Accepted Manuscript Experimental Analysis and Numerical Simulation of Pasta Dough Extrusion Process Fabrizio Sarghini, Annalisa Romano, Paolo Masi PII:
S0260-8774(15)30001-7
DOI:
10.1016/j.jfoodeng.2015.09.029
Reference:
JFOE 8343
To appear in:
Journal of Food Engineering
Received Date: 17 March 2015 Revised Date:
23 September 2015
Accepted Date: 30 September 2015
Please cite this article as: Sarghini, F., Romano, A., Masi, P., Experimental Analysis and Numerical Simulation of Pasta Dough Extrusion Process, Journal of Food Engineering (2015), doi: 10.1016/ j.jfoodeng.2015.09.029. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Experimental Analysis and Numerical Simulation of Pasta Dough Extrusion Process Fabrizio Sarghinia,, Annalisa Romanob , Paolo Masia,b
University of Naples Federico II, Dept. of Agricultural Sciences, Italy b University of Naples Federico II, CAISIAL, Italy
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Abstract
Pasta extrusion simulation still represent a powerful challenge from a computational point of view, for both the complexity of the rheological properties of semolina dough and the process itself, in which a polymerization phenomena, driven by a combination of pressure and temperature and strongly influ-
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enced by moisture content, takes place in the final part of the extruder barrel. In this work an integrated experimental-numerical approach is proposed for numerical simulation of pasta extrusion. An extensive set of rheological data in industrial range of moisture content (MC) and temperature obtained us-
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ing a capillary rheometer is reported. To overcome the reduced accuracy of Arrhenius models for pasta dough viscosity published in literature, a numer-
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ical approach based on local Taylor expansion is proposed, matching exactly experimental data. The proposed model was then validated numerically comparing numerical results obtained in the framework of Computational Fluid Corresponding author Email address:
[email protected], fax no. Sarghini ) I
Preprint submitted to Journal of Food Engineering
+39 081 7754942 (Fabrizio
September 23, 2015
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Dynamics with experimental data obtained by using an experimental labo-
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ratory extruder (Sercom press, mod INRA). A moving mesh approach was adopted to model the screw dynamics inside the press barrel and a modified version of OpenFoam solver was developed. Rheological test and numerical
simulations reciprocally validate each others: errors in rheological character-
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ization would results in errors in numerical results, while wrong numerical modeling would not match experimental extrusion data. The proposed tool
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represent a validated basis for pasta production process optimization and reverse engineering of die design. Keywords:
Capillary rheology, Semolina Dough, Pasta Dough, Extrusion, Numerical
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1. Introduction
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modeling, CFD, Moving mesh
Pasta production can be considered a mature technological process, con-
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sidering markets acceptance and the widespread use of the final product.
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Nonetheless, several problems are still present in industrial production: non
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uniform pressure distribution and consequent uneven extrusion velocity (es-
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pecially in high mass flow rate equipment), resulting in quality differences in the same production batch, the presence of some recirculation zones into the extrusion bell possibly causing molds, incomplete mixing of semolina powder
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and water. Nonetheless, the geometries of the extruder bells, apart from
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small changes, are still similar to those designed thirty years ago. The pres3
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ence of hand-made compensation disks to correct flow uneven velocities in
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the die still shows that experimental pilot plant can not completely substitute
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the full scale experiments, due to implicit difficulties in scale-up, operation
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which is not straightforward (and expensive). A powerful optimization tool,
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when properly used, is represented by numerical simulations: such approach,
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coupled together with a posteriori experimental evidence, can be considered
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the modern basis of any process optimization. From this point of view,
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numerical and experimental comparisons represent a powerful reciprocal val-
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idating tool. Moreover, a reliable numerical model introduce the possibility
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to perform reverse engineering optimization of pasta final product, i.e. the
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reverse design of extruder’s die starting from the shape of the final product.
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After the work of Le Roux and Vernier [9], very little attention had been
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paid to the process itself, and industrial plants still continue to suffer from
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the aforementioned problems. Something had been done by introducing in
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line mixers rather than using the traditional paddle ones, trying to reduce
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the effects on the final products of non-homogeneous water-semolina mixing,
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but design details of several critical parts are almost the same. From a point
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of view of modeling and simulations, although a lot of work has been done
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on flour dough extrusion, semolina dough extrusion still remain a partially investigate topic: only one simulation was published by Dhanasekharan and Kokini in 2003 [2], and a validated experimental-numerical model in indus-
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trial production range is still missing, mainly bacause of the complexity of
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rheological model involved. A work by Fabbri and Lorenzini [3] was limited 4
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to the extrusion bell and very limited attention to the rheological properties
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of pasta dough was devoted. Aim of this work is: a) to provide updated re-
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liable rheological data for semolina dough rheology in an extensive range of
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industrial production parameters, b) to develop an accurate numerical model
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based on Computational Fluid Dynamics analysis and c) validate the model
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with experimental test. The proposed numerical model takes into account all
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complex features present in pasta extrusion phenomena, including the screw
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rotational movement, by adopting a moving mesh approach. A limited num-
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ber of works investigated in general the rheological properties of pasta dough
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in order to obtain a better understanding of the basic rheology or mixing be-
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havior(Le Roux and Vernier [9],[10]); nonetheless, an extensive investigation
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of these properties in real production ranges of variability of temperature
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and Moisture Content (MC) has not been published yet. Rheological char-
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acteristics of cereal doughs using a capillary rheometer have been previously
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described in the literature (Bagley, [1]; Singh and Smith, [19]; Cuq et al.,[20];
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Hicks and See,[21]). Most of the studies were focused on bread dough, while
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the behavior of semolina dough during extrusion has not been extensively
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studied (Chillo et al., [22],Le Roux et al.[9]) A recently published work by de
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la Pena et al.[6] partially closed the gap, although the authors did not cover
all the ranges of temperature and MC involved in industrial production and
required for numerical simulations of full scale plant. Following the work of
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[9], rheological experiments show that ”pasta dough is a viscoelastic system,
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exhibiting complex rheological behavior. However, for engineering computa5
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tions, it is necessary to restrict it to a more simple purely viscous behavior.
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In fact, elastic effects can be neglected because shearing flows are dominant
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through the screw channel and the die (except in converging sections). For
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these reasons, the behavior of a semolina/water dough system was character-
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ized on a capillary rheometer”. While viscoelatic behavior is typical of wheat
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gliadin and glutenin suspensions [11], as in this work the engineering point
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of view is dominant , following results in previously mentioned works, it is
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reasonable to assume a viscoplastic solid-like behavior that can be described
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using a power-law model. In the work of de la Pena et al. [6], focused on
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the effects of moisture and dough formulation on rheological properties of
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pasta dough during extrusion at fixed temperature, the authors experienced
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difficulties in reproducibility of data; difficulties in rheological experiments
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of semolina dough were reported also in [9] attributed to ”flow instabilities
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due to heterogeneous hydration pressure oscillations or slip at the capillary
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wall made it impossible to obtain satisfactory results.”
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2. Materials and Methods
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2.1. The experimental analysis of semolina dough rheological behavior
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The class I semolina was provided in 2kg bags by a major pasta producer
with the following analytical characteristics: • Ashes: =0.87% • Proteins =13.12% 6
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• Moisture content = 15.4% and stored in air tight closed containers.
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A careful preparation of experimental samples was considered, and a par-
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ticularly attention devoted to mixing conditions, trying to minimize MC
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distribution non-uniformity to obtain reliable and reproducible results. The
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mixtures, with variable humidity from 30% to 36%, were prepared by mix-
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ing 750 g of semolina and a suitable quantity of hot water (T = 450 C)
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slowly poured into a discontinuous mixer (Kitchen Aid Classic, 250W, Inc.,
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St. Joseph, Michigan, USA) at speed equal 70 rpm (data obtained using a
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digital tachometer) for a time of 6 minutes. The hydrated semolina obtained
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after mixing is an incoherent material that can be considered granular, and
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aggregates can be separated using a sieve analysis a procedure commonly
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used in civil or soil engineering to assess the particle size distribution (also
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called gradation) of a granular material (ASTM C136 / C136M - 14 , Stan-
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dard Test Method for Sieve Analysis of Fine and Coarse Aggregates). The
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mixing time was chosen by using a series of sieves to obtain the granulometric
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distribution of hydrated semolina agglomerates and the standard deviation
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of MC was computed vs. mixing time. As a matter of fact, the hydration of
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semolina is a critical stage that precedes the extrusion: during this operation, the target is to achieve a uniform distribution of moisture in the entire mass
of the dough and a complete penetration of water inside the particles of the
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hydrated semolina [5]. Both of these processes require to fully develop in a
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certain period of time and are favored by the mixing. In practice it may hap7
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pens that the mixing time is not sufficient to obtain a homogeneous blend of
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semolina and water, and consequently the feed composition may vary from
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point to point, possibly fluctuating over time. The fact that finer durum
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semolina results in quicker and better water absorption and, therefore, in a
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shorter mixing time to give a homogeneous dough is extensively discussed in
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Manser and Biihler [12] (the paper was not available, but the reader can find
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some results in[13]), who compare the mixing times of semolina with differ-
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ent particle size distributions. On the contrary, it means that for a small
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mixing time the water distribution could be uneven. Relative humidity dis-
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tribution per granulometric classes was obtained by separating in 6 fractions
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the agglomerates extracted at different time steps, using 6 sieves:
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1. fraction 1=sieve no. 1 : mesh < 2mm
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2. fraction 2=sieve no. 2 : 2 mm ≤ mesh ≤ 4 mm
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3. fraction 3=sieve no. 3 : 4 mm ≤ mesh ≤ 5.6 mm
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4. fraction 4=sieve no. 4 : 5.6 mm ≤ mesh ≤ 8 mm
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5. fraction 5=sieve no. 5 : 8 mm ≤ mesh ≤ 11.6 mm
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6. fraction 6=sieve no. 6 : 11.6 mm ≤ mesh ≤ 16 mm
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The moisture content of each sample was then determined by the AACC
method number 44-15.02, 1999. Three samples, weighing approximately 2
g, were dried for 24 h at T = 1050 C. Samples were removed from the oven
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and immediately placed in a desiccator prior to weighing after cooling and
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within 30 min. The dried samples weight was subtracted to the respective 8
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Figure 1: Gradation analysis of water-semolina agglomerates vs time
Figure 2: Standard deviation of MC in the mixture vs. time
initial weight. The results were calculated as percentage of water per sample
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weight (%)
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Results shown in Fig. 1 (granulometric classes distribution of agglom-
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erates vs tme) and Fig. 2 (standard deviation of MC in the mixture vs.
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time) underline that for this type of mixer after 6 minutes the mixing can
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be considered mostly complete and MC distribution does not change locally
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anymore.
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The water penetration in granular aggregates was cross checked using
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experimental rhological test. To this purpose, in Fig. 3b the viscosity curves
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for the different sieved fractions of the mixture (nominal MC 32.5% ) were
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compared with the theoretical curve expected by applying the rule of mixture.
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This rule is based on the assumption that the viscosity of the mixture is
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given by the sum of the weighted fractions of the individual viscosity of the
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aggregates classes, expressed in the form:
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ηtot =
4 X
ηk xk
(1)
k=1
where xk are the fractions in weight of the collected samples in the various
sieves, and ηk are their viscosity. 9
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Figure 3: Influence of mixing time in moisture distribution and viscosity in semolina granulometric classes: a) 1 min, b=6 min
The rheological curve of the total mixture for a nominal value RH =
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32.5% shows for the 6 minutes mixing case an acceptable correspondence
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between the values of viscosity of the mixture and those expected by ap-
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plying the rule of mixture based on data for the individual fractions. The
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RH = 32% dominate the rheological behavior of the mixture, as fraction
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1 accounts for 82 % and fraction 2 for 15%, and together with previously
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showed graps we can infer that mixing can be considered mostly complete.
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On the other hand, (Fig. 3a) mixing semolina and water for 1 minute, 40
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% of semolina aggregates forming clusters of large dimension (sieve 3, sieve
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2) whose moisture contents is larger than the nominal one (35% − 36%).
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The remaining 60% is included in clusters of small dimension with moisture
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content less then the nominal value.
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The sample, thus prepared, was stored at room temperature until its use in a closed container to limit dehydration.
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Rheological measurements were obtained by using a capillary rheometer
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(mod. RH2100, Rosand Precision Ltd, Stourbridge, UK ) equipped with an
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heating system and a precision PRT (Platinum Resistance Thermometer) sensor for temperature control of the barrel. Experiments were performed after the dough was allowed to rest at the required temperature in the barrel
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for 4 min to allow the sample to equilibrate in a air tight closed container,
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and experiments were performed in different days for each parameters com10
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bination. As underlined in [4], the rise time required to achieve a steady pressure
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reading in a capillary rheometer operated at constant piston speed can be
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very short or very long depending on the amount of the material in the barrel,
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its isothermal compressibility, the flow rate and the geometrical characteris-
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tics of the dies used. When a short die having a large diameter is used, a
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maximum can also be obtained in the pressure transient, which is solely due
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to the compressibility of the material. In any case, experimental results in
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this work and in de la Pena et. al. work [6] et al. at 32% RH and 45o C
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are quite similar. Rheological measurements were performed in a capillary
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rheometer at shear rates in the range 10−400s−1 , corresponding to the range
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(∝ 200s−1) in extrusion operations performed with the laboratory extrusion
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unit (a SERCOM laboratory extruder model INRA,Montpellier, see [10] for
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details. A numerical simulation based on data already published, previous
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works and industrial data confirmed the range). Two different capillaries
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were used: the first one had diameter D1 = 1 mm and length L=16 mm, the
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second one D2 = 1, 5 mm and L=24 mm. In both cases the entrance pressure
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corrections (Bagley correction) were made using an orifice die (D = 1 mm,
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L/D ≃ 0; D = 1, 5 mm, L/D ≃ 0). Pressure data were measured using a
pressure transducer positioned just above the capillary entrance, and they were converted in shear stress and shear viscosity using the Rabinowitsch
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correction, due to the non-Newtonian characteristics of the test material. In
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our experiments we did not experienced strong pressure oscillations as re11
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ported in previously mentioned works. Particular attention was devoted to
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avoid the slippage phenomena, that is due to the lack of interaction between
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the capillary wall and the material itself. It is important to analyze this
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phenomenon, since the hypothesis of constant tangential stress at the wall
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and pressure gradient along the capillary, except in the input section, it is
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valid ,in fact , only by imposing the condition of perfect adherence of the test
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material to the wall. In the presence of slip, this condition is not fulfilled,
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resulting in unreliable pressure data and viscosity values. In this case the
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flow velocity at a given pressure difference compared to the corresponding
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shear rate is higher ([15]). The phenomenon of slippage between the sample
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and the metal surface of the capillary implies that to the generic velocity
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profile we should sum a sliding velocity that depends on the local value of
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the pressure: this is why the traditional method of Mooney is no longer valid
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to estimate the actual values of viscosity. It is necessary to identify the val-
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ues of the critical speed in order to consider , for the determination of the
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curves of viscosity , only those values related to a shear rate below the critical
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value. Following the work of Hatzikiriakos and Dealy [4], plotting the curves
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of apparent flow obtained with capillaries of different diameters but with the
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same L/D ratio in order to maintain constant the effect of pressure on the viscosity, it resulted that the curves diverge above a critical shear rate value, approximately 400s−1 . Results at different temperatures for MC=32% are reported in Mooney diagrams plotted in Fig. 4.
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Figure 4: Determination of critical shear rate at RH=32% and T = 45o C,T = 50o C,T = 55o C
Although some plots present data obtained also using higher values of
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the apparent shear rate, their values were purged in data fitting and must
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be considered carefully. Experiments were performed by varying several pa-
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rameters: moisture content (MC) from 30% to 36%, more realistic from an
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industrial point of view respect to the range used in Le Roux work (44%-
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48%) and temperature ranging from 35o C to 80o C. Results presented in this
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work were treated statistically to compute k and n in the power-law model
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using Sigmaplot V.10 software, and final results were averaged using 8 out of
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10 data for the mean value for each different water-semolina preparation, as
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maximum and minimum were dumped; each rheological test (i.e. each hy-
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dration and mixing preparation) repeated 3 times. The 10 experiments were
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performed in different days to check results independence from environmental
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conditions or manual errors.
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2.2. Pre-compression effects on rheological experiments
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While the semolina-water mixture moves along the extruder channel and
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in the die, it is submitted to an increasing pressure, commonly rising from 1 to 100 atmospheres. The effect of this compression is to homogenize the dough in the final part of the extruder. In order to investigate the possible influence
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of compression effects on rheological test, and consequently the reliability of
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viscosity data in the final part of the extruder screw, the polymerization phe-
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Figure 5: Influence of pre-compression on viscosity curves at RH=32% and T = 35o C Figure 6: Influence of pre-compression on viscosity curves at RH=32% and T=55o C
nomenon was artificially induced by pre-compressing the samples at different
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pressure levels before being tested in the capillary rheometer. In these exper-
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iments, 10 grams of semolina-water mixtures having RH = 32% were placed
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in a 14 mm internal diameter steel cylinder and compressed with a piston by
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means of an Instron dynamometer (Instron ltd, Buckinghamshire UK) at 80
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atm and 150 atm. The compressed cylinders were inserted into the rheometer
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barrel and tested at two different temperatures (35oC −55o C), and the viscos-
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ity curves are shown in Figures 5 and 6 for measurements performed at 35o C
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and 55o C, respectively. It can be noticed that, once the dough has been ho-
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mogenized, at both temperatures the influence of the pre-compression effects
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on the rheological behaviour of the semolina-water mixture is negligible.
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3. Results
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3.1. Temperature and MC effects on rheological behavior of pasta dough
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A typical experimental diagram of the apparent viscosity vs shear rate at
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fixed temperature obtained with capillary measurements is shown in Fig. 7 Although the temperature varies during extrusion operation in a small
range, (35o C-50oC), a larger temperature interval (35o C-80o C) was explored Figure 7: Apparent viscosity experimental results for T = 35o C at different values of MC
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to gain also some partial information about macroscopic effects of thermal
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denaturation of gluten on the mixture rheological response. This is because
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temperature may change inside the extruder barrel due to viscous dissipation
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effects, as shown in Fig.13 (reported in a following section for comparison
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with numerical simulation data) for an extrusion experiment in which the
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thermostatic bath was set at 45oC. The trend can be clearly identified, show-
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ing that viscosity increases as MC decreases: for example, comparing the
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fractions at MC=36% and at MC= 32%, the former has a viscosity values
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less than one order of magnitude respect to the latter. This sensitivity of
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the rheological response to the variation of the water content of the semolina
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dough can be observed at all considered temperatures. It is accepted that the
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lubricant role is played by gliadine because their globular shspe allowing the
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movement of the glutenin fibers constituting the gluten network that entraps
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weat granules; the water content influences the degree of network formation,
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and in an indirect way plays the role of lubricant too. In industrial produc-
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tion range, an increase of MC involves a reduction of viscosity. Conversely,
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the water, within the range explored does not seem to interfere with the rhe-
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ological behavior of pastes that always appears to be pseudoplastic, following
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a power-law model, in accordance with results of [9] and [6]. In general one
can notice that increasing the moisture content and increasing the temperature, the viscosity of the dough decreases: the larger the moisture content
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the smaller the influence of the temperature. The same conclusions can be
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drawn by considering the parametric representation shown in Figures 8 and 9 15
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Figure 8: Power law k consistency coefficient Figure 9: Power law flow index n coefficient
where the flow index, n, and the consistency, k relative to the mixture having
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different moisture content were plotted versus temperature. Increasing the
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temperature, the flow index increases till T=55-60oC then it decreases, and
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this behavior is related to structure formation processes starting at tempera-
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ture above T=50o C - 60o C, which can reflect in a negative way on the pasta
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final quality from an industrial point of view.
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Extended k and n coefficients are tabulated for the use in following nu-
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merical simulations in Table 1, while std. deviations are plotted in Fig. 8
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and Fig. 9 .
At this point a complete set of rheological data in industrial production
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parameters range was obtained using the experimental test, and they can be
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used perform a numerical simulation of the real extrusion process.
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3.2. Numerical modeling of rheological data
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Although consistent experimental data can be obtained experimentally,
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it is not straightforward to develop a generalized rheological model taking
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into account temperature dependent structural modifications due to starch
gelatinization, relative humidity effects and shear rate influence. A review of dough rheological models used in numerical applications is presented in
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the work of Hosseinalipour et al. [23]. Most of applications are based on
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the power-law models, due to their ability to predict velocity and pressure 16
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Table 1: Variation of k (kPa sn and n respect to relative humidity and temperature
T ( C) 35
k
n
0
55
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k
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109340.70 68209.72 27958.86 17066.97 81949.88 27919.99 9838.48 8879.85 33042.81 18623.81 9821.87 7372.91 33642.60 29476.20 22777.39 15238.78
0.3984 0.4020 0.4191 0.4372 0.3586 0.4888 0.4974 0.4338 0.4540 0.4910 0.4508 0.4229 0.2910 0.3071 0.3282 0.3551
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T ( C) 40 0
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Water content 30 % 32 % 34 % 36 % 30 % 32 % 34 % 36 % 30 % 32 % 34 % 36 % 30 % 32 % 34 % 36 %
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119257.38 54333.71 17924.02 11778.92 41705.23 23307.17 9758.88 6641.63 34738,72 20992.37 13463.74 9356.96
n
0.3365 0,4160 0.4393 0.4229 0.4510 0.4997 0.4936 0.4778 0.4051 0.4242 0.4293 0.4349
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distributions in uniform flows [19] and represent the simplest representa-
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tion of shear thinning behavior [38]. However, they encounters the following
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shortcomings: these models should be applied over only a limited range of
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shear rates and therefore the fitted values of k and n will depend on the
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range of shear rates [25]; the dimensions of the flow consistency coefficient,
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k, depend on the numerical value of n and therefore the k values should not
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be compared when the n values differ [25]; they are seldom able to provide
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accurate predictions of measurements of Specific Mechanical Energy (SME)
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and Residence Time Distribution (RTD) [24]. The worst one in numerical
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applications is that they are not able to predict viscosity at near zero shear
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rate [25]. Such near-zero shear rate zone can be present in pasta extruders,
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and actually they are responsible for molds formation in the bell region.
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Modifying the model of Morgan et al. [26], Mackey et al. [27] proposed
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an Arrhenius model for the viscosity of starch-based products related. This
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model provides accurate results for predicting the viscosity of relatively pure
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starches such as potato flour [27] and corn starch [14] and does not account
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for non starch components. They incorporated the effects of shear rate, tem-
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perature, moisture content, time-temperature history, and strain history [14].
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However, in their work on rheological analysis of whole wheat flour doughs, results showed lack of accuracy, attributed by the authors to the presence
of flour components such as bran, protein, and lipids, which the model does
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not account for, probably altering the starch gelatinization kinetics. This
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model was used in the numerical simulation performed by Dhanasekharan 18
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Figure 10: Apparent viscosity experimental data compared with Mackey and Ofoli, Leroux and Vergnes Arrhenius models for MC=32% and T=45oC
and Kokini [2]. As a matter of fact, viscosity in pasta dough computed with
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Mackey and Ofoli model tends to be overestimated, differing significantly
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from experimental rheological data, while viscosity values computed with
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the model proposed in the work of Leroux and Vergnes at higher percent-
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age of MC (43%) are even more distant from experimental results. See for
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example the graph reported in Fig. 10 for MC=32% and T=45o C.
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This is why we did not use the Mackey and Ofoli or the model Arrhenius
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model in the following numerical simulations. On the ther hand, to develop a
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single accurate constitutive equation for pasta dough would require a deeper
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knowledge of the characteristics and network formation dynamics of this
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complex material, which is out of the purpose of the present work. What
319
we need numerically is a coherent numerical representation of the rheological
320
data obtained experimentally, and under the hypothesis that the tempera-
321
ture changes of k and n can be represented mathematically with a continuous
322
function in the range of interest, a data fitting model cross matching experi-
323
mental data represents a sufficient and somehow more accurate approach to
325
326
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calculate the correct local apparent viscosity. For this reason, in our approach temperature (and MC effects if required,
not applied in the present case) effects on viscosity µ are expressed by us-
327
ing a third order truncated Taylor expansion relating local shear stress and
328
temperature. 19
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(2)
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3 n X (T − Tref )n ∂ µ(γ) ˙ µ(T, γ(x)) ˙ = µ0 (T, γ) ˙ + ∂T n n! n=1 329
where x is the coordinates vector.
330
To reduce numerical interpolation errors the Taylor expansion is done directly on apparent viscosity rather then on k and n.
SC
331
n The unknowns first order term µ0 (T, γ) ˙ and derivatives ∂ n µ(γ)/∂T ˙ were
333
obtained algebraically ( solved symbolically using Mathematica software) by
334
solving for each point x a 4x4 linear system at fixed MC imposing
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˙ = µ(Ti , γ) ˙ exp , Ti = {35O C, 40O C, 45O C, 50O C} µ(Ti , γ(x))
(3)
˙ is the 3D volume average shear rate(as we use a Control Volwhere γ(x)
336
ume approach) obtained by numerically solving the time dependent Navier
337
Stokes equations, related to the second invariant of the deformation gradient
338
tensor (the symmetric part of the velocity gradient tensor) S :
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340
341
(4)
where U(x) is the local velocity vector, and
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q γ(x) ˙ = (2S : S)
1 Sij = 2
∂Ui ∂Uj + ∂xj ∂xi
(5)
The numerical procedure to solve the system is the following:
1. for each time step and each control volume compute numerically the 20
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343
temperature and the local average shear rate γ(x) ˙ ; 2. using the experimentally derived power-law model
τ = k γ˙ n
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(6)
compute apparent viscosity at different temperatures (Ti = {35O C, 40O C, 45O C, 50O C})
345
(we select 4 temperatures out of 6 up to 60O C depending on local tem-
346
perature) ;
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350
351
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3. impose the computed values in Taylor expansion equation at 4 selected temperatures to match exactly the experimental values; 4. solve the 4x4 linear system to obtain the first order term and the 3 unknown derivatives of the Taylor expansion;
5. solve the Navier Stokes equations with the new apparent viscosity at
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computed temperature and restart the cycle. Using the previously described approach in each point the local Taylor
354
expansion matches exactly the experimental viscosity values at the same
355
shear rate and experimental temperatures, as the constitutive relation be-
356
tween shear rate and stress tensor remains the power-law model. A special
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consideration is devoted to pasta dough behavior at low shear rate, as the
model predicts an infinite viscosity at zero shear rate. Close to zero shear
viscosities were obtained using creep measurements at vanishing shear rates
360
in the work of Dus and Kokini [28] for hard wheat flour dough. While in the
361
experimental analysis inside cylindrical barrel this situation does not appear, 21
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in numerical analysis of real extruder bell configuration very low shear rate
363
zones can be present. Due to the relevant difference between flour dough and
364
semolina dough, a cut-off level for low shear rate was arbitrarily set to 1 in
365
numerical simulations. This resulted is a continuous regular distribution of
366
viscosity as shown in Fig. 21.
367
3.3. Numerical models for CFD simulations
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Numerical simulations of extrusion test were performed using a control
369
volumes Navier Stokes solver (OpenFoam v 2.1), and part of the code was
370
rewritten by the authors to consider thermal effects for a moving mesh
371
approach of non-newtonian flows. Although the complete system is non-
372
homogeneous, continous equations can be applied in the final part of the
373
extruder barrel, where compression effects allows to consider the system ho-
374
mogeneous from an engineering point of view. The reference continuity,
375
momentum and energy equations for the general non-Newtonian case are the
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following:
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(7)
∂ (ρU) + ∇ · (ρU ⊗ U) = −∇p + ∇ · τ + ρg ∂t
(8)
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∂ρ + ∇ · (ρU) = 0 ∂t
∂ (ρe) + ∇ · (ρUe) = ∇ · k∇T − p∇ · U + τ : ∇U ∂t 22
(9)
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378
where e = h −
p ρ
is the internal energy, h is the sensible enthalpy, U is
the velocity vector, τ is the stress tensor related to the strain rate by: 2 T τ = µ ∇U + (∇U) − δ∇ · U 3
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(10)
and τ : ∇U is the viscous dissipation term. In our case compressibility
380
effects can be neglected, as the compacting and melting part of the press
381
was modeled using a theoretical mathematical approach described in the
382
following paragraph, so that continuity equation becomes
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∇·U=0
(11)
Although the gravitational term was included in simulations, in this spe-
384
cific case body forces are negligible in comparison between viscous and pres-
385
sure forces, along with the equally insignificant centripetal and Coriolis ac-
386
celerations. To account for possible mixing effects at the end of the screw
387
barrel, the screw rotation was modeled applying a moving mesh approach,
388
the Arbitrary Mesh Interface (AMI) for non-conformal patches according to
389
the implementation based on the algorithm described in [16]. This technique
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allows simulation across disconnected, but adjacent, mesh domains, where
the domains can be stationary or move relative to one another. The implementation in OpenFoam is fully parallelised, with the AMI being either
393
distributed across several subdomains, or confined to a single subdomain by
394
the new constrained decomposition. A modified version of pimpleDyMFoam 23
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solver for non Newtonian fluids and heat transfer with moving mesh was
396
adopted. A centered cubic scheme was adopted for vectors field, an explicit
397
non-orthogonal correction for surface normal gradient, a fourth order least
398
squares scheme for gradient, an unbounded fourth order conservative scheme
399
for Laplacian and divergence operators, and a blended second order implicit
400
scheme in time was used to stabilize the computation. A blended (PIM-
401
PLE) pressure-implicit split-operator (PISO) and semi-implicit method for
402
pressure-linked equations (SIMPLE) scheme was adopted to solve the result-
403
ing system. Grid independence of results was checked by using several grid
404
ranging from 104 to 106 control volumes. The minimum volume was order of
405
10−15
406
order of 10−9
407
trol volumes, and the computation was performed on a 64 cores workstation
408
with 256 Gb of memory.
409
3.4. Numerical results
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m3 , located near the homogenization screen, and the maximum was
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m3 . Results shown in this work are obtained with 1 · 106 con-
Since the work by Dhanasekharan and Kokini in 2003 [2] focused on
411
numerical simulation of pasta extrusion, literature on numerical simulation
412
of pasta dough extrusion is almost none, excluding the work of Fabbri [3]
413
414
415
416
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already mentioned. Although the leading edge characteristics of their work when it was published, showing that important parameters for extruder’s
optimization could be obtained numerically, several issues were not assessed
in [2]: the rheological model was not validated in the industrial range of
24
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temperature and MC, simulations were under-resolved (9000-17.000 elements
418
are not enough to correctly capture thermal gradients,and under-resolved
419
gradients could have a strong impact on viscous dissipation calculation, and
420
moreover grid independence of results was not checked), and no comparison
421
with an experimental setup was proposed. This work is aimed to close the
422
gap and propose a validated numerical tool for pasta extrusion simulation.
423
Using the previously derived numerical model for the apparent viscosity, the
424
accuracy of the numerical and experimental analysis was cross checked in
425
a pasta laboratory extruder. The geometry of the Sercom press barrel and
426
screw used for experimental test is described in Figure.11: under a paddle
427
mixer (not shown), the extruder barrel is followed by a final cone allowing
428
the 90o bending of the flow into the extrusion bell. At the bottom of the bell
429
an homogenization screen (1x1 mm square holes) is positioned, followed by a
430
dual die configuration, with each die extruding 7 spaghetti. A temperature
431
and pressure probe was inserted into the extrusion bell in a non disturbing
432
position respect to the main flow. The constant pitch extruder is untapered,
433
with the following dimensions: barrel internal diameter W=36 mm, screw
434
channel height H=9.5 mm, screw pitch p=20 mm, screw channel width 12.54
436
437
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417
mm.
The heat capacity Cp was set to 2 kJ/kg oC and thermal conductivity
k=0.242 W/mo C (Andrieu & Gonnet, [29]). The generalized Brinkman num-
438
ber Br* computed according to definition in [32], has a value of -5, so that the
439
the hypothesis of constant thermal properties may be reasonably accepted. 25
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Figure 11: Internal geometry of the Sercom press (a) and computational grid (b)
The water-semolina mixing obtained using the integrated paddle mixer
441
resulted to be unsatisfactory, as the MC was not evenly distributed into the
442
raw material also after 20 minutes. For this reason the hydrated semolina in
443
experimental test was previously prepared in the batch Kitchen Aid mixer
444
used for rheological tests, following the same procedure described in the pre-
445
vious section, and the batch mixer was left on only to facilitate the insertion
446
of hydrated semolina into the screw barrel.
447
3.5. Comparison between numerical and experimental data
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Experiments in the Sercom press facility provided several data to compare
449
with for each combination of temperature, MC and screw speed: the tem-
450
perature and pressure in the bell probe, and the mass flow rate at the exit.
451
Depending upon the material being extruded and the operating conditions,
452
in a single-screw extruder up to four fundamentally different regions can be
453
distinguished, including the feed zone, where the screw channel is not com-
454
pletely filled and loose powder is gradually consolidated to a coherent solid
455
mass, the solids conveying zone where powder is compacted and transported
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to a good approximation as a plug, and the melting zone, where the material begins to melt and form a paste. When all the material has been melted or
fused, it enters the metering or pumping zone, where the material reaches
459
its maximal temperature and pressure In our work only the metering zone
460
was simulated using CFD, in order to use only the continuum Navier Stokes 26
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equations and dropping the further difficulty to model the compacting phe-
462
nomena using a different set of equations (granular compressible flows). The
463
transport of hydrated semolina as powder in the feeding zone is comparable
464
to the conveying of polymer powder, and the solid conveying zone and the
465
melting zone were modeled using he model derived by Darnell and Mol [31]
466
and improved hy Tadmor and Klein [17]. Although several improved models
467
are present in literature (Weert et al.[30]) , for our purpose the original for-
468
mulation was used, where the balance of pressure and friction forces on the
469
solid determines the increase in pressure ∆P on a slab of thickness ∆z:
W + 2H f1 ∆z − 1 (cos(φ + γ) − f2 sin(φ + γ)) − f2 H WH (12)
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∆P = P0 exp
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461
where P0 is the pressure in the preceding slab, f1 and f2 are the friction
471
coefficients on the barrel and screw (Coulomb wall boundary conditions: the
472
friction coefficients on the barrel and screw surfaces are, in general, different
473
due to dfferent surface machining and temperatures), H and W are the screw
474
and internal barrel channel dimensions respectively, γ is the helix angle and
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477
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φ is the solid conveying angle (see Fig. 12), defined by the volumetric flow
rate Q as:
Q = U0 W H cos γ −
sin γ tan(φ + γ)
(13)
where U0 is the longitudinal component of the barrel velocity. In our 27
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Figure 12: The velocities and angles used to model pressure in solid conveying zone of the extruder, where vextruder denotes the motion of the plug relative to the engine as a whole, vscrew denotes the motion of the plug in the down channel direction relative to the screw, and vbarrel is the velocity difference between the barrel and the internal plug.
work we adopted f1 = 1 to take into account the rugosity of the internal
479
surface of extruder barrel, while for the screw f2 = 0.35 was assumed (see
480
[9] for a discussion about these hypothesis). To identify the beginning of the
481
metering section, we followed the work of Le Roux and Vernier [9] assuming
482
that the transition between powdery hydrated semolina and homogeneous
483
dough occurred in the screw when the local pressure was higher than a char-
484
acteristic value of 2 MPa, which resulted to be in proximity of the 8th turn
485
of the screw, so that only 10 out of 18 real extruder turns were numerically
486
modeled for CFD analysis. This assumption was verified by interrupting an
487
experimental run, extracting the screw and the dough together, and check-
488
ing the temperature (necessary to setup correct boundary conditions at the
489
inflow) and the degree of compaction of the semolina inside. Given the uncer-
490
tainty in setting the real pressure at the exit of the compression and melting
491
part of the screw computed with the Tadmor model, corresponding to the
492
inflow of the numerical domain, mass flow rate at the inflow and screw speed
494
495
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were instead set matching experimental data, and temperature and pressure
in the bell were used for comparison. The pressure inside the bell to be
compared with the experimental probe was computed setting the value of
496
the numerical pressure to 20 atm at the inflow; in the following results, we
497
assume that the beginning of the metering section is the same for all mass 28
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Figure 13: Influence of viscous dissipative effects in a extrusion experiment: numerical and experimental data (thermostatic bath temperature set at T=45oC)
flow rates, although a more detailed application of the proposed approach
499
would require to repeat the same procedure for each mass flow rate. The no
500
slip approximation at the barrel was adopted as barrel of the extruder was
501
grooved to minimaze slip phenomena; nonetheless a small slip component at
502
the barrel wall is always present, but lack of experimental data obliged to
503
adopt the no slip assumption. The main responsible for dough heating is
504
the viscous dissipation, an always positive term describing the conversion of
505
mechanical energy to heat, which can be computed instantaneously as:
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2 2 # ∂u2 ∂u3 + τ : ∇v = 2µapp + + ∂x2 ∂x3 " 2 2 2 # ∂u2 ∂u1 ∂u2 ∂u3 ∂u1 ∂u3 µapp =0 + + + + + ∂x1 ∂x2 ∂x3 ∂x2 ∂x3 ∂x1 ∂u1 ∂x1
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2
(14)
The first numerical-experimental comparison was done using the temper-
507
ature history into the extrusion bell during the initial transitory. Results
508
comparing numerical and experimental data during the transitory startup
510
511
512
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of the extruder are shown in Fig. 13; screw rotation set to 20 rpm, thermostatic bath temperature set at Tb ath = 45o C and time 0 was computed
synchronizing the numerical and physical temperature probes for T=46.5C. Several simulation were also performed by varying the screw speed (vary-
29
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Figure 14: Numerical and experimental data comparison for pressure vs mass flow rate in the extruder bell Figure 15: Pressure contours on a longitudinal plane
ing from 10 to 30 rpm )and the mass flow rate, and results compared with ex-
514
periments are reported in Fig. 14 after 20 min of extrusion process (Tbarrel =
515
45o C), showing a very good agreement.
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513
The following results give us an insight in the flow dynamics inside the
517
extruder, and are referred to the case of screw speed set to 20 rpm, Tset =
518
45o C, corresponding to a mass low rate of 6.45 kg/h. The pressure contours
519
on a longitudinal plane is shown in Fig.15, showing the maximum at the end
520
of the metering section as expected.
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The effect of viscous dissipation is more evident by comparing the global
522
temperature field with and without thermostatic bath (adiabatic conditions),
523
as shown in Fig. 16 (a) and (b). The adiabatic simulation was used to
524
computed the Specific Mechanical Energy (SME) of the system, defined as
525
the amount of mechanical energy dissipated as heat per unit mass inside
526
the material with and without considering the heat exchange due to the
527
thermostatic jacket.
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The mechanical energy input transferred by the mechanical shaft to rotate
the screw is mostly lost as heat through viscous dissipation, and an energy
Figure 16: Temperature flow field in thermostatic enforced conditions at T=45oC in the barrel and extrusion bell (a) and adiabatic conditions (b)
30
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Figure 17: Details of temperature(a), viscous dissipation (b), velocity magnitude (c), Axial velocity(d) and radial velocity(e) in a section of the screw (from turn 3 to 7 of the screw flight) Figure 18: Velocity profiles on a normal section (at the center of the channel) at different values of X/L
balance indicates that SME must be equal to the work input from the drive
531
motor into the extruded material, therefore providing a good characterization
532
of the extrusion process [18]. In our case the SME of the extruder at 20 rpm
533
was 290 kJ/kg without the thermostatic jacket on, and 130 kJ/kg in the
534
other case, with a clearance of the screw at the barrel wall set equal to 0.
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A interesting insight provided by the numerical simulation can be ob-
536
tained comparing the temperature , viscous dissipation and velocity in dif-
537
ferent sections of the screw (Fig.17 ) While the velocity field remain almost
538
unchanged from one turn of the screw to another. In Fig.18 velocity profiles
539
on a normal section (at the center of the channel) at different values of X/L
540
(turns of the crew) are plotted,
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535
while the temperature field shows a more complex pattern.
542
The physical mechanism of temperature increase is the following: viscous
543
dissipation (a) generates heat near the wall, particularly near the barrel where
545
546
547
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velocity gradient are more intense; the velocity field (c) is dominated by the axial velocity (d), considering as main axes the helical path passing trough the center of normal sections to the screw shaft. The generated heat is then transported by convection in axial direction, while in the radial direction
31
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Figure 19: Velocity contours field and streamtraces on a normal longitudinal section Figure 20: Viscous dissipation contours in the extruder screw (a) and bell(b) (kgm−1 s−3 )
convective exchanges are limited (e), resulting in a complex temperature field
549
(b) which can not properly be described by using a single normal profile. The
550
analysis of global velocity field shows that no mixing is present neither in the
551
screw nor in the bell: only at the end of the screw a relative intensity mixing
552
is present, as shown in Fig 19
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553
Viscous dissipation is strongly localized on the screw flight near the ex-
554
ternal barrel and in proximity of homogenizing grid as shown in Fig.20 (a)
555
and (b), where the velocity gradients are more intense. Maximum values
556
were reported inside the die extrusion channels.
The presence of low shear zones involves as a consequence high local
558
viscosity values, opposing the mixing like in the centre of the channel or
559
inducing local recirculation zones near the homogenizing grid, a shown in
560
Fig. 21
561
4. Conclusions
563
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In this work a combination of experimental data and numerical models
was proposed and validated to develop a numerical tool to be used to analyze and optimize pasta production process and equipments. In the first Figure 21: Viscosity contours in a longitudinal plane y=0)
32
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part extensive rheological experiments were performed, providing data to
566
model viscosity in all ranges of temperatures and MC interested in indus-
567
trial production. These data are cane be considered an essential basis to
568
build a reliable numerical model. Simulations were then performed by us-
569
ing a modified version of OpenFoam, an open source finite volumes Navier
570
Stokes solver written in C++, whose reliability has been extensively tested
571
in industrial problems. Part of the code was rewritten by the authors to take
572
into account thermal effects for a moving mesh approach of non-newtonian
573
flows. A non-newtonian power law temperature dependent model was used
574
to mimic the rheological behavior of pasta dough respect to the local shear
575
rate, adopting a truncated Taylor expansion to model the temperature de-
576
pendence, and results were then validated on an laboratory extruder, solving
577
the unassessed questions about accuracy of both numerical models and rheo-
578
logical data present in previuosly published works. Significant results confirm
579
that the mixing in the extruder is quite limited, highlighting the necessity to
580
carefully improve the water-semolina mixing before the hydrated semolina
581
enters into the extruder. Variability of local MC conditions can generate
582
unevenly hydrated semolina, with serious consequences on the quality of the
584
585
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final product, considering that the more stressing conditions are induced in the die almost without further mixing. The significant variability of viscosity order of magnitude in the extruder is an other important result to
586
consider, explaining why in low shear zone the high viscosity values corre-
587
sponding to low shear rate values induce local recirculations zones (dead flow 33
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zones) where molds can develop in full scale plants. The analysis of velocity
589
and temperature flow field shows that only adopting an accurate numerical
590
discretization of the domain is possible to capture significant details pro-
591
viding global information like SME or Residence Time Distribution. This
592
integrated experimental-numerical model can be used non only to obtain a
593
better understanding of the phenomena involved in pasta extrusion, but also
594
in equipment optimization and reverse die design.
595
5. Acknowledgement
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Nestl`e is gratefully acknowledged for financial support for rheological experimental investigation.
598
References
599
References
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Shokrpour,
M.(2012).A re-
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view of dough rheological models used in numerical applications,
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Journal of Computational and Applied Research in Mechanical
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Engineering,1,2,129-147.
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[24] Leonard, A. L. Cisneros, F., Kokini ,J. L.(1999). Use of the Rubber
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Elasticity Theory to Characterize the Viscoelastic Properties of Wheat
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Flour Doughs., American Association of Cereal Chemists, Inc. , Vol. 76(2), pp. 243-248.
[25] Chhabra, R.P., Richardson, J.F. (1999). Non-Newtonian Flow in the Process Industries, Butterworth-Heinemann,Oxford.
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[26] Morgan, R. G. Steffe, J. F. , Ofoli, R. Y.(1989). A Generalized Viscosity
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Model for Extrusion of Protein Doughs., Journal of Process Engineering
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, Vol. 2, 57-78.
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[27] Mackey, K. L. Ofoli, R. Y. Morgan, R. G. and Steffe, J. F., (1989)
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”Rheological Modeling of Potato Flour During Extrusion Cooking. ”,
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Journal of Food Process Engineering , Vol. 12, 1-11.
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[28] Dus, S. J., Kokini, J.L.,(1990), Prediction of the nonlinear viscoelastic
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properties of a hard wheat flour dough using the Bird-Carreau consti-
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tutive model,Journal of Rheology 34(7),1069-1084.
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[29] Andrieu, J., Gonnet, E., and Laurent, M., (1989). Thermal con-
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ductivity and diffisivity of extruded durum wheat pasta Lebensm.-
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Wiss.u.Technol. 22: 6-10.
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[30] Weert,X. , Lawrence,C. J., Adams,M. J., Briscoe,B. J.(2001). Screw
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extrusion of food powders: prediction and performance, Chemical En-
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gineering Science, 56, 1933-1949
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[31] Darnell. W. H., Mol. E. A. J. (1956). Solids conveying in extruders.
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[32] Coelho, P.M., Pinhoa, F.T., (2009),A generalized Brinkman number for non-Newtonian duct flows,J. Non-Newtonian Fluid Mech. 156 , 202-206
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Figure Captions:
Fig.2: Standard deviation of MC in the mixture vs. time.
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Fig.1: Gradation analysis of water-semolina agglomerations vs time.
Fig. 3 Influence of mixing time in moisture distribution and viscosity in semolina granulometric classes: a) 1 min, b=6 min.
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Fig 4: Determination of critical shear rate at RH=32% and T = 45°C,T = 50°C,T =55°C.
Fig5: Influence of pre-compression on viscosity curves at RH=32% and T=35°C.
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Fig6: Influence of pre-compression on viscosity curves at RH=32% and T=55°C.
Fig.7: Apparent viscosity experimental results for T=35°C at different values of MC. Fig.8: Power law k consistency coefficient for different temperatures and MC. Fig.9: Power law flow index n for different temperatures and MC.
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Fig. 10: Apparent viscosity experimental data compared with Mackey and Ofoli, Leroux and Vergnes Arrhenius models for MC=32% and T=45°C. Fig.11: Internal geometry of the Sercom experimental extruders (a) and computational grid (b).
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Fig. 12: The velocities and angles used to model pressure in solid conveying zone of the extruder, where vextruder denotes the motion of the plug relative to the engine as a whole, vscrew denotes the motion of the plug in the down channel direction relative to the screw, and vbarrel is the velocity difference between the barrel and the internal plug.
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Fig.13: Influence of viscous dissipative effects in a extrusion experiment: numerical and experimental data (thermostatic bath temperature set at T=45°C). Fig.14: Numerical and experimental data comparison for pressure vs mass flow rate in the extruder bell. Fig.15: Pressure contours on a longitudinal plane (y=0). Fig.16: Temperature flow field in thermostatic enforced conditions at T=45°C in the barrel and extrusion bell (a) and adiabatic conditions (b). Fig.17: Details of temperature(a), viscous dissipation (b), velocity magnitude (c), Axial velocity(d) and radial velocity(e) in a section of the screw (from turn 3 to 7 of the screw flight). Fig.18: Velocity profiles on a normal section (at the center of the channel) at different values of X/L.
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Fig.19: Velocity contours field and streamtraces on a normal longitudinal section. Fig.20: Viscous dissipation contours in the extruder barrel (a) and bell (b) (kg m-1s-3).
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Fig.21: Viscosity contours in a longitudinal plane (y=0).
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94.51 86.83 79.15 71.46 63.78 56.10 48.41 40.73 33.05 25.37 17.68 10.00
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Highlights.
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Extensive experimental results of semolina dough rheology are presented; Arrhenius models for temperature and MC dependence does not fit experiments; Experimental data were modeled using a multivariate Taylor expansion approach ; CFD simulations of extrusion process using the moving mesh approach are presented; Results are validated with experimental data showing a very good agreement.
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