COMSOL 6.4 - Pasta Extrusion

The pasta extrusion process consists of several steps. After mixing semolina and water, the hydrated semolina is discharged into an extrusion barrel. In the first part of the extruder, the compression and homogenization sections, the dough is in a granular state. In the next section, the metering zone of the extruder, the material is fully melted and the domain is fully filled with the melt.

This example shows how to simulate the nonisothermal flow of the dough in the metering zone of the pasta extruder taking into account temperature dependent material properties of the hydrated semolina dough.

Model Definition

This model is inspired by Ref. 1, and it consist of a screw that feeds the dough through the extrusion bell toward the extrusion holes, where the spaghetti is made. The screw consist of 10 turns. In the bell, the dough is pressed through a screen with 1-mm holes and further into two outlets with 7 spaghetti strands in each one. The material swelling after the dough exits the extrusion holes is neglected in this model. The geometry is shown in Figure 1.

Since the viscosity of the melt is high, the Reynolds number, which describes the ratio of inertia to viscous forces, is low. At low Reynolds numbers, viscous forces dominate over inertia forces. Thus, the latter may be neglected in the Navier–Stokes equations and the interface can be used.

The dough exhibits shear thinning (pseudoplastic) behavior. The power-law model is a common choice for modeling the flow of a dough. To avoid an unphysical infinite viscosity at zero shear rate, COMSOL Multiphysics implements the power-law model as,

(1)

where m is the fluid consistency coefficient, n is flow behavior index,

denotes a reference shear rate, and

is a lower shear rate limit.

Figure 1: Geometry of a pasta screw extruder similar to the one presented in Ref. 1.

Because of viscous heating inside the barrel, the temperature variations during the extrusion operation can be significant. The viscosity of the dough decreases with temperature. To adequately describe the flow, temperature dependent material properties should be used. Rheology experiments (Ref. 1) show that the viscosity is also moisture dependent. The viscosity of the dough decreases with increasing moisture content. As moisture content rises, the influence of the temperature on the viscosity decreases. In this model, the moisture content is assumed to be constant. Temperature dependent coefficients for the non-Newtonian power-law model are obtained by interpolation from a set of measured viscosities for a range of temperatures and 30% moisture content.

To solve the equations for conservation of energy, mass and momentum in the fluid domain, the interface is used. The interface contains a coupling between the and the interfaces, and accounts for viscous dissipation.

The screw is encapsulated in a rotating domain with an angular velocity of 20 rpm. The model utilizes the frozen rotor approach to compute a steady-state flow velocity and a temperature field. A frozen rotor analysis is a memory- and time-efficient steady-state approximation. In a sense, this approach can be described as freezing the motion of the moving part in a given position and then observing the resulting flow field with the rotor in that fixed position.

The inlet is set as an with a boundary stress of 2 MPa. At the outlet, the pressure is set to 0 Pa. For the heat-transfer equation, a heat flux with a heat transfer coefficient of 50 W/(m2·K) and an external temperature of 45°C is set on all outer walls of the extruder. The inlet has a fixed temperature of 45°C, and at the outlet boundaries conditions are applied.

Results and Discussion

The results of the frozen rotor simulation are shown in Figure 2 through Figure 5.

Figure 4 shows the temperature distribution. The temperature increases due to viscous heat dissipation. The viscous heating is generated in the areas with a high shear rate (Figure 5), near the wall of the barrel and inside the extrusion dies. The heat generated near the barrel wall is convected in the axial direction in a helical path along the screw.

The apparent viscosity decreases with increasing temperature (Figure 4). High values of the viscosity in the low-shear-rate zones near the rotating screw lead to poor mixing of the dough.

The velocity plot (Figure 2) shows an uneven velocity distribution in the extrusion channels. This results in different mass flow rates through the extrusion holes and may lead to varying quality of the final product.

Figure 2: Velocity profile in the screw extruder.

Figure 3: Temperature profile in the screw extruder.

Figure 4: Apparent viscosity.

Figure 5: Shear rate.

Reference

1. F. Sarghini, A. Romano, and P. Masi, “Experimental Analysis and Numerical Simulation of Pasta Dough Extrusion Process,” J. Food Eng., vol. 176, pp. 56–70, 2016.

Polymer_Flow_Module/Tutorials/pasta_extrusion

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select > > > .

Click .

Click

In the tree, select > .

Click

Geometry 1

Create the geometry. To simplify this step, insert a prepared geometry sequence.

In the toolbar, click and choose .

Browse to the model’s Application Libraries folder and double-click the file pasta_extrusion_geom_sequence.mph.

In the toolbar, click

Disable the analysis of the geometry as the remaining small geometric details are needed.

In the window, under click .

In the window for , locate the section.

Clear the checkbox.

In the toolbar, click

Moving Mesh

Rotating Domain 1

In the window, under > click .

In the window for , locate the section.

From the list, choose .

Click to expand the section. Locate the section. In the f text field, type 20[RPM].

Locate the section. Specify the urot vector as


1	X
0	Z

Next, define the material properties. The physics interface and the chosen fluid model will suggest which material properties are required to solve the model. Therefore, before creating a semolina dough material, choose the Power law model in the interface.

Laminar Flow (spf)

Fluid Properties 1

In the window, under > click .

In the window for , locate the section.

Find the subsection. From the list, choose .

Materials

Material 1 (mat1)

In the window, under right-click and choose .

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Fluid consistency coefficient	m_pow	m30(T)	Pa·s	Power law
Flow behavior index	n_pow	n30(T)	1	Power law
Heat capacity at constant pressure	Cp	2000	J/(kg·K)	Basic
Thermal conductivity	k_iso ; kii = k_iso, kij = 0	0.242	W/(m·K)	Basic
Density	rho	1200	kg/m³	Basic