 15 m and the air velocity was in the range of 15–25 m s� 1. However, Fig. 3a clearly shows that under these conditions, the specific energy consumption can-not be below 6,000–7,000 kJ kg� 1 at best. In contrast, in most industrial dryers, the same air velocity range is used but with pipes longer than 40 m, which explains why they achieve good energy efficiency.

Moreover, although this is not presented in the fig-ures, another consequence of using shorter pipes with a high dilution is that the temperature of the starch tends to rise, which may alter its quality. As an illus-tration, under the default configuration, the dilution ratio had to be kept lower than 13, to keep the maximum temperature reached by the starch below 70°C. Although the predicted starch temperature was approximate (due to the assumptions on heat transfer), this result explains the gelatinization problems reported by small-scale starch producers.

Accordingly, using longer pipes is crucial, to ensure both the energy efficiency of the dryers and the quality of the product. It provides for a longer residence time, allowing the starch to dry while using a limited air flow (or dilution) and while keeping the temperature of the starch low. The dilution ratio is physically limited by the quantity of water that the drying air can take up until saturation. In theory, the minimum air mass flow rate may be evaluated by considering that, at best, the drying air undergoes an adiabatic moistening up to saturation.[35] In the present case, for instance, the adia-batic dilution ratio was 8.13, while the lowest value reached in the simulation was 9.6, i.e., 18% higher.

Figure 3. Results of numerical simulation obtained by varying pipe diameter with all other variables set to default values. It illustrates the effect of pipe geometry: (a) presents the pipe length at which the starch moisture meets the target and the specific energy consumption as a function of dilution ratio, while (b) shows the particle residence as a function of pipe length.

DRYING TECHNOLOGY 403

Eventually, another important finding is that processing capacity had almost no influence on dryer performance. Simulations were run using starch feed rates ranging from 0.02 to 2 kg s� 1, and the results obtained were almost identical, though with a very small advantage for high-capacity dryers in terms of energy consumption when at the higher end of pipe length. The consequence of this result is that it seems the design rules are the same for small- and high-capacity dryers. Therefore, the results shown in Fig. 3 are valid for any processing capacity and the same applies to all simula-tion results presented in the following sections.

Effect of inlet air velocity Having analyzed the influence of geometry, the results of the simulations are presented as 2-axis graphs, show-ing Qs against Lpipe. So, the value of the pipe diameter is not displayed (though it decreased with increasing pipe length). This approach helps simplify the illustration of the results, presenting them as Pareto fronts.

Figure 4 illustrates the results of the simulations run for three different inlet air velocities. Note that the case 15 m s� 1 corresponds to the default configuration, already presented in the previous section. The inlet air velocity appears to have had a strong effect on the required pipe length and the energy consumption. In particular, increasing the air velocity increased the spe-cific energy consumption for the same pipe length. This effect was particularly pronounced for short pipes but weakened rapidly for longer pipes. This can be explained by the fact that air velocity directly affects residence time, thus, the pipe length required to dry a given amount of starch increases with increasing air velocity.

As an illustration, consider a 15-m-long dryer. Using an air velocity of 10 m s� 1, it would be possible to dry

the starch to the target moisture content with an energy consumption of about 4,000 kJ kg� 1, but this would use about 7,000 kJ kg� 1 at 15 m s� 1, and would not even be possible at 20 m s� 1. However, for dryers longer than 30 m, these gaps are largely reduced. Indeed, in longer dryers, the starch and air come closer to thermodyn-amic equilibrium and the drying rate is low in the last section of the pipe, making them less sensitive to velocity changes.

Effects of air temperature Using the same method as for air velocity, the influence of air temperature was analyzed, with the results pre-sented in Fig. 5. Simulations were conducted for three temperature levels: 140, 160, and 180°C. The results clearly show the strong effect of this parameter; at a fixed pipe length and feed rate, a higher air temperature allows the starch to be dried using a smaller air mass flow (i.e., using a pipe of smaller diameter), resulting in higher energy efficiency. This effect results from the intensification of mass transfer at high temperatures. Increasing the air temperature also increases the particle temperature, which has mostly two effects: (i) increasing the diffusivity of water in starch and (ii) displacing the sorption by reducing the water activity at the surface of starch particles. Thereby, both the diffusivity and the concentration gradient are increased. As for air velocity, and for the same reasons, the effect is less pronounced for dryers with longer pipes.

Increasing the air temperature may be an efficient way to limit a dryer’s energy consumption, but to a lim-ited extent, since gelatinization problems may arise if the particle temperature exceeds 60°C during a long period of time. For instance, in the simulation of dryer TH-2 presented in Fig. 2, the starch reached a maximum temperature of 62.5°C for an inlet

Figure 4. Effect of inlet air velocity on the required pipe length and the specific energy consumption.

Figure 5. Effect of inlet air temperature on the required pipe length and the specific energy consumption.

404 A. CHAPUIS ET AL.

temperature of 175°C. Moreover, the air temperature is not the only factor; the starch temperature is also con-ditioned by the dilution ratio. For this reason, the air temperature should be carefully monitored and high temperatures should be avoided where the drying pipe is short and the dilution is high.

Effects of particle diameter Finally, the effects of particle diameter were analyzed, for diameters ranging from 210 to 270 µm, with the results of this analysis presented in Fig. 6. The effect seen was very similar to that of air temperature and velocity, that is, the smaller the particles, the faster the drying rate. However, unlike air velocity and tempera-ture, particle size is difficult to control. On this, it is essential to use a good feeding system that enables the proper disaggregation of the starch cake when it enters the drying pipe; otherwise, the only way to overcome the slow drying of large particles is to use a dryer with a long pipe.

Given the very small size and relatively low density of starch particles, the effect of particle size on residence time in the study was negligible. Within the range of diameters considered here, the particles were all entrained by the airflow with a slip velocity of the order of 1 m s� 1. Moreover, it was also observed that the par-ticle size had no influence on the temperature taken by the particles at equivalent air mass flow rates (or dilutions). Actually, the higher energy flux (per unit volume) received by small particles was compensated for by the higher drying rates resulting from faster diffusion, thus maintaining particle temperature.

General design guidelines In this section, we synthesize the observations made from the previous results to provide general guidelines

for the design of energy-efficient flash dryers. The first step is to choose the lowest acceptable air velocity. Among the industrial dryers considered in this work, dryer PA-2 used the lowest inlet air velocity, at 10 m s� 1. However, this dryer also used a pipe restric-tion 10 m after the feed point to raise the air velocity above 8 m s� 1, suggesting that lower velocities might have caused entrainment issues. Thus, if lower air velo-cities are to be used, experimental trials should be conducted to determine the threshold value. Anyway, according to Fig. 3, by applying an air velocity of 10 m s� 1, energy-efficient dryers may be designed with relatively short pipes (3,350 kJ kg� 1 at 20 m).

For air temperature, the maximum allowable tem-perature that should be used for cassava starch, in light of the constraints imposed by product quality require-ments, is 180°C, since a temperature over this may heat the starch particles over 60°C and cause gelatinization. However, it should also be noted that the use of a tem-perature lower than 140°C considerably increases the drying time, meaning a long pipe will be required to achieve reasonable energy efficiency levels. Another factor that needs to be considered when choosing the operating temperature is the gap between the inlet and target moisture content of the starch. If this gap is large, high temperatures should be used.

Finally, the pipe diameter and length have to be defined. At this point, the question of the investment cost required may be important, especially for small- scale dryers. As for most industrial equipment, economies of scale arise when increasing the capacity. For large-capacity dryers, long pipes may be easily affordable, enabling high energy efficiency levels (and thus low operating costs) and providing greater oper-ational flexibility. On the other hand, for small-capacity dryers, the investment costs may limit the possibility of using very long pipes. Whatever the case, it is not advis-able to build dryer pipes shorter than 20–25 m, as this requires the use of inappropriately high dilution, some-thing that will likely cause gelatinization issues and lead to low energy efficiency levels.

As a result, choosing the right diameter implies choosing the correct dilution ratio. The most con-venient way to do this would be to use the model presented here to estimate the dilution. Without a model available, this has to be estimated based on the theoretical minimum, i.e., the mass flow rate that would produce adiabatically saturated exhaust air. This pro-vides the lower bound for the dilution ratio, which then has to be increased by 15–50% depending on the chosen pipe length and temperature. If the chosen diameter is too low, the dryer will not reach the desired processing capacity, whereas if it is too large, it will be necessary to

Figure 6. Effect of particle size on the required pipe length and the specific energy consumption.

DRYING TECHNOLOGY 405

reduce either the air velocity (if possible) or the air tem-perature, to avoid overdrying the starch. Therefore, in case of doubt, it is preferable to slightly oversize the diameter.

One design possibility not investigated in the model is the use of a drying pipe with a variable diameter, to improve control over the drying and energy perfor-mance of the dryer and ultimately improve the pro-duct’s quality. This technique is already being used with industrial dryers such as the TH-2 and PA-2 mod-els presented in Table 1, and with the Thermo Venturi Dryers made by Mitchell Dryers Ltd (Carlisle, Cumbria, UK). Using this design, the drying material is fed into a venturi section at a high air velocity, as this ensures a good dispersion of the solids and helps break up larger particles. Then, the pipe’s diameter is progressively enlarged to decrease the air velocity and provide a suitable residence time.

Conclusion

In this study, a one-dimensional model was developed to describe the drying of particles in a pneumatic con-veying dryer using a water-diffusion-driven mechanism. The study model was successfully applied to a cassava starch dryer, to calculate the velocity, moisture content, and temperature profiles of the particles and drying air passing along a dryer’s tube, under steady-state oper-ation. Simulations were then run using field data taken from five industrial starch dryers and using particle diameter as a fitting parameter. Fitted diameters in the range 210–245 µm were used.

The model’s outputs were consistent with the field data in terms of product moisture content and exhaust air temperature levels. The predicted drying profiles were relevant in terms of physical meaning and thus provided a good understanding of the drying process, though further experimental trials will be necessary to confirm their validity.

Then, a numerical analysis method based on a series of simulations was conducted to provide guidelines for the design of small-scale flash dryers. The results show that there is a marked trade-off between dryer length and energy consumption. The effects of pipe geometry, air inlet conditions, and particle diameter were also assessed, and it was found that the scale (capacity) has a negligible effect on energy efficiency. The residence time, which is mostly determined by the pipe length and the air velocity, clearly appeared as the most influ-ential factor and should be systematically maximized. The use of drying pipes longer than 25 m allows one to dry the starch while using a limited air mass flow rate (i.e., low dilution ratio), which is crucial to ensure

(i) good energy efficiency levels and (ii) that the product temperature is kept low, so preserving its quality. Finally, air temperature should be set to the maximum allowed in light of product quality constraints, as it improves the energy efficiency of the dryer. The results of these simulations provide a greater insight into the starch drying mechanisms that take place within pneu-matic dryers. Despite numerous interactions, in this study, the relative influence of different design variables was clarified and general design guidelines proposed.

Acknowledgments

We would like to thank members of the SEPO Research Group, and in particular, Pr Warinthorn Songkasiri and Dr Kanchana Saengchan from King Mongkut University of Technology in Thonburi, Thailand, for their helpful discussions about the results.

Funding

This work received support from the CGIAR Research Program on Roots, Tubers and Bananas.

Nomenclature

Ap particle surface (m2) A0p projected area of a particle (m2) C volume concentration of water (kg m� 3) Cp heat capacity (J kg� 1 K� 1) CD drag coefficient (-) d particle diameter (m) D pipe diameter (m) Dws diffusivity of water in starch (m2 s� 1) e void fraction of the bed of particles (-) f coefficient of friction with the pipe wall (-) g acceleration of gravity (m s� 2) h convection coefficient [or specific enthalpy

(J kg� 1) where specified] (W m� 2 K� 1) Ls net isosteric heat of desorption of water from

starch (J kg� 1) Lpipe total length of the drying pipe (m) _m mass flow rate (kg s� 1)

pv water vapor pressure (Pa) psat saturation vapor pressure of water (Pa) _q heat flux from the air to the particle

(W m� 2) _Qloss heat loss through the pipe wall per meter of

pipe (W m� 1) Qs specific heat consumption (kJ kg� 1 of w) r radial position within a particle (m) ρ density (kg m� 3) S section of the drying pipe (m2) t time (s)

406 A. CHAPUIS ET AL.

T temperature (K) u velocity (m s� 1) Vp volume of a particle (m3) _w water mass flux from particle to air, called

drying rate (kg m� 2 s� 1) X particle moisture content on dry basis (d.b.)

(kg kg� 1 ds) Y air moisture content on d.b. (kg kg� 1 da)

Indices and subscript a moist air da dry air ds dry starch particle i initial state (dryer inlet) f final state (dryer outlet) p wet starch particles v water vapor w liquid water

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