- Email: [email protected]
A thermomechanical approach to pasta extrusion
Journal of Food Engineering 26 ( 1995) 35 1- 368 Copyright 0 1995 Elsevier Science Limited Printed in Great Britain. All rights reserved 0260.8774/95/$9.50 0260.8774(94)00060-3
A Thermomechanical
Approach to Pasta Extrusion
D. Le Roux, B. Vergnes” CEMEF,
Ecole des Mines de Paris, BP 207, 06904 Sophia-Antipolis
M. Chaurand INRA, Laboratoire
(Received
de Technologie
Cedex, France
& J. Abkcassis
des Ctrt?ales, 2, Place Viala, 34060 Montpellier Cedex 1, France
23 March 1994; revised version received 20 August 1994; accepted 4 October 1994)
ABSTRACT Pasta products are traditionally made by extruding hydrated semolina at low temperature in a screw press. A previous experimental study on a fully-instrumented press has determined the influence of various process variables (hydration, control temperature and screw speed) on flow parameters, such as energy, pressure and temperature, and on pasta quality In the present study, the hydrated durum wheat semolina was characterized by the determination of friction coefficients and compressibility curves, and by capillary rheological measurements. Flow in the screw press and in the die was modelled by adapting the classical theory of single-screw extrusion for synthetic polymers. To account for the specific screw geometry (deep and curved channel), an approximate analytical model was developed and validated by experiment.
NOTATION CP
D E/R
f
h’
Heat capacity (J/kg “C) Capillary diameter (m) Activation energy (K) Barrel friction coefficient Screw friction coefficient Heat transfer coefficient (W/m* “C)
*To whom correspondence
should be addressed. 351
352
D. Le Roux et al.
Channel depth (m) Consistency (Pa sm) Capillary length (m) Power law index Hydration level (% d.b.) Pressure (Pa) Pressure on the previous slab (Pa) Mass flow rate (kg/h) Volumetric flow rate (m3/s) Capillary radius (m) Specific mechanical energy (kJ/kg) Temperature on the previous slab Barrel control temperature Linear velocity of the barrel (m/s) Channel width (m) Viscous dissipation (W/m”) ^j P1 AP
AT AZ VI P ;
Shear rate (s-l) Flight angle at the barrel Increase of pressure (Pa) Increase of temperature (“C) Slab thickness (Cartesian coordinates) Viscosity (Pa 9 Density (kg/m ) Shear stress (N/m2) Solid conveying angle
INTRODUCTION Continuous industrial extrusion of pasta developed after the second world war (Feillet, 1986). Recent progress in drying techniques using high (Pavan, 1979) and very high (Frances & Ollivier, 1986) temperatures has considerably increased the capacity of the production lines, which are now often limited by the screw press performance. The maximum output of commercial presses is usually around 2.5 tons/h. The literature on pasta extrusion is limited and mainly focused on the quality of the final products (Renaudin, 1951; Walsh et al., 1971; Menger, 1977; Medvedev et al., 1984) and on the physicochemical changes experienced by the components (mainly proteins) during the process (Dexter & Matsuo, 1977; Matsuo et al., 1978; Wasik, 1978; Medvedev et al., 1987; Pagani et al., 1989). Very little attention has been paid to the process itself. Studies on single screw extrusion are often restricted to extrusion cooking (Mercier et al., 1989; Kokini et al., 1992) and the governing mechanisms along the screw for pasta extrusion are poorly understood. Abecassis et al. (1994) recently developed an experimental study on a fully instrumented laboratory screw press. They have shown how temperature, hydration and residence time modify the cooking quality of pasta. The present study intends to develop this approach, by proposing a thermomechanical model of the pasta extrusion process, able to describe the
A thermomechanical approach to pasta extrusiorl
353
changes in the main flow variables (pressure, temperature, shear rate) along the screw. Such a model, validated through the previous experimental study, improves the understanding of the process and helps to optimize screw design and operating conditions to obtain the best product quality.
EXPERIMENTAL
STUDY OF PASTA EXTRUSION
Experimental devices All experiments were conducted on a special laboratory screw press, designed by the AFREM company (Lyon, France) and described in detail by AbCcassis et al. (1994). The layout of the press is given in Fig. 1. The screw had constant channel depth and pitch. The main geometrical dimensions were: barrel diameter, 48.5 mm, screw diameter, 265 mm, screw pitch, 30 mm, channel width, 25 mm. Two zones with interrupted flights were situated near the screw tip. A special module called ‘trefilette’ (a removable helical part) was attached to the screw tip to stabilize the rotating flow before entering the die. The temperature of the barrel was controlled by circulation of water. A spaghetti die was used, with 112 teflon-coated capillaries of diameter 1.65 mm. Pressure and temperature transducers were mounted at 12 positions along the barrel. Motor-torque was measured to examine the energy balance. Energy, flow rate and pressure measurements The specific mechanical energy (SME) imparted to the dough was in the range -27-122 kJ/kg, depending on processing conditions. These values are typical for pasta extrusion (Harper, 1978) and are much lower than those measured on a twin-screw extrusion cooker (300-900 kJ/kg, Della Valle et al., 1989). This is because the temperature is lower and there is no starch transformation during the pasta extrusion process.
TREFILETTE P
I
I
,
I
IA
m
PRE-DIE
I Fig. 1.
Laboratory
screw press and spaghetti die used in the experiments.
D. Le Roux et al.
354
The mass flow rate varied between 15 and 37 kg/h and was directly speed (15-30 rev/mm). Pressure proportional to the screw rotation increased regularly along the screw, with a maximum value at the end, between 3 and 18 MPa. In some cases, mainly in the absence of the pre-die (see Fig. l), the head pressure was too low to completely fill the screw channel. Temperature measurements The product temperature measured at the die exit varied between 41 and 71°C and seemed mainly controlled by the regulated temperature of the barrel (respectively 35 and 70°C). There appeared to be little viscous dissipation due to the shearing of the viscous dough, even at high screw speed (30 revimin). Product viscosity The main variables affecting cooking quality were temperature, semolina at low hydration and screw speed. The best quality was obtained temperature, high hydration and high rotation speed. These parameters are directly connected to the dough viscosity, which thus seems to play an important role in the process.
PHYSICAL
CHARACTERIZATION
OF HYDRATED
SEMOLINA
Commercial durum wheat semolina was used for the extrusion experiments. The semolina was mixed at 30°C with water for the required levels of hydration (44 and 48% on dry basis) for 20 min. After mixing, hydrated semolina appeared as a weakly aggregated powder. Passing through the screw, this mixture was subjected to pressure and temperature and changed to a homogeneous dough, flowing like a viscous fluid. It is thus necessary to characterize the product properties in these two different states (heterogeneous powder and homogeneous dough) and moreover to define the transition from one state to the other. Hydrated semolina powder was characterized by friction and compressibility measurements. The viscous behaviour of the dough was studied by capillary rheometry. Friction measurements The conveying of a solid powder in an extruder results directly from the friction forces between the solid bed, the screw and the barrel surfaces (Darnell & Mol, 1956). Friction coefficients between a metallic surface and compacted hydrated semolina were measured using a specific rotating cell, similar to the classical Jenike system (Peiti & Vergnes, 1989). The torque necessary to rotate the cell at a given speed was measured as a function of the pressure applied to the cell. The friction coefficient was defined as the ratio of shear stress (deduced from the torque) to the pressure. Experiments were carried out at ambient temperature for the two levels of hydration
A thermomechanical
0 Fig. 2.
1
Friction experiment:
variation
hydration
355
approach to pasta extrusion
2
3 4 PRESSURE (MPa)
in shear stress with levels (0, 44%; l, 48%).
pressure
for
two
used in the experimental design (44 and 48% d.b.). Results are presented in Fig. 2. Two distinct curves were obtained, depending on the hydration. On each curve, three successive zones can be observed. At low pressure, when the product was not yet compacted, the evolution of the shear stress r was linear and the friction followed approximately a Coulomb law: r = fP. The friction coefficients f were equal to 0.19 and 0.36, for hydrations of 44 and 48%, respectively. These values are comparable to those cited by Della Valle and Vergnes (1994) on wheat starch and wheat flour. An effect of hydration on friction coefficients was also observed by these authors. For pressures between 1 and 1.5 MPa, the shear stress increased rapidly and its variation was no longer linear. At higher pressures (above 2 MPa), the stress tends to stabilize at maximum values of O-5 and 0.7 MPa, respectively. The product was then highly compacted and tended to flow much more like a fluid than a solid. From these preliminary results, it can be assumed that the transition pressure between powder and dough is probably between 1.5 and 2 MPa. Compressibility
measurements
Hydrated semolina was placed in a cylindrical compression chamber (diameter 8.75 cm; length 14 cm). The descent of a piston at a constant speed (4 mm/s) induced an increase in pressure, measured by a stress load cell seated under the system. The piston displacement was used to compute the volume and thus to quantify the change in product density with the pressure. A typical result is presented in Fig. 3. In semi-logarithmic coordinates, a classical shape with two distinct areas (Tharrault & Launay, 1990) can be observed. Under l-2 MPa, the density of the hydrated semolina increased rapidly, from apparent values of 0.94 and 1.09 at 44 and 48%, respectively, up to 1.25. Above l-2 MPa, the increase was linear, identical for both hydration levels, and led to a limiting value of 1.31. The first zone is usually connected to particle rearrangement, and the second
D. Le Roux et al.
356
OJ
8
1
Fig. 3.
1
10 PRESSURE (MPa) Compressibility measurement: variation in density with pressure for two hydration levels (0, 44%; l, 48%).
one to particle deformation. The compressibility the definition of Ehlerman and Schubert (1987): P (P>= Pm&
b may be calculated
from
+b 1ogP)
Values obtained were a = 0.92 and b = 4.4 x lo-‘. This order of magnitude is consistent with the previous work of Barbosa Canovas et al. (1987) on various products. in behaviour appeared around 2 MPa, Once again, a change corresponding here to a highly compacted material. Therefore. the assumption &as made that Ihe- transition between powdery hydrated semolina and homogeneous dough occurred in the screw when the local pressure was higher than a characteristic value of 2 MPa. Rheological measurements Dough is a viscoelastic system, exhibiting complex rheological behaviour. However, for engineering computations, it is necessary to restrict it to a more simple purely viscous behaviour. In fact, elastic effects can be neglected because shearing flows are dominant through the screw channel and the die (except in converging sections). For these reasons, the behaviour of a semolina/water dough system was characterized on a capillary rheometer with pre-shearing, previously used for studying the rheology of molten starches (Vergnes & Villemaire, 1987). This rheometer comprises an annular shearing chamber, in series with a classical capillary system. A controlled mechanical treatment was imposed on the product through the rotation of the inner piston (in this case, 100 rev/min for 60 s) before the rheological measurement, to homogenize the material. Different levels of hydration (40, 44 and 48%, d.b.) and temperature (35, 55 and 70°C) were studied. First of all, the difficulty in obtaining reliable measurements must bc stressed. In some cases, flow instabilities due to heterogeneous hydration pressure oscillations or slip at the capillary wall made it impossible to obtain
A thermomechanical
approach to pasta extrusion
357
satisfactory results. These problems were exacerbated at high pressure or high shear rate. To avoid these difficulties, capillaries were selected with a large diameter (0=3 mm) and short length (L=25 mm). The entrance pressure corrections were made using an orifice die (0=3 mm, L /D=O). Examples of viscosity curves are presented in Fig. 4, showing the influence of temperature. Despite a small scatter of the data, the viscous behaviour can be reasonably described by a classical power law: (2)
~=Klj*‘+’
From viscosity curves at different temperatures, it is classical to obtain a mastercurve by applying the principle of time-temperature unique superposition, if no structural change or reaction occurs in the product. The same principle applies also for time-hydration superposition (Vergnes et al., 1993). Using the data at low temperatures (35 and 55°C) it was shown that power law behaviour remained valid over a wide range of shear rates, typically O-l-1000 ss’, which covers the entire range expected in extrusion (Fig. 5). The power law index, m, increased slightly with hydration, but remained in the range 0.4-0.5. The consistency, K, varied with hydration and temperature, according to exponential laws. Above 55°C it was observed that the influence of hydration decreased. For the temperature an unusual dependence was observed at 70°C perhaps due to the heat denaturation of gluten. In the usual range of extrusion temperatures (35-55°C) the following expression for K correlated well with experiment:
K=Ko exp( -c&f)
exp(E/RT)
(3)
where EIR=4330 K, Ko=3.1x 10’ Pa s”‘, (x=22.3 and M is the normalized hydration. Equation (3) predicts the viscous behaviour of the hydrated semolina used in the experiments with a precision of _t 15%. These results are similar to those obtained by Nazarov et al. (1971) on durum wheat semolina hydrated at 43%.
SHEAR RATE (s-l) Fig. 4.
Viscosity measurement: influence of temperature on viscosity at 40% hydration (m, 35°C; (1,55°C; l , 70°C).
3.58
SHEAR RATE (s-l)
Fig. 5.
Mastercurve of viscosity at 55°C and 44% hydration obtained
at 40%, 44%, 48% and 3.X,
(superposition 55°C).
of data
This power law model predicts an infinite viscosity at zero shear rate. In fact, this is not a problem when computing global pressure/flow rate relationships and this very simple law is largely sufficient for describing the flow that is considered. Another specific experiment was carried out to simulate the flow in the final part of the spaghetti die, where teflon inserts were used to improve the surface smoothness of the product. A capillary was machined in a Teflon block, with dimensions identical to the usual carbide capillary. The results are shown in Fig. 6. There was a ratio of about three between the pressures measured with carbide or teflon capillaries, which demonstrated a drastic change in boundary conditions. Through the Teflon inserts, the semolina dough slips at the wall, with global flow conditions close to a plug flow. By comparing the flow rate at constant pressure drop, it was estimated that the slip velocity was about 96% of the mean product velocity. Despite some experimental difficulties and even if these experiments have yet to be completed, they were largely sufficient for describing the flow in the present work. FLOW COMPUTATION Theoretical approaches to pasta extrusion are rather limited in the literature. However, the single screw extrusion of synthetic polymers has been studied for more than 30 years. Readers are referred to the well known books of Tadmor and Klein (1970) or Rauwendaal (1986), for example. In the present work, a classical continuum mechanics approach is applied to the specific behaviour of hydrated semolina.
A thermomechanical
approach to pasta extrusion
#P--P 0
Fig. 6. Variation
0
in pressure
0.01
-a-
359
p--------n 0.03 0.02 FLOW RATE (cmYs)
with flow rate (5o”C, 48%) for capillaries (0) and Teflon (3).
in carbide
General assumptions A slab method is generally used to study flows along an extrusion screw channel. The cross-section, perpendicular to the channel axis, is approximated by a rectangular surface. The screw is assumed to be fixed and the barrel to rotate around the screw, in order to obtain a stationary geometry. The screw channel is totally filled and the material properties (density, viscosity, thermal conductivity and heat capacity) are constant in each slab. Thus, the velocity and temperature field are locally independent of the longitudinal coordinate. By solving the mechanical and thermal balance on a given slab, the local increases in pressure AP and temperature AT are obtained. By computing from one slab to the next, the global evolution of the parameters along the screw are determined. Powder conveying section The transport of hydrated semolina as powder in the feeding zone is comparable to the conveying of polymer powder. The model derived by Darnell and Mol (1956) and improved by Tadmor and Klein (1970) can then be used without modification. The balance of pressure and friction forces on the solid determines the increase in pressure AP on a slab thickness AZ: (4) where PO is the pressure in the preceding slab, H and W are the channel dimensions, f, and f2 are the friction coefficients on the barrel and screw, respectively, 7, is the helix angle and b, is the solid conveying angle, defined
D. Le Roux et al.
360
by the volumetric
flow rate QV: sin yl Qv=U,,WH
cosy] tg(d+Yd
>
where U,, is the longitudinal component of barrel velocity. In fact, the barrel and screw friction coefficients are the key parameters which allow the hydrated semolina to be conveyed and compacted. For different values of screw friction coefficient, the minimal value of barrel friction coefficient necessary to build up the pressure at a given flow rate are presented in Fig. 7. Experimental values of friction coefficients between 0.2 and 0.4, corresponding to the screw (smooth surface) have been previously measured. It can be seen that, under these conditions, the barrel friction coefficient must be higher than O-5 to correctly convey the semolina. To obtain these high values, longitudinal grooves are machined along the barrel around its inner surface. For a screw friction coefficient of O-45, the powder conveying becomes very difficult (f, = 1). To take into account the presence of grooves along the barrel, a value of 1 for the barrel friction coefficient is chosen in the computation. Temperature changes in the powder conveying section are due to heat dissipation by friction against the barrel, which is then transmitted to the solid and to the regulation fluid. Computation of the temperature field (Le Roux, 1993) showed that the temperature rise was localized near the barrel wall and that the average temperature increase was about 5°C for a channel length of 10 cm, under typical experimental conditions (225 rev/min, 46% hydration). Dough flowing section Two different and successive approaches have been developed to model the dough flow in the screw channel. In a first step, a finite element software f 2 = 0.45
f 2 = 0.35
f 2 = 0.25
f2=
: 0.05
f2= = 0.02 f2=
NORMALIZED
:o
FLOW RATE 7. Minii num value of barrel friction coefficient f, as function of non m alin:ed A* I ,_ .a _ ,r, r-,r*\ r I.,-,I r . . . coernclenrJZ. PP 0 now rate Q - (IL -=y/u,,wn ), for amerent values orr screw rricnon
1Fig. n
361
A thermomechanical approach to pasta extrusion
was used to obtain a precise description of the local flow field in the real channel geometry. Then an approximate one-dimensional model able to describe the globality of the process was applied. The finite element software was previously applied to extrusion cooking longitudinal flow of a (Barr& & Vergnes, 1990). The two-dimensional power law fluid in the real geometry of the channel, in cylindrical coordinates, is considered. The velocity field corresponding to standard hydration 44%, experimental conditions (screw speed 20 rev/min, temperature WC, pressure gradient 12 MPalm) is given in Fig. 8. The velocity decreased monotonically from the barrel to the screw. No recirculating regions were observed under these conditions, but a large zone existed at the channel bottom, where the product moved very slowly (less than 10 mm/s, when the barrel velocity was 50 mm/s) and thus may induce a certain heterogeneity in the final product. Considering the product as isothermal, the finite element model can also be used to compute characteristic curves, i.e. relationships between flow rate and local pressure gradient l/K dPld0. During the experiments, the values of l/K dPld6 were between 1 and 3. Figure 9 shows that, at low values of power law index and for the screw design considered here, the flow rate is strongly dependent on pressure gradient. Finite element simulation is powerful, but necessitates large computer facilities and is not appropriate to the computation of a global process. To build a general software for pasta extrusion, it is more suitable to return to a simplified approach, based on a slab method as presented in the solid conveying section. However, this approximate model must take into account wall side effects and channel curvature. It has been proved, using the finite element method, that neglecting these effects could induce an error on flow rate higher than 50% (Le Roux, 1993). The basic idea is to start from the classical analytical solution of the flow of a power law fluid without wall side effects, and to modify this solution
0
IO
20
30
40
50
60
VELOCITY (mm/s) Fig. 8.
Velocity contours in the screw channel and corresponding velocity profile on the symmetry axis (evenly spread between 0 and 50 mm/s).
D.Le Roux et al.
362
20 25 30 35 MASS FLOW RATE (kg/h) Fig. 9.
gradient (l/K cP/dH) relationship for the reference screw (m, finite element simulation: q, approximate method).
Flow rate/pressure
through correction factors accounting for the wall. The correction factors are only dependent on the ratios W/R and W/H, defining the channel geometry. The details of the method can be found in Le Roux (1993) and will be published separately. Here the principles of the computation are just summarized. The analytical expressions of the flow rate are known in the following conditions: Q ,: Newtonian, without wall side effects, Q2: Newtonian, with wall side effects, Q3: power law, without wall side effects. For a given pressure gradient l/K dP/dO, the flow rate Q for a power law fluid with wall side effects will be defined by: Q (l/K dPldO) =
Q z( l/K dP/dO) Q ,(1/K @/de)
where the correction
Q,(l/KdPldB)+AQ
factor AQ is given by:
AQ = Qo-
Q dl/K dpoidtr) Q , (l/K dPold0)
Q.41K dP,ldB)
(7)
in v$iyh Q,, is only dependent on channel geometry and (l/K) (dP,,/dO) (UO/ is the pressure gradient corresponding to the flow rate Q0 for a H) Newtonian fluid with wall side effects. It can be seen in Fig. 9 that the results of this approximate method, in which all computations are analytic, are very close to those obtained by the finite element model. The mean temperature change was calculated by solving the thermal balance, including transport, convection and dissipation terms: pC,QvAT
= hWRZ(TR-
To) dO+ I@
(8)
A thetmomechanical
363
approach to pasta extrusion
where the viscous dissipation I$’ was estimated by assuming that the global energy provided to the dough was not affected by side effects, which was verified for a power law index, m, between 0.2 and 05. The screw was considered as adiabatic. The following values were chosen for the thermal calculations: heat transfer coefficient h = 300 W/m2 “C, heat capacity C, = 2 kJ/kg “C (Andrieu & Gonnet, 1989).
RESULTS
AND DISCUSSION
Flow along the screw Pressure and temperature evolution along the screw were computed for the flow rate measured at the central point (screw speed 20 rev/min, barrel temperature 40°C) of the experimental design (Abecassis et al., 1994) and three hydration levels (Fig. 10). Consistent with the rheological measurements, the pressure is lower at higher hydration levels because the viscosity decreases with hydration. In the conveying zone, the pressure increases very rapidly, until attaining 2 MPa where the dough is assumed to be fully compacted. This is achieved within 1-2 turns, depending on hydration level. Then, the pressure develops regularly, interrupted only by the screw portions without flights, along which the pressure slightly decreases. The ‘trefilette’ appears to increase pressure locally. Temperatures also change regularly, but are less dependent on hydration (Fig. 11). The temperature increase due to friction and heat transfer is important in the feeding zone, and is higher at 48% hydration because this zone is longer. In contrast, the temperature rise due to viscous dissipation is lower at 48%, because the viscosity is lower. These effects compensate and. finally, whatever the hydration, the exit values are around 53°C which is higher than the controlled barrel temperature (40°C).
‘0.0
0.1
0.2
POSITION
Fig. 10. Pressure
0.3
0.4
0.5
ALONG THE SCREW (m)
profiles along the screw for three (83,experimental values at 46% hydration).
hydration
levels
D.Le Rouxet al.
364 60
Barrel temperature
0
0.1
0.2
0.3
0.4
0.5
POSITION ALONG THE SCREW (m) Fig. 11.
Mean
temperature profiles along the screw for three ,46%. , ..,., 48%). (----, 44%; -
hydration
levels
The experimental pressure measurements at 46% hydration are also indicated in Fig. 10. The computed values are in good agreement with the experiments. More generally, the theoretical model has been applied to all points of the experimental design (with the pre-die), by imposing the experimental flow rates. For pressure, as well as for torque and temperature, the theoretical model gives a good estimation of the screw press behaviour, for a large range of processing conditions. Coupling screw and die Bows The preceding results have been obtained by imposing the flow rate in the screw flow model. In fact, the real flow rate results from the equilibrium between the screw and the die, under the given processing conditions (screw speed, thermal regulation). The whole die is composed of different elements (connecting pipe, predie and die, with teflon inserts), in which Poiseuille flows can be considered. In fact, in converging parts, elongational flow occurs, but, due to the lack of knowledge concerning the elongational behaviour of pasta dough, shearing flow conditions are assumed. Locally, on a given element, pressure losses thus depend on the viscous behaviour and flow rate through:
where L and R are the dimensions of the element. Figure 12 shows that the pressure drop through the die is correctly described only by taking into account slip conditions along the Teflon inserts. Otherwise, the pressure drop is largely overestimated by the computation.
A thermomechanical approach to pasta extrusion
365
MEASURED PRESSURE (MPa) Fig. 12.
Comparison between experimental and computed pressure drop through the spaghetti die (n, without slip conditions; n, with slip conditions).
Coupling screw and die flow leads to a predictive model of pasta extrusion. This model was applied to all the experimental design points (with the pre-die). Figure 13(a) shows that the flow rate is well predicted, with less than 10% error. Higher discrepancies are observed on the head pressure (Fig. 13(b)). Nevertheless, the results are satisfactory and sufficient to permit the use of the theoretical model for optimizing screw design and processing conditions.
CONCLUSION The thermomechanical approach of pasta extrusion presented in this paper gives a new perspective for the understanding of the process. A physical study of the hydrated semolina characterized the flow behaviour of both powder and dough states. A yield pressure of 2 MPa has been chosen as a transition point between these states. The viscous behaviour of the dough is described by a power law, with exponential dependencies on hydration and temperature. The flow along the screw channel was computed using finite element simulation and an approximate model, derived from classical analyses of plastics extrusion. General purpose software, incorporating the coupling between the screw and die, allowed accurate calculation of the evolution along the screw of the pressure, temperature, torque, dough viscosity, and flow rate for given processing conditions. Comparison with previous experiments on a laboratory screw press were satisfactory. New perspectives for optimizing screw geometry and press processing conditions now present themselves. The next step would be to correlate the
D.Le Roux et al.
366
40 a)
30
20
10
L
O_
10
0
MEASURED
20
30
20
I
40
FLOW RATE (kg/h)
I
,
b)
15
K)I
ca
10
o* / *
z
5
0 0
5
10
15
20
MEASURED PRESSURE (MPa) Fig. 13.
Comparison
between
experiments and computations: head pressure.
(a) flow rate; (b)
A thermomechanical
physical parameters quality.
involved
approach to pasta extrusion
in the process
367
with the final pasta cooking
ACKNOWLEDGEMENT This work was supported by a grant from MinistCre de la Recherche la Technologie, through the Aliment 2000 program.
et de
REFERENCES AbCcassis, J., Abbou,
R., Chaurand, M., Morel, M. H. & Vernoux, P. (1994). Influence of extrusion conditions on extrusion speed, temperature and pressure in the extruder and on pasta quality. Cereal Chem., 71, 247-53. Andrieu, J. & Gonnet, E. (1989). Thermal conductivity and diffusivity of extruded durum wheat pasta. Lehensm. Wk. u. Technol., 22, 6-10. Barbosa Canovas, G. V., Malave-Lopez, J. & Peleg, M. (1987). Density and compressibility of selected food powders mixtures. J. Food Proc. Engng, 10, l-10. Barr& C. & Vergnes, B. (1990). Recent developments in modelling twin screw extrusion cooking. In Processing and Quality of Foods, Vol. I, eds P. Zeuthen, J. C. Cheftel, C. Eriksson, T. R. Gormley, P. Linko & K. Paulus. Elsevier, London, pp. 257-62. Darnell, W. H. & MO], E. A. J. (1956). Solids conveying in extruders. SPE J., 12, 20-7. Della Valle, G. & Vergnes, B. (1994). Proprietts thermophysiques et rheologiques des substrats utilises en cuisson-extrusion. In La Cuisson-Extrusion, eds P. Colonna & G. Della Valle. Lavoisier, Paris, pp. 439-68. Della Valle, G., Kozlowski, A., Colonna, P. & Tayeb, J. (1989). Starch transformation estimated by the energy balance on a twin-screw extruder. Lebensm.
Wiss. u. Technol.. 22, 279-86.
Dexter, J. E. & Matsuo, R. R. (1977). Changes in semolina proteins during spaghetti processing. Cereal Chem .. 54, 882-94. Ehlermann, D. A. E. & Schubert, H. (1987). Compressibility characteristics of food powders by compression tests. In Physical Properties of Food, ed. R. Jowitt. Elsevier, London. Feillet, P. (1986). L’industrie des pates alimentaires: technologie de fabrication, qualite des produits finis et des matieres premieres. Ind. Agric. Alim ., 103, 979-89. Frances, Y. & Ollivier, J. L. (1986). L’utilisation des tres hautes temperatures pour le sechage des pates alimentaires. Ind. Agric. Alim., 5, 471-5. Harper, J. M. (1987). Extrusion processing of food. Food Technol., 32, 67-72. Kokini, J. L., Ho, C. T. & Karwe, M. V. (1992)._ Food Extrusion. Science and Technology. Marcel Dekker, New York. Le Roux, D. (1993). Etude experimentale et modelisation de l’extrusion des pates alimentaires. PhD Dissertation, Ecole des Mines de Paris. Matsuo, R. R., Dexter, J. E. & Dronzek, B. L. (1978). Scanning electron microscopy study of spaghetti processing. Cereal Chem ., 55, 744-53. Medvedev, G. M., Malandeeva, N. I., Argianova, 1. V. & Semko, V. T. (1984). Influenza della temperatura d’impasto sulle proprieta tisiche des semilavorato e sulla qualita delle paste alimentari. Tee. Molitoria, 35, 416-18. Medvedev, G. M., Malandeeva, N. I. & Kovalskaja, L. P. (1987). Variazioni delle proprieta dei componenti dell’impasto per pasta alimentare durante la sua termolavorazione. Tee. Molitoria, 38, 865-8.
368
D. Le Roux et al.
Menger, A. (1977). Influsso della materia prima e de1 procedimento sulla qualita della pasta alimentare. Tee. Molitotiu, 28, 83-90. Mercier, C., Linko, P. & Harper, J. M. (1989). Extrusion Cooking. AACC, St Paul, MN. Nazarov, N., Azarov, B. & Chaplin, M. (1971). Izvesttju Vyssikh Hchebnyck Zuvedenj, 2,149-Y51.
Pagani, M. A., Resmini, P. & Dalbon, G. (1989). Influence of the extrusion process on characteristics and structure of pasta. Food Microstract., 8, 173-82. Pavan, G. (1979). L’impiego dell’alta temperatura nel process0 di essicazione delle paste alimentari. Tee. Molitoriu, 30, 362-70. Peiti, C. & Vergnes, B. (1989). Mesure de coefficients de frottement de divers tchantillons de farine. Research Report, CEMEF, Ecole des Mines de Paris. Rauwendaal, C. (1986). Polymer Extrusion. Hanser, Munich. Renaudin, C. (1951). La Fabrication Industrielle des Pates Alimentuires. Dunod, Paris. Tadmor, Z. & Klein, I. (1970). Engineering Principles of Plusticating Extrusion. Van Nostrand, New York. Tharrault, J. F. & Launay, B. (1990). Compactage sous pression de farines de ble et de formules type pain plat. Ind. Agric. Alim., 6, 533-5. Vergnes, B. & Villemaire, J. P. (1987). Rheological behaviour of low moisture molten maize starch. Rheol. Acta, 26, 570-6. Vergnes, B., Della Valle, G. & Tayeb, J. (1993). A specific slit die rheometer for extruded starchy products. Design, validation and application to maize starch. Rheol. Acta, 32, 465-76.
Walsh, D. E., Ebeling, K. A. & Dick, J. W. (1971). A linear programming approach to spaghetti processing. Cereal Sci. Today, 16, 385-9. Wasik, R. J. (1978). Relationship of protein composition of durum wheat with pasta quality and the effects of processing and cooking on these proteins. Can. Inst. Food Sci. Technol., 11, 129-33.
A Thermomechanical
Approach to Pasta Extrusion
D. Le Roux, B. Vergnes” CEMEF,
Ecole des Mines de Paris, BP 207, 06904 Sophia-Antipolis
M. Chaurand INRA, Laboratoire
(Received
de Technologie
Cedex, France
& J. Abkcassis
des Ctrt?ales, 2, Place Viala, 34060 Montpellier Cedex 1, France
23 March 1994; revised version received 20 August 1994; accepted 4 October 1994)
ABSTRACT Pasta products are traditionally made by extruding hydrated semolina at low temperature in a screw press. A previous experimental study on a fully-instrumented press has determined the influence of various process variables (hydration, control temperature and screw speed) on flow parameters, such as energy, pressure and temperature, and on pasta quality In the present study, the hydrated durum wheat semolina was characterized by the determination of friction coefficients and compressibility curves, and by capillary rheological measurements. Flow in the screw press and in the die was modelled by adapting the classical theory of single-screw extrusion for synthetic polymers. To account for the specific screw geometry (deep and curved channel), an approximate analytical model was developed and validated by experiment.
NOTATION CP
D E/R
f
h’
Heat capacity (J/kg “C) Capillary diameter (m) Activation energy (K) Barrel friction coefficient Screw friction coefficient Heat transfer coefficient (W/m* “C)
*To whom correspondence
should be addressed. 351
352
D. Le Roux et al.
Channel depth (m) Consistency (Pa sm) Capillary length (m) Power law index Hydration level (% d.b.) Pressure (Pa) Pressure on the previous slab (Pa) Mass flow rate (kg/h) Volumetric flow rate (m3/s) Capillary radius (m) Specific mechanical energy (kJ/kg) Temperature on the previous slab Barrel control temperature Linear velocity of the barrel (m/s) Channel width (m) Viscous dissipation (W/m”) ^j P1 AP
AT AZ VI P ;
Shear rate (s-l) Flight angle at the barrel Increase of pressure (Pa) Increase of temperature (“C) Slab thickness (Cartesian coordinates) Viscosity (Pa 9 Density (kg/m ) Shear stress (N/m2) Solid conveying angle
INTRODUCTION Continuous industrial extrusion of pasta developed after the second world war (Feillet, 1986). Recent progress in drying techniques using high (Pavan, 1979) and very high (Frances & Ollivier, 1986) temperatures has considerably increased the capacity of the production lines, which are now often limited by the screw press performance. The maximum output of commercial presses is usually around 2.5 tons/h. The literature on pasta extrusion is limited and mainly focused on the quality of the final products (Renaudin, 1951; Walsh et al., 1971; Menger, 1977; Medvedev et al., 1984) and on the physicochemical changes experienced by the components (mainly proteins) during the process (Dexter & Matsuo, 1977; Matsuo et al., 1978; Wasik, 1978; Medvedev et al., 1987; Pagani et al., 1989). Very little attention has been paid to the process itself. Studies on single screw extrusion are often restricted to extrusion cooking (Mercier et al., 1989; Kokini et al., 1992) and the governing mechanisms along the screw for pasta extrusion are poorly understood. Abecassis et al. (1994) recently developed an experimental study on a fully instrumented laboratory screw press. They have shown how temperature, hydration and residence time modify the cooking quality of pasta. The present study intends to develop this approach, by proposing a thermomechanical model of the pasta extrusion process, able to describe the
A thermomechanical approach to pasta extrusiorl
353
changes in the main flow variables (pressure, temperature, shear rate) along the screw. Such a model, validated through the previous experimental study, improves the understanding of the process and helps to optimize screw design and operating conditions to obtain the best product quality.
EXPERIMENTAL
STUDY OF PASTA EXTRUSION
Experimental devices All experiments were conducted on a special laboratory screw press, designed by the AFREM company (Lyon, France) and described in detail by AbCcassis et al. (1994). The layout of the press is given in Fig. 1. The screw had constant channel depth and pitch. The main geometrical dimensions were: barrel diameter, 48.5 mm, screw diameter, 265 mm, screw pitch, 30 mm, channel width, 25 mm. Two zones with interrupted flights were situated near the screw tip. A special module called ‘trefilette’ (a removable helical part) was attached to the screw tip to stabilize the rotating flow before entering the die. The temperature of the barrel was controlled by circulation of water. A spaghetti die was used, with 112 teflon-coated capillaries of diameter 1.65 mm. Pressure and temperature transducers were mounted at 12 positions along the barrel. Motor-torque was measured to examine the energy balance. Energy, flow rate and pressure measurements The specific mechanical energy (SME) imparted to the dough was in the range -27-122 kJ/kg, depending on processing conditions. These values are typical for pasta extrusion (Harper, 1978) and are much lower than those measured on a twin-screw extrusion cooker (300-900 kJ/kg, Della Valle et al., 1989). This is because the temperature is lower and there is no starch transformation during the pasta extrusion process.
TREFILETTE P
I
I
,
I
IA
m
PRE-DIE
I Fig. 1.
Laboratory
screw press and spaghetti die used in the experiments.
D. Le Roux et al.
354
The mass flow rate varied between 15 and 37 kg/h and was directly speed (15-30 rev/mm). Pressure proportional to the screw rotation increased regularly along the screw, with a maximum value at the end, between 3 and 18 MPa. In some cases, mainly in the absence of the pre-die (see Fig. l), the head pressure was too low to completely fill the screw channel. Temperature measurements The product temperature measured at the die exit varied between 41 and 71°C and seemed mainly controlled by the regulated temperature of the barrel (respectively 35 and 70°C). There appeared to be little viscous dissipation due to the shearing of the viscous dough, even at high screw speed (30 revimin). Product viscosity The main variables affecting cooking quality were temperature, semolina at low hydration and screw speed. The best quality was obtained temperature, high hydration and high rotation speed. These parameters are directly connected to the dough viscosity, which thus seems to play an important role in the process.
PHYSICAL
CHARACTERIZATION
OF HYDRATED
SEMOLINA
Commercial durum wheat semolina was used for the extrusion experiments. The semolina was mixed at 30°C with water for the required levels of hydration (44 and 48% on dry basis) for 20 min. After mixing, hydrated semolina appeared as a weakly aggregated powder. Passing through the screw, this mixture was subjected to pressure and temperature and changed to a homogeneous dough, flowing like a viscous fluid. It is thus necessary to characterize the product properties in these two different states (heterogeneous powder and homogeneous dough) and moreover to define the transition from one state to the other. Hydrated semolina powder was characterized by friction and compressibility measurements. The viscous behaviour of the dough was studied by capillary rheometry. Friction measurements The conveying of a solid powder in an extruder results directly from the friction forces between the solid bed, the screw and the barrel surfaces (Darnell & Mol, 1956). Friction coefficients between a metallic surface and compacted hydrated semolina were measured using a specific rotating cell, similar to the classical Jenike system (Peiti & Vergnes, 1989). The torque necessary to rotate the cell at a given speed was measured as a function of the pressure applied to the cell. The friction coefficient was defined as the ratio of shear stress (deduced from the torque) to the pressure. Experiments were carried out at ambient temperature for the two levels of hydration
A thermomechanical
0 Fig. 2.
1
Friction experiment:
variation
hydration
355
approach to pasta extrusion
2
3 4 PRESSURE (MPa)
in shear stress with levels (0, 44%; l, 48%).
pressure
for
two
used in the experimental design (44 and 48% d.b.). Results are presented in Fig. 2. Two distinct curves were obtained, depending on the hydration. On each curve, three successive zones can be observed. At low pressure, when the product was not yet compacted, the evolution of the shear stress r was linear and the friction followed approximately a Coulomb law: r = fP. The friction coefficients f were equal to 0.19 and 0.36, for hydrations of 44 and 48%, respectively. These values are comparable to those cited by Della Valle and Vergnes (1994) on wheat starch and wheat flour. An effect of hydration on friction coefficients was also observed by these authors. For pressures between 1 and 1.5 MPa, the shear stress increased rapidly and its variation was no longer linear. At higher pressures (above 2 MPa), the stress tends to stabilize at maximum values of O-5 and 0.7 MPa, respectively. The product was then highly compacted and tended to flow much more like a fluid than a solid. From these preliminary results, it can be assumed that the transition pressure between powder and dough is probably between 1.5 and 2 MPa. Compressibility
measurements
Hydrated semolina was placed in a cylindrical compression chamber (diameter 8.75 cm; length 14 cm). The descent of a piston at a constant speed (4 mm/s) induced an increase in pressure, measured by a stress load cell seated under the system. The piston displacement was used to compute the volume and thus to quantify the change in product density with the pressure. A typical result is presented in Fig. 3. In semi-logarithmic coordinates, a classical shape with two distinct areas (Tharrault & Launay, 1990) can be observed. Under l-2 MPa, the density of the hydrated semolina increased rapidly, from apparent values of 0.94 and 1.09 at 44 and 48%, respectively, up to 1.25. Above l-2 MPa, the increase was linear, identical for both hydration levels, and led to a limiting value of 1.31. The first zone is usually connected to particle rearrangement, and the second
D. Le Roux et al.
356
OJ
8
1
Fig. 3.
1
10 PRESSURE (MPa) Compressibility measurement: variation in density with pressure for two hydration levels (0, 44%; l, 48%).
one to particle deformation. The compressibility the definition of Ehlerman and Schubert (1987): P (P>= Pm&
b may be calculated
from
+b 1ogP)
Values obtained were a = 0.92 and b = 4.4 x lo-‘. This order of magnitude is consistent with the previous work of Barbosa Canovas et al. (1987) on various products. in behaviour appeared around 2 MPa, Once again, a change corresponding here to a highly compacted material. Therefore. the assumption &as made that Ihe- transition between powdery hydrated semolina and homogeneous dough occurred in the screw when the local pressure was higher than a characteristic value of 2 MPa. Rheological measurements Dough is a viscoelastic system, exhibiting complex rheological behaviour. However, for engineering computations, it is necessary to restrict it to a more simple purely viscous behaviour. In fact, elastic effects can be neglected because shearing flows are dominant through the screw channel and the die (except in converging sections). For these reasons, the behaviour of a semolina/water dough system was characterized on a capillary rheometer with pre-shearing, previously used for studying the rheology of molten starches (Vergnes & Villemaire, 1987). This rheometer comprises an annular shearing chamber, in series with a classical capillary system. A controlled mechanical treatment was imposed on the product through the rotation of the inner piston (in this case, 100 rev/min for 60 s) before the rheological measurement, to homogenize the material. Different levels of hydration (40, 44 and 48%, d.b.) and temperature (35, 55 and 70°C) were studied. First of all, the difficulty in obtaining reliable measurements must bc stressed. In some cases, flow instabilities due to heterogeneous hydration pressure oscillations or slip at the capillary wall made it impossible to obtain
A thermomechanical
approach to pasta extrusion
357
satisfactory results. These problems were exacerbated at high pressure or high shear rate. To avoid these difficulties, capillaries were selected with a large diameter (0=3 mm) and short length (L=25 mm). The entrance pressure corrections were made using an orifice die (0=3 mm, L /D=O). Examples of viscosity curves are presented in Fig. 4, showing the influence of temperature. Despite a small scatter of the data, the viscous behaviour can be reasonably described by a classical power law: (2)
~=Klj*‘+’
From viscosity curves at different temperatures, it is classical to obtain a mastercurve by applying the principle of time-temperature unique superposition, if no structural change or reaction occurs in the product. The same principle applies also for time-hydration superposition (Vergnes et al., 1993). Using the data at low temperatures (35 and 55°C) it was shown that power law behaviour remained valid over a wide range of shear rates, typically O-l-1000 ss’, which covers the entire range expected in extrusion (Fig. 5). The power law index, m, increased slightly with hydration, but remained in the range 0.4-0.5. The consistency, K, varied with hydration and temperature, according to exponential laws. Above 55°C it was observed that the influence of hydration decreased. For the temperature an unusual dependence was observed at 70°C perhaps due to the heat denaturation of gluten. In the usual range of extrusion temperatures (35-55°C) the following expression for K correlated well with experiment:
K=Ko exp( -c&f)
exp(E/RT)
(3)
where EIR=4330 K, Ko=3.1x 10’ Pa s”‘, (x=22.3 and M is the normalized hydration. Equation (3) predicts the viscous behaviour of the hydrated semolina used in the experiments with a precision of _t 15%. These results are similar to those obtained by Nazarov et al. (1971) on durum wheat semolina hydrated at 43%.
SHEAR RATE (s-l) Fig. 4.
Viscosity measurement: influence of temperature on viscosity at 40% hydration (m, 35°C; (1,55°C; l , 70°C).
3.58
SHEAR RATE (s-l)
Fig. 5.
Mastercurve of viscosity at 55°C and 44% hydration obtained
at 40%, 44%, 48% and 3.X,
(superposition 55°C).
of data
This power law model predicts an infinite viscosity at zero shear rate. In fact, this is not a problem when computing global pressure/flow rate relationships and this very simple law is largely sufficient for describing the flow that is considered. Another specific experiment was carried out to simulate the flow in the final part of the spaghetti die, where teflon inserts were used to improve the surface smoothness of the product. A capillary was machined in a Teflon block, with dimensions identical to the usual carbide capillary. The results are shown in Fig. 6. There was a ratio of about three between the pressures measured with carbide or teflon capillaries, which demonstrated a drastic change in boundary conditions. Through the Teflon inserts, the semolina dough slips at the wall, with global flow conditions close to a plug flow. By comparing the flow rate at constant pressure drop, it was estimated that the slip velocity was about 96% of the mean product velocity. Despite some experimental difficulties and even if these experiments have yet to be completed, they were largely sufficient for describing the flow in the present work. FLOW COMPUTATION Theoretical approaches to pasta extrusion are rather limited in the literature. However, the single screw extrusion of synthetic polymers has been studied for more than 30 years. Readers are referred to the well known books of Tadmor and Klein (1970) or Rauwendaal (1986), for example. In the present work, a classical continuum mechanics approach is applied to the specific behaviour of hydrated semolina.
A thermomechanical
approach to pasta extrusion
#P--P 0
Fig. 6. Variation
0
in pressure
0.01
-a-
359
p--------n 0.03 0.02 FLOW RATE (cmYs)
with flow rate (5o”C, 48%) for capillaries (0) and Teflon (3).
in carbide
General assumptions A slab method is generally used to study flows along an extrusion screw channel. The cross-section, perpendicular to the channel axis, is approximated by a rectangular surface. The screw is assumed to be fixed and the barrel to rotate around the screw, in order to obtain a stationary geometry. The screw channel is totally filled and the material properties (density, viscosity, thermal conductivity and heat capacity) are constant in each slab. Thus, the velocity and temperature field are locally independent of the longitudinal coordinate. By solving the mechanical and thermal balance on a given slab, the local increases in pressure AP and temperature AT are obtained. By computing from one slab to the next, the global evolution of the parameters along the screw are determined. Powder conveying section The transport of hydrated semolina as powder in the feeding zone is comparable to the conveying of polymer powder. The model derived by Darnell and Mol (1956) and improved by Tadmor and Klein (1970) can then be used without modification. The balance of pressure and friction forces on the solid determines the increase in pressure AP on a slab thickness AZ: (4) where PO is the pressure in the preceding slab, H and W are the channel dimensions, f, and f2 are the friction coefficients on the barrel and screw, respectively, 7, is the helix angle and b, is the solid conveying angle, defined
D. Le Roux et al.
360
by the volumetric
flow rate QV: sin yl Qv=U,,WH
cosy] tg(d+Yd
>
where U,, is the longitudinal component of barrel velocity. In fact, the barrel and screw friction coefficients are the key parameters which allow the hydrated semolina to be conveyed and compacted. For different values of screw friction coefficient, the minimal value of barrel friction coefficient necessary to build up the pressure at a given flow rate are presented in Fig. 7. Experimental values of friction coefficients between 0.2 and 0.4, corresponding to the screw (smooth surface) have been previously measured. It can be seen that, under these conditions, the barrel friction coefficient must be higher than O-5 to correctly convey the semolina. To obtain these high values, longitudinal grooves are machined along the barrel around its inner surface. For a screw friction coefficient of O-45, the powder conveying becomes very difficult (f, = 1). To take into account the presence of grooves along the barrel, a value of 1 for the barrel friction coefficient is chosen in the computation. Temperature changes in the powder conveying section are due to heat dissipation by friction against the barrel, which is then transmitted to the solid and to the regulation fluid. Computation of the temperature field (Le Roux, 1993) showed that the temperature rise was localized near the barrel wall and that the average temperature increase was about 5°C for a channel length of 10 cm, under typical experimental conditions (225 rev/min, 46% hydration). Dough flowing section Two different and successive approaches have been developed to model the dough flow in the screw channel. In a first step, a finite element software f 2 = 0.45
f 2 = 0.35
f 2 = 0.25
f2=
: 0.05
f2= = 0.02 f2=
NORMALIZED
:o
FLOW RATE 7. Minii num value of barrel friction coefficient f, as function of non m alin:ed A* I ,_ .a _ ,r, r-,r*\ r I.,-,I r . . . coernclenrJZ. PP 0 now rate Q - (IL -=y/u,,wn ), for amerent values orr screw rricnon
1Fig. n
361
A thermomechanical approach to pasta extrusion
was used to obtain a precise description of the local flow field in the real channel geometry. Then an approximate one-dimensional model able to describe the globality of the process was applied. The finite element software was previously applied to extrusion cooking longitudinal flow of a (Barr& & Vergnes, 1990). The two-dimensional power law fluid in the real geometry of the channel, in cylindrical coordinates, is considered. The velocity field corresponding to standard hydration 44%, experimental conditions (screw speed 20 rev/min, temperature WC, pressure gradient 12 MPalm) is given in Fig. 8. The velocity decreased monotonically from the barrel to the screw. No recirculating regions were observed under these conditions, but a large zone existed at the channel bottom, where the product moved very slowly (less than 10 mm/s, when the barrel velocity was 50 mm/s) and thus may induce a certain heterogeneity in the final product. Considering the product as isothermal, the finite element model can also be used to compute characteristic curves, i.e. relationships between flow rate and local pressure gradient l/K dPld0. During the experiments, the values of l/K dPld6 were between 1 and 3. Figure 9 shows that, at low values of power law index and for the screw design considered here, the flow rate is strongly dependent on pressure gradient. Finite element simulation is powerful, but necessitates large computer facilities and is not appropriate to the computation of a global process. To build a general software for pasta extrusion, it is more suitable to return to a simplified approach, based on a slab method as presented in the solid conveying section. However, this approximate model must take into account wall side effects and channel curvature. It has been proved, using the finite element method, that neglecting these effects could induce an error on flow rate higher than 50% (Le Roux, 1993). The basic idea is to start from the classical analytical solution of the flow of a power law fluid without wall side effects, and to modify this solution
0
IO
20
30
40
50
60
VELOCITY (mm/s) Fig. 8.
Velocity contours in the screw channel and corresponding velocity profile on the symmetry axis (evenly spread between 0 and 50 mm/s).
D.Le Roux et al.
362
20 25 30 35 MASS FLOW RATE (kg/h) Fig. 9.
gradient (l/K cP/dH) relationship for the reference screw (m, finite element simulation: q, approximate method).
Flow rate/pressure
through correction factors accounting for the wall. The correction factors are only dependent on the ratios W/R and W/H, defining the channel geometry. The details of the method can be found in Le Roux (1993) and will be published separately. Here the principles of the computation are just summarized. The analytical expressions of the flow rate are known in the following conditions: Q ,: Newtonian, without wall side effects, Q2: Newtonian, with wall side effects, Q3: power law, without wall side effects. For a given pressure gradient l/K dP/dO, the flow rate Q for a power law fluid with wall side effects will be defined by: Q (l/K dPldO) =
Q z( l/K dP/dO) Q ,(1/K @/de)
where the correction
Q,(l/KdPldB)+AQ
factor AQ is given by:
AQ = Qo-
Q dl/K dpoidtr) Q , (l/K dPold0)
Q.41K dP,ldB)
(7)
in v$iyh Q,, is only dependent on channel geometry and (l/K) (dP,,/dO) (UO/ is the pressure gradient corresponding to the flow rate Q0 for a H) Newtonian fluid with wall side effects. It can be seen in Fig. 9 that the results of this approximate method, in which all computations are analytic, are very close to those obtained by the finite element model. The mean temperature change was calculated by solving the thermal balance, including transport, convection and dissipation terms: pC,QvAT
= hWRZ(TR-
To) dO+ I@
(8)
A thetmomechanical
363
approach to pasta extrusion
where the viscous dissipation I$’ was estimated by assuming that the global energy provided to the dough was not affected by side effects, which was verified for a power law index, m, between 0.2 and 05. The screw was considered as adiabatic. The following values were chosen for the thermal calculations: heat transfer coefficient h = 300 W/m2 “C, heat capacity C, = 2 kJ/kg “C (Andrieu & Gonnet, 1989).
RESULTS
AND DISCUSSION
Flow along the screw Pressure and temperature evolution along the screw were computed for the flow rate measured at the central point (screw speed 20 rev/min, barrel temperature 40°C) of the experimental design (Abecassis et al., 1994) and three hydration levels (Fig. 10). Consistent with the rheological measurements, the pressure is lower at higher hydration levels because the viscosity decreases with hydration. In the conveying zone, the pressure increases very rapidly, until attaining 2 MPa where the dough is assumed to be fully compacted. This is achieved within 1-2 turns, depending on hydration level. Then, the pressure develops regularly, interrupted only by the screw portions without flights, along which the pressure slightly decreases. The ‘trefilette’ appears to increase pressure locally. Temperatures also change regularly, but are less dependent on hydration (Fig. 11). The temperature increase due to friction and heat transfer is important in the feeding zone, and is higher at 48% hydration because this zone is longer. In contrast, the temperature rise due to viscous dissipation is lower at 48%, because the viscosity is lower. These effects compensate and. finally, whatever the hydration, the exit values are around 53°C which is higher than the controlled barrel temperature (40°C).
‘0.0
0.1
0.2
POSITION
Fig. 10. Pressure
0.3
0.4
0.5
ALONG THE SCREW (m)
profiles along the screw for three (83,experimental values at 46% hydration).
hydration
levels
D.Le Rouxet al.
364 60
Barrel temperature
0
0.1
0.2
0.3
0.4
0.5
POSITION ALONG THE SCREW (m) Fig. 11.
Mean
temperature profiles along the screw for three ,46%. , ..,., 48%). (----, 44%; -
hydration
levels
The experimental pressure measurements at 46% hydration are also indicated in Fig. 10. The computed values are in good agreement with the experiments. More generally, the theoretical model has been applied to all points of the experimental design (with the pre-die), by imposing the experimental flow rates. For pressure, as well as for torque and temperature, the theoretical model gives a good estimation of the screw press behaviour, for a large range of processing conditions. Coupling screw and die Bows The preceding results have been obtained by imposing the flow rate in the screw flow model. In fact, the real flow rate results from the equilibrium between the screw and the die, under the given processing conditions (screw speed, thermal regulation). The whole die is composed of different elements (connecting pipe, predie and die, with teflon inserts), in which Poiseuille flows can be considered. In fact, in converging parts, elongational flow occurs, but, due to the lack of knowledge concerning the elongational behaviour of pasta dough, shearing flow conditions are assumed. Locally, on a given element, pressure losses thus depend on the viscous behaviour and flow rate through:
where L and R are the dimensions of the element. Figure 12 shows that the pressure drop through the die is correctly described only by taking into account slip conditions along the Teflon inserts. Otherwise, the pressure drop is largely overestimated by the computation.
A thermomechanical approach to pasta extrusion
365
MEASURED PRESSURE (MPa) Fig. 12.
Comparison between experimental and computed pressure drop through the spaghetti die (n, without slip conditions; n, with slip conditions).
Coupling screw and die flow leads to a predictive model of pasta extrusion. This model was applied to all the experimental design points (with the pre-die). Figure 13(a) shows that the flow rate is well predicted, with less than 10% error. Higher discrepancies are observed on the head pressure (Fig. 13(b)). Nevertheless, the results are satisfactory and sufficient to permit the use of the theoretical model for optimizing screw design and processing conditions.
CONCLUSION The thermomechanical approach of pasta extrusion presented in this paper gives a new perspective for the understanding of the process. A physical study of the hydrated semolina characterized the flow behaviour of both powder and dough states. A yield pressure of 2 MPa has been chosen as a transition point between these states. The viscous behaviour of the dough is described by a power law, with exponential dependencies on hydration and temperature. The flow along the screw channel was computed using finite element simulation and an approximate model, derived from classical analyses of plastics extrusion. General purpose software, incorporating the coupling between the screw and die, allowed accurate calculation of the evolution along the screw of the pressure, temperature, torque, dough viscosity, and flow rate for given processing conditions. Comparison with previous experiments on a laboratory screw press were satisfactory. New perspectives for optimizing screw geometry and press processing conditions now present themselves. The next step would be to correlate the
D.Le Roux et al.
366
40 a)
30
20
10
L
O_
10
0
MEASURED
20
30
20
I
40
FLOW RATE (kg/h)
I
,
b)
15
K)I
ca
10
o* / *
z
5
0 0
5
10
15
20
MEASURED PRESSURE (MPa) Fig. 13.
Comparison
between
experiments and computations: head pressure.
(a) flow rate; (b)
A thermomechanical
physical parameters quality.
involved
approach to pasta extrusion
in the process
367
with the final pasta cooking
ACKNOWLEDGEMENT This work was supported by a grant from MinistCre de la Recherche la Technologie, through the Aliment 2000 program.
et de
REFERENCES AbCcassis, J., Abbou,
R., Chaurand, M., Morel, M. H. & Vernoux, P. (1994). Influence of extrusion conditions on extrusion speed, temperature and pressure in the extruder and on pasta quality. Cereal Chem., 71, 247-53. Andrieu, J. & Gonnet, E. (1989). Thermal conductivity and diffusivity of extruded durum wheat pasta. Lehensm. Wk. u. Technol., 22, 6-10. Barbosa Canovas, G. V., Malave-Lopez, J. & Peleg, M. (1987). Density and compressibility of selected food powders mixtures. J. Food Proc. Engng, 10, l-10. Barr& C. & Vergnes, B. (1990). Recent developments in modelling twin screw extrusion cooking. In Processing and Quality of Foods, Vol. I, eds P. Zeuthen, J. C. Cheftel, C. Eriksson, T. R. Gormley, P. Linko & K. Paulus. Elsevier, London, pp. 257-62. Darnell, W. H. & MO], E. A. J. (1956). Solids conveying in extruders. SPE J., 12, 20-7. Della Valle, G. & Vergnes, B. (1994). Proprietts thermophysiques et rheologiques des substrats utilises en cuisson-extrusion. In La Cuisson-Extrusion, eds P. Colonna & G. Della Valle. Lavoisier, Paris, pp. 439-68. Della Valle, G., Kozlowski, A., Colonna, P. & Tayeb, J. (1989). Starch transformation estimated by the energy balance on a twin-screw extruder. Lebensm.
Wiss. u. Technol.. 22, 279-86.
Dexter, J. E. & Matsuo, R. R. (1977). Changes in semolina proteins during spaghetti processing. Cereal Chem .. 54, 882-94. Ehlermann, D. A. E. & Schubert, H. (1987). Compressibility characteristics of food powders by compression tests. In Physical Properties of Food, ed. R. Jowitt. Elsevier, London. Feillet, P. (1986). L’industrie des pates alimentaires: technologie de fabrication, qualite des produits finis et des matieres premieres. Ind. Agric. Alim ., 103, 979-89. Frances, Y. & Ollivier, J. L. (1986). L’utilisation des tres hautes temperatures pour le sechage des pates alimentaires. Ind. Agric. Alim., 5, 471-5. Harper, J. M. (1987). Extrusion processing of food. Food Technol., 32, 67-72. Kokini, J. L., Ho, C. T. & Karwe, M. V. (1992)._ Food Extrusion. Science and Technology. Marcel Dekker, New York. Le Roux, D. (1993). Etude experimentale et modelisation de l’extrusion des pates alimentaires. PhD Dissertation, Ecole des Mines de Paris. Matsuo, R. R., Dexter, J. E. & Dronzek, B. L. (1978). Scanning electron microscopy study of spaghetti processing. Cereal Chem ., 55, 744-53. Medvedev, G. M., Malandeeva, N. I., Argianova, 1. V. & Semko, V. T. (1984). Influenza della temperatura d’impasto sulle proprieta tisiche des semilavorato e sulla qualita delle paste alimentari. Tee. Molitoria, 35, 416-18. Medvedev, G. M., Malandeeva, N. I. & Kovalskaja, L. P. (1987). Variazioni delle proprieta dei componenti dell’impasto per pasta alimentare durante la sua termolavorazione. Tee. Molitoria, 38, 865-8.
368
D. Le Roux et al.
Menger, A. (1977). Influsso della materia prima e de1 procedimento sulla qualita della pasta alimentare. Tee. Molitotiu, 28, 83-90. Mercier, C., Linko, P. & Harper, J. M. (1989). Extrusion Cooking. AACC, St Paul, MN. Nazarov, N., Azarov, B. & Chaplin, M. (1971). Izvesttju Vyssikh Hchebnyck Zuvedenj, 2,149-Y51.
Pagani, M. A., Resmini, P. & Dalbon, G. (1989). Influence of the extrusion process on characteristics and structure of pasta. Food Microstract., 8, 173-82. Pavan, G. (1979). L’impiego dell’alta temperatura nel process0 di essicazione delle paste alimentari. Tee. Molitoriu, 30, 362-70. Peiti, C. & Vergnes, B. (1989). Mesure de coefficients de frottement de divers tchantillons de farine. Research Report, CEMEF, Ecole des Mines de Paris. Rauwendaal, C. (1986). Polymer Extrusion. Hanser, Munich. Renaudin, C. (1951). La Fabrication Industrielle des Pates Alimentuires. Dunod, Paris. Tadmor, Z. & Klein, I. (1970). Engineering Principles of Plusticating Extrusion. Van Nostrand, New York. Tharrault, J. F. & Launay, B. (1990). Compactage sous pression de farines de ble et de formules type pain plat. Ind. Agric. Alim., 6, 533-5. Vergnes, B. & Villemaire, J. P. (1987). Rheological behaviour of low moisture molten maize starch. Rheol. Acta, 26, 570-6. Vergnes, B., Della Valle, G. & Tayeb, J. (1993). A specific slit die rheometer for extruded starchy products. Design, validation and application to maize starch. Rheol. Acta, 32, 465-76.
Walsh, D. E., Ebeling, K. A. & Dick, J. W. (1971). A linear programming approach to spaghetti processing. Cereal Sci. Today, 16, 385-9. Wasik, R. J. (1978). Relationship of protein composition of durum wheat with pasta quality and the effects of processing and cooking on these proteins. Can. Inst. Food Sci. Technol., 11, 129-33.