COMSOL 6.4 - Screw Conveyor

A screw conveyor is a mechanical device that is commonly used to move bulk granular materials. They can be used to transport the materials either horizontally or over an incline, which also allows for elevating the material. Additional specialized tasks such as heating, cooling, drying and mixing can also be incorporated along with the transport process. Screw conveyors are widely used across various industries including food processing, pharmaceuticals, chemical industries, agriculture, cosmetics, and plastics.

A screw conveyor typically consists of a U-shaped trough or a tube with a rotating central shaft along its length. The central shaft contains helical screw that is rotated about its axis. The amount of material transported and its speed is affected by several factors including the material and contact properties of the grains and the walls, filling level of the trough, and rotational speed. The mass-flow rate is often proportional to the rotational speed.

This example uses the Granular Flow interface to model the transport of grains using a screw conveyor operated at a constant rotational speed. This model also shows the use of a Bounding Box feature to avoid scenarios that may adversely affect the performance of the Granular Flow interface. The mass-flow rate through the conveyor is evaluated using a Model Method.

Model Definition

The geometry consists of a cylindrical tube with a casing radius of 20.4 cm and a length of 1.3 m. A central shaft of radius 10 cm runs through the length of the tube. The central shaft has helical screw blades attached to it with a pitch of 20 cm and a gap of 4 mm between the blade and the tube. The overall length of the shaft is such that there are six turns of the helix. The tube and the screw are rotated to have an inclination of 10 degrees. The grains enter the tube via conical hopper and exit via a circular outlet at the other end of the tube. The geometry is presented in Figure 1.

The grains have a density of 4200 kg/m3 and a diameter of 10 mm. The grains are released in ten batches of 2500 grains each with an interval of 0.5 s. The screw is rotated at a constant angular speed of 120 rpm. The transport of the grains is simulated for a total of 20 s. The mass-flow rate through the screw conveyor is measured by evaluating the overall mass of the grains that pass through an imaginary plane in the middle of the tube.

Figure 1: Model geometry.

Notes About the COMSOL Implementation

The model is solved using a single study step. The grains are released into the conical hopper using the feature. The rotation of the screw is controlled by the settings in the feature. The grains can pass through the interior boundaries and out of the tube using an feature. The grains exiting the tube can continue moving away from the trough, which can adversely affect the performance of the Granular Flow interface.

The maximum allowed time step taken by the in Granular Flow is often limited by the collision time scales of the grain-grain and grain-wall interactions. The collision time scales are often strongly dependent on the material properties such as density and Young’s modulus with stiffer grains generally exhibiting smaller collision times, thus requiring even smaller time steps. In many instances however, the stiffness of the grains and walls have a very limited effect on the bulk behavior of granular materials, and the materials can thus be made artificially less stiff in order to speed up the simulations.

A feature is used to remove such grains from the simulation. An user-defined variable is added to each grain to keep track of the grains that pass through an imaginary plane. The mass-flow rate can then be obtained by counting the overall mass of the grains that pass through the plane in a given time window divided by the length of the time window. This averaging of the time series data is achieved by adding and running a Model Method.

Model methods can only be set up in the COMSOL Desktop environment on the Windows version of COMSOL Multiphysics.

Results and Discussion

A snapshot of the grain positions in the middle of the transport process is shown in Figure 2. The grains are colored based on their release time. The inclination and the gap between the blade and the tube causes some grains to be left behind at one end of the tube, while most of the grains are transported to the other end. There grain colors indicate that some amount of mixing occurs during the transport.

The forces experienced by the screw due to the grain impact is an important factor in the design and operation of a screw conveyor. Figure 3 shows the forces at the same instant of time as in Figure 2. It is clear that the maximum forces are experienced near the parts of the screw that is exposed to the largest number of grains. These forces can then be used to evaluate the power draw required to operate the conveyor and the wear rate of the screw blades.

Finally, Figure 4 presents the plot of the mass-flow rate as defined as the overall rate mass of the grains that transit an imaginary plane. Since the plane is located in the middle of the tube, the calculated flow rate is 0 in the beginning. It slowly rises until it reaches a peak of about 3.8 kg/s before it starts decreasing as the bulk of the grains pass through the plane. This peak could be interpreted as the overall mass-flow rate of the device when operated under similar conditions in a continuous configuration as opposed to the batch configuration used in this model.

Figure 2: Grain positions at the end of 10 seconds. The grains are colored by their release time.

Figure 3: Forces on the screw at the end of 10 seconds.

Figure 4: Mass-flow rate as a function of time.

Granular_Flow_Module/Transport/screw_conveyor

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

In the toolbar, click and choose .

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

In the toolbar, click

Click the

button in the toolbar.

Click the

button in the toolbar.

Click the

button in the toolbar. The geometry should look like Figure 1.

Global Definitions

Parameters 2

In the toolbar, click

and choose > .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
dg	10[mm]	0.01 m	Grain diameter
om	120[rpm]	2 1/s	Angular speed
N	2500	2500	Number of grains per release

Geometry 1

Work Plane 3 (wp3)

In the toolbar, click

In the window for , locate the section.

From the list, choose .

On the object , select Edge 3 only.

Click to select the

toggle button for .

On the object , select Boundary 2 only.

Select the checkbox.

In the toolbar, click

and choose .

Definitions

System from Geometry 2 (sys2)

In the window for , locate the section.

From the list, choose .

Variables 1

In the toolbar, click

and choose .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Unit	Description
include	gran.mg(abs(sys2.x1-(L+2sw)/2)<dg/2)	kg	Boolean for inclusion

Materials

Grains

In the toolbar, click

In the window for , type Grains in the text field.

Click to expand the section. In the tree, select > .

Click

In the tree, select > .

Click

In the tree, select > .

Click

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Density	rho	4200	kg/m³	Basic
Poisson’s ratio	nu	0.4	1	Basic
Young’s modulus	E	11[MPa]	Pa	Basic

Walls

In the toolbar, click

In the window for , type Walls in the text field.

Locate the section. From the list, choose .

From the list, choose .

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Young’s modulus	E	25[MPa]	Pa	Basic
Poisson’s ratio	nu	0.35	1	Basic

Granular Flow (gran)

Grain Properties 1

In the window, under > click .

In the window for , locate the section.

From the list, choose .

Locate the section. In the dg text field, type dg.

Release 1

In the toolbar, click

and choose .

Select Domain 2 only.

In the window for , locate the section.

In the text field, type range(0,0.5,4.5).

Locate the section. In the table, enter the following settings:


Released grain properties	Number of grains
Grain Properties 1	N

Screw

In the toolbar, click

and choose .

In the window for , type Screw in the text field.

Locate the section. From the list, choose .

In the ω text field, type om.

Specify the eax vector as


sys2.e_x11	X
sys2.e_x12	Y
sys2.e_x13	Z

Force Accumulator 1

In the toolbar, click

and choose .

Contact Between Grains 1

In the window, under > click .

In the window for , locate the section.

In the en text field, type 0.8.

In the et text field, type 0.7.

In the μs text field, type 0.4.

In the μr text field, type 0.3.

In the μtw text field, type 0.25.

Contact with Walls 1

In the window, click .

In the window for , locate the section.

In the en text field, type 0.85.

In the et text field, type 0.76.

In the μs text field, type 0.5.

In the μr text field, type 0.2.

In the μtw text field, type 0.18.

Outlet 1

In the toolbar, click

and choose .

Select Boundaries 21, 71, and 72 only.

Bounding Box 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Study 1

Step 1: Time Dependent

In the window, under click .

In the window for , locate the section.

In the text field, type range(0,0.25,20).

In the toolbar, click

Results

Grain Positions (gran)

In the window for , locate the section.

From the list, choose .

Click the

button in the toolbar.

Click the

button in the toolbar.

Click the

button in the toolbar.

In the window, expand the node.

Color Expression 1

In the window, expand the > > node, then click .

In the window for , locate the section.

In the text field, type gran.rti.

In the toolbar, click

. The plot should look like Figure 2.

Forces on the screw

In the toolbar, click

In the window for , type Forces on the screw in the text field.

Locate the section. From the list, choose .

From the list, choose .

Locate the section. Clear the checkbox.

Surface 1

In the toolbar, click

In the window for , locate the section.

In the text field, type gran.wp2.facc1.wf.

Locate the section. From the list, choose .

Deformation 1

In the toolbar, click

In the window for , locate the section.

In the text field, type comp1.gran.x-x.

In the text field, type comp1.gran.y-y.

In the text field, type comp1.gran.z-z.

Locate the section.

Select the checkbox. In the associated text field, type 1.0.

Surface 1

In the window, click .

Selection 1

In the toolbar, click

In the window for , locate the section.

From the list, choose .

In the toolbar, click

. The plot should look like Figure 3.

Grain Positions

In the toolbar, click

and choose .

In the window for , type Grain Positions in the text field.

Locate the section. From the list, choose .

Click the

button in the toolbar. This plays the animation of the grains being transported by the screw conveyor.

Forces on the Screw

Right-click and choose .

In the window for , type Forces on the Screw in the text field.

Locate the section. From the list, choose .

Click the

button in the toolbar. This plays the animation of the forces on the screw conveyor resulting from the grain-wall contacts.

Application Builder

The mass flow rate can be computed using an Application Method. These may be added to an existing model via a using the . Note that the is only available in the Windows® version of the COMSOL Desktop. But once the is created, it can be run in both the Linux and Mac versions.

In the toolbar, click

Methods

The code for the computing and plotting the mass flow rate can be simplified by using utility classes.

util1

In the toolbar, click

and choose .

In the window, right-click and choose .

Copy the code for the utilities createGrainEval, createGridDataSets, updateDatsets, plotFlowRate and getPlotFeature and paste it into the editor for util1.

// Create the Grain evaluations
public static NumericalFeature createGrainEval(String tag, String data, String level, NumericalFeatureList numericalList) {
   NumericalFeature grn;
   if (numericalList.index(tag) == -1)
     grn = model.result().numerical().create(tag, "Grain");
   else
     grn = numericalList.get(tag);
   grn.setIndex("looplevelinput", level, 0);
   grn.set("data", data);
   return grn;
}

/* Create the interpolation functions and the grid data sets*/
public static void createGridDataSets(String[] myTags, int num_steps, double[][] data) {
   FunctionFeatureList functionList = model.func();
   FunctionFeature functionFeature;

   for (int i = 0; i < myTags.length; i++) {
     if (functionList.index(myTags[i]) == -1) {
       functionFeature = functionList.create(myTags[i], "Interpolation");
       functionFeature.label(myTags[i]);
       with(functionFeature);
         set("funcname", myTags[i]);
         set("interp", "piecewisecubic");
         set("extrap", "const");
         set("defineprimfun", true);
       endwith();
     }
     else {
       functionFeature = functionList.get(myTags[i]);
     }

     with(functionFeature);
       set("table", new String[0][0]);
       for (int k = 0; k < num_steps; k++) {
         setIndex("table", data[k][0], k, 0);
         setIndex("table", data[k][i+1], k, 1);
       }
     endwith();

     String pmin = toString(data[0][0]);
     String pmax = toString(data[num_steps-1][0]);
     String[] params = {pmin, pmax, "out"};
     util1.updateDatsets(i, params, myTags);
   }
}

/** Create or update the grid datasets. */
public static void updateDatsets(int i, String[] param,
                                  String[] tagList) {
   DatasetFeature dataFeature;
   if (model.result().dataset().index(tagList[i]) == -1) {
     dataFeature = model.result().dataset().create(tagList[i], "Grid1D");
     dataFeature.label(tagList[i]);
   }
   else {
     dataFeature = model.result().dataset().get(tagList[i]);
   }
   with(dataFeature);
     set("source", "function");
     set("function", tagList[i]);
     set("parmin1", param[0]);
     set("parmax1", param[1]);
     set("par1", param[2]);
   endwith();
}

/* Add the line plots for the flow rate */
public static void plotFlowRate(String[] myList, String[] myTags)
{
   // Create or get the plot group
   ResultFeature myPlot = util1.getPlotFeature("Flow Rate");
   // Create or get the line graphs
   ResultFeatureList myPlotList = myPlot.feature();

   int num_plots = myList.length;
   for (int i = 0; i < num_plots; i++) {
     if (myPlotList.index(myTags[i]) == -1) {
       ResultFeature miPlotLine = myPlot.create(myTags[i], "LineGraph");
       String expr_str = myTags[i]+"(out)";
       with(miPlotLine);
         set("xdata", "expr");
         set("expr", expr_str);
         set("xdataexpr", "out");
         set("xdatadescractive", true);
         set("xdatadescr", "Time (s)");
         set("data", myTags[i]);
         set("descr", "Flow Rate");
         set("legend", true);
         set("autodescr", true);
         set("autosolution", false);
         set("descractive", true);
         set("smooth", "none");
         set("resolution", "norefine");
         set("linewidth", 2);
       endwith();
     }
   }
}

/** Create or get the plot feature. */
public static ResultFeature getPlotFeature(String pLabel) {
   ResultFeature myPlot;
   String pTag = "";
   String pLabel_in = pLabel;
   String[] rTag = model.result().tags();

   for (int i = 0; i < rTag.length; i++) {
     if (findIn(model.result(rTag[i]).label(), pLabel_in) > -1) {
       pTag = rTag[i];
       pLabel = model.result(rTag[i]).label();
     }
   }

   if (pTag.length() == 0) {
     pTag = model.result().uniquetag("pg");
     myPlot = model.result().create(pTag, "PlotGroup1D");
     myPlot.label(pLabel);
     with(myPlot);
       set("data", "none");
       set("titletype", "none");
       set("legendpos", "upperright");
       set("ylabelactive", true);
       set("ylabel", "Mass flow rate (kg/s)");
     endwith();
   }
   else
     myPlot = model.result().get(pTag);
   return myPlot;
}

Global Method

Now add a to compute the mass flow rate that uses the utility functions.

In the toolbar, click and choose .

In the dialog, type computeMassFlowRate in the text field.

Click .

Add the inputs and their default values for the method computeMassFlowRate.

In the window for , locate the section.

Find the subsection. Click

In the table, enter the following settings:


Name	Type	Default	Description	Unit
window	String	11	Length of smoothing window

computeMassFlowRate

In the window, under click .

Copy the code for method computeMassFlowRate and paste it into the editor.

int twin = Integer.parseInt(window);
if (twin%2 == 0)
   twin++;

NumericalFeatureList numericalList = model.result().numerical();
NumericalFeature grn1 = util1.createGrainEval("grn1", "gran1", "all", numericalList);
grn1.set("expr", "include");
double[][] out = transpose(grn1.getReal());

// Get the output time parameters
String tlist = model.study("std1").feature("time").getString("tlist");
String[] tlist_arr = tlist.split(",");
double t_beg = model.param().evaluate(tlist_arr[0].split("\\(")[1]);
double dt = model.param().evaluate(tlist_arr[1]);

int numSteps = out.length;
int numGrains = out[0].length;

double[][] flowRate = new double[numSteps-twin+1][2];
for (int i = twin/2; i < numSteps-twin/2; i++) {
   flowRate[i-twin/2][0] = t_beg+i*dt;
   flowRate[i-twin/2][1] = 0;
   for (int j = 0; j < numGrains; j++) {
     for (int k = i-twin/2; k <= i+twin/2; k++) {
       if (out[k][j] > 0.0) {
         flowRate[i-twin/2][1] += out[k][j];
         break;
       }
     }
   }
   flowRate[i-twin/2][1] /= (twin*dt);
}

String[] myList = new String[]{"FlowRate"};
String[] myTags = new String[]{"flr"};

util1.createGridDataSets(myTags, flowRate.length, flowRate);
util1.plotFlowRate(myList, myTags);

Methods

In the toolbar, click

to switch to the main desktop.

Add a to computeMassFlowRate in order to run it.

In the toolbar, click

and choose .

Global Definitions

Compute Mass Flow Rate

In the window, under click .

In the window for , type Compute Mass Flow Rate in the text field.

Click

. Click if the Confirm Run Method dialogue box appears. This produces an feature which is then used to create the plot of the mass flow rate as a function of time.

Results

Flow Rate

In the window, under click .

In the toolbar, click