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Centrifugal Pump
Introduction
Centrifugal pumps are widely used in the industry and can be found in various applications. These pumps belong to the axisymmetric work-absorbing turbomachinery category for which fluid is transported through the conversion of rotational kinetic energy into hydrodynamic energy. In most applications, fluid enters the pump along the rotating axis and is accelerated by the impeller. The flow is expelled radially outward into a diffuser, or volute chamber, from where it exits. The rotational kinetic energy of the pump is typically supplied by an engine or a motor.
Figure 1: Geometry of the semiopen centrifugal pump.
The current model represents a semiopen centrifugal pump with seven vanes. For the semiopen impeller, the vanes are attached to the hub with a shroud on one side of the impeller. The volute has a spiral shape and the outer radius of the impeller is 10 cm. The size of the modeled pump is typical for automotive applications. The geometry in this work is highly parameterized, allowing straightforward modifications of the geometry to study different configurations of the centrifugal pump if needed.
Model Definition
This model shows how to set up rotating machinery simulations with the frozen rotor approach for centrifugal pumps. The equations that govern the physics are the Navier-Stokes equations and the continuity equation.
A frozen rotor is a cost and time efficient steady-state approximation where individual zones are assigned rotational different speeds. The flow in each of these zones is solved using the moving reference frame equations. 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.
Turbulence is modeled with the k-ω model. This is a widely used model for turbomachinery simulations, with good performance for swirling flows and in the near-wall region.
The pressure condition at the inlet and outlet is set up using the aveop operator:
and
The problem is solved for different total pressure values, ptot, at the inlet in order to obtain a pump curve for the specific geometry considered here.
Results and Discussion
The mass flow is monitored by two probe plots, one at the inlet and one at the outlet. Figure 2 shows that the mass flow at the inlet and the outlet are the equal, which means that mass conservation is achieved.
Figure 2: Mass flow probes at the inlet and the outlet.
Note that the five jumps in the curve represent a change in the given total pressure value at the inlet.
Figure 3: Distribution of the pressure and the velocity magnitude.
Examples of the pressure and velocity magnitude distributions are given in Figure 3. The solution clearly shows a rise in pressure and the corresponding change in velocity from the incoming (inlet) flow, radially toward the volute.
Finally, Figure 4 shows the pump performance curve. The total pressure at the inlet is expressed in terms of the pressure head, H, which is equal to
This curve is central when designing a pump for a given application. Choosing the right pump configuration maximizes the pump and system efficiency, prolongs the life of the system and reduces operational costs.
Table 1 shows the relation between shaft power consumption and pump efficiency.
Table 1: Performance data.
p_tot_in (bar)
Shaft power consumption (Nm/s)
Pump efficiency
-0.050
54.7
0.276
-0.075
52.6
0.382
-0.100
49.8
0.473
-0.125
45.7
0.555
-0.150
39.6
0.620
Figure 4: Pump curve.
Application Library path: Mixer_Module/Tutorials/centrifugal_pump
Modeling Instructions
Begin by loading the geometry file.
From the File menu, choose Open.
Browse to the model’s Application Libraries folder and double-click the file centrifugal_pump_geom_sequence.mph.
Global Definitions
Parameters 1
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
In the table, enter the following settings:
Name
Expression
Value
Description
p_tot_in
0.075[bar]
7500 Pa
Total pressure at the inlet
rot_rpm
1000[rpm]
16.667 1/s
Rotational speed
T_ref
20[degC]
293.15 K
Reference temperature
Geometry 1
Partition Domains 1 (pard1)
1
In the Geometry toolbar, click  Booleans and Partitions and choose Partition Domains.
2
In the Settings window for Partition Domains, locate the Partition Domains section.
3
From the Partition with list, choose Extended faces.
4
On the object cmf2, select Boundaries 13, 14, 73, and 94 only.
5
Find the Domains to partition subsection. Select the  Activate Selection toggle button.
6
On the object cmf2, select Domain 1 only.
7
Click  Build Selected.
Add Physics
1
In the Home toolbar, click  Add Physics to open the Add Physics window.
2
Go to the Add Physics window.
3
In the tree, select Fluid Flow>Single-Phase Flow>Rotating Machinery, Fluid Flow>Turbulent Flow>Turbulent Flow, k-ω.
4
Click Add to Component 1 in the window toolbar.
5
In the Home toolbar, click  Add Physics to close the Add Physics window.
Add Material
1
In the Home toolbar, click  Add Material to open the Add Material window.
2
Go to the Add Material window.
3
In the tree, select Built-in>Water, liquid.
4
Click Add to Component in the window toolbar.
5
In the Home toolbar, click  Add Material to close the Add Material window.
Definitions
Boundary Probe 1 (bnd1)
1
In the Definitions toolbar, click  Probes and choose Boundary Probe.
2
In the Settings window for Boundary Probe, type m_in in the Variable name text field.
3
Locate the Probe Type section. From the Type list, choose Integral.
4
Locate the Source Selection section. From the Selection list, choose Manual.
5
Click  Clear Selection.
6
Select Boundary 58 only.
7
Locate the Expression section. In the Expression text field, type -rhoRef*(u*nx+v*ny+w*nz).
8
Click to expand the Table and Window Settings section. Click  Add Plot Window.
Boundary Probe 2 (bnd2)
1
In the Definitions toolbar, click  Probes and choose Boundary Probe.
2
In the Settings window for Boundary Probe, type m_out in the Variable name text field.
3
Locate the Probe Type section. From the Type list, choose Integral.
4
Locate the Source Selection section. From the Selection list, choose Manual.
5
Click  Clear Selection.
6
Select Boundary 9 only.
7
Locate the Expression section. In the Expression text field, type rhoRef*(u*nx+v*ny+w*nz).
8
Locate the Table and Window Settings section. From the Plot window list, choose Probe Plot 1.
Integration 1 (intop1)
1
In the Definitions toolbar, click  Nonlocal Couplings and choose Integration.
2
In the Settings window for Integration, type int_rot in the Operator name text field.
3
Locate the Source Selection section. From the Geometric entity level list, choose Boundary.
4
From the Selection list, choose Walls 2.
Integration 2 (intop2)
1
In the Definitions toolbar, click  Nonlocal Couplings and choose Integration.
2
In the Settings window for Integration, type int_in in the Operator name text field.
3
Locate the Source Selection section. From the Geometric entity level list, choose Boundary.
4
Click  Paste Selection.
5
In the Paste Selection dialog box, type 57 in the Selection text field.
6
Click OK.
Integration 3 (intop3)
1
In the Definitions toolbar, click  Nonlocal Couplings and choose Integration.
2
In the Settings window for Integration, type int_out in the Operator name text field.
3
Locate the Source Selection section. From the Geometric entity level list, choose Boundary.
4
Click  Paste Selection.
5
In the Paste Selection dialog box, type 6 in the Selection text field.
6
Click OK.
Average 1 (aveop1)
1
In the Definitions toolbar, click  Nonlocal Couplings and choose Average.
2
In the Settings window for Average, locate the Source Selection section.
3
From the Geometric entity level list, choose Boundary.
4
Click  Paste Selection.
5
In the Paste Selection dialog box, type 58 in the Selection text field.
6
Click OK.
Average 2 (aveop2)
1
In the Definitions toolbar, click  Nonlocal Couplings and choose Average.
2
In the Settings window for Average, locate the Source Selection section.
3
From the Geometric entity level list, choose Point.
4
Select Point 4 only.
Variables 1
1
In the Model Builder window, right-click Definitions and choose Variables.
2
In the Settings window for Variables, locate the Variables section.
3
In the table, enter the following settings:
Name
Expression
Unit
Description
rhoRef
aveop2(spf.rhoref)
kg/m³
Reference density
delta_p
int_out(p)/int_out(1)-int_in(p)/int_in(1)
N/m²
Static pressure increase
delta_p_tot
((int_out(p+1/2*rhoRef*spf.U^2)/int_out(1)-int_in(p+1/2*rhoRef*spf.U^2)/int_in(1)))
N/m²
Total pressure increase
Torque
int_rot(+spf.T_stressx*y-spf.T_stressy*x)
N·m
Torque
Power
abs(int_rot(rot1.alphat)*Torque/int_rot(1))
N·m/s
Shaft power consumption
flowrate
int_in(u*nx+v*ny+w*nz)
m³/s
Flow rate
massflow
rhoRef*flowrate
kg/s
Mass flow
H_power
abs(massflow*delta_p_tot/rhoRef)
N·m/s
Power given to fluid
H
delta_p_tot/(rhoRef*g_const)
m
Head
eta
H_power/Power
 
Pump efficiency
Rotating Domain 1
1
In the Model Builder window, click Rotating Domain 1.
2
In the Settings window for Rotating Domain, locate the Domain Selection section.
3
From the Selection list, choose Rotating Domain 1.
4
Locate the Rotation section. In the f text field, type rot_rpm.
5
Locate the Axis section. Specify the urot vector as
0
X
0
Y
-1
Z
Turbulent Flow, k-ω (spf)
Inlet 1
1
In the Model Builder window, under Component 1 (comp1) right-click Turbulent Flow, k-ω (spf) and choose Inlet.
2
Select Boundary 58 only.
3
In the Settings window for Inlet, locate the Boundary Condition section.
4
From the list, choose Pressure.
5
Locate the Pressure Conditions section. From the Pressure list, choose Total.
6
Select the Average check box.
7
In the p0 text field, type p_tot_in.
8
Locate the Turbulence Conditions section. In the Uref text field, type 3[m/s].
Outlet 1
1
In the Physics toolbar, click  Boundaries and choose Outlet.
2
In the Settings window for Outlet, locate the Pressure Conditions section.
3
From the Pressure list, choose Total.
4
Select Boundary 9 only.
Wall 2
1
In the Physics toolbar, click  Boundaries and choose Wall.
2
In the Settings window for Wall, locate the Boundary Selection section.
3
Click  Paste Selection.
4
In the Paste Selection dialog box, type 64, 65, 87, 93 in the Selection text field.
5
Click OK.
6
In the Settings window for Wall, click to expand the Wall Movement section.
7
From the Translational velocity list, choose Zero (Fixed wall).
The Translational velocity is set to Zero (Fixed Wall) to ensure zero velocity at the lower wall. If set to Automatic from frame, it will rotate since it is adjacent to the Rotating Domain.
Mesh 1
Size
In the Model Builder window, under Component 1 (comp1) right-click Mesh 1 and choose Edit Physics-Induced Sequence.
Size 1
1
In the Settings window for Size, locate the Element Size section.
2
From the Predefined list, choose Normal.
Free Tetrahedral 1
1
In the Model Builder window, click Free Tetrahedral 1.
2
In the Settings window for Free Tetrahedral, locate the Domain Selection section.
3
From the Geometric entity level list, choose Domain.
4
Click  Paste Selection.
5
In the Paste Selection dialog box, type 1, 3, 4, 5 in the Selection text field.
6
Click OK.
Boundary Layers 1
1
In the Model Builder window, click Boundary Layers 1.
2
In the Settings window for Boundary Layers, locate the Geometric Entity Selection section.
3
Click  Clear Selection.
4
Click  Paste Selection.
5
In the Paste Selection dialog box, type 1, 3, 4, 5 in the Selection text field.
6
Click OK.
7
In the Settings window for Boundary Layers, click to expand the Corner Settings section.
8
In the Minimum angle for trimming text field, type 280.
Boundary Layer Properties 1
1
In the Model Builder window, expand the Boundary Layers 1 node, then click Boundary Layer Properties 1.
2
In the Settings window for Boundary Layer Properties, locate the Boundary Layer Properties section.
3
In the Number of boundary layers text field, type 5.
4
From the Thickness of first layer list, choose Manual.
5
In the Thickness text field, type 2.5e-4.
Boundary Layer Properties 2
1
Right-click Component 1 (comp1)>Mesh 1>Boundary Layers 1>Boundary Layer Properties 1 and choose Duplicate.
2
In the Settings window for Boundary Layer Properties, locate the Boundary Layer Properties section.
3
In the Thickness text field, type 6e-5.
4
Select Boundaries 24, 27, 31, 36, 42, 45, 48, 75, and 105 only.
Boundary Layer Properties 3
1
Right-click Boundary Layer Properties 2 and choose Duplicate.
2
Select Boundaries 15, 64–69, 87–90, 92, and 93 only.
3
In the Settings window for Boundary Layer Properties, locate the Boundary Layer Properties section.
4
In the Thickness text field, type 2e-4.
Swept 1
In the Mesh toolbar, click  Swept.
Distribution 1
1
Right-click Swept 1 and choose Distribution.
2
In the Settings window for Distribution, locate the Domain Selection section.
3
From the Selection list, choose Manual.
4
Click  Clear Selection.
5
Click  Paste Selection.
6
In the Paste Selection dialog box, type 6 in the Selection text field.
7
Click OK.
8
In the Settings window for Distribution, locate the Distribution section.
9
From the Distribution type list, choose Predefined.
10
In the Number of elements text field, type 10.
11
In the Element ratio text field, type 4.
Distribution 2
1
In the Model Builder window, right-click Swept 1 and choose Distribution.
2
In the Settings window for Distribution, locate the Domain Selection section.
3
Click  Clear Selection.
4
Click  Paste Selection.
5
In the Paste Selection dialog box, type 2 in the Selection text field.
6
Click OK.
7
In the Settings window for Distribution, locate the Distribution section.
8
From the Distribution type list, choose Predefined.
9
In the Number of elements text field, type 20.
10
In the Element ratio text field, type 4.
Use mapped mesh to improve the mesh quality.
Mapped 1
1
In the Mesh toolbar, click  Boundary and choose Mapped.
2
Select Boundaries 113 and 11 only.
Distribution 1
1
In the Model Builder window, right-click Mapped 1 and choose Distribution.
2
Select Edges 247 and 36 only.
3
In the Settings window for Distribution, locate the Distribution section.
4
In the Number of elements text field, type 20.
Distribution 2
1
In the Model Builder window, right-click Mapped 1 and choose Distribution.
2
Select Edges 245 and 16 only.
3
In the Settings window for Distribution, locate the Distribution section.
4
In the Number of elements text field, type 3.
Use mapped mesh to improve the mesh quality.
Mapped 2
1
In the Mesh toolbar, click  Boundary and choose Mapped.
2
Select Boundaries 39, 54, 55, 83, 84, and 97 only.
Distribution 1
1
In the Model Builder window, right-click Mapped 2 and choose Distribution.
2
Select Edges 66 and 159 only.
3
In the Settings window for Distribution, locate the Distribution section.
4
In the Number of elements text field, type 20.
Distribution 2
1
In the Model Builder window, right-click Mapped 2 and choose Distribution.
2
Select Edges 158, 189, and 190 only.
3
In the Settings window for Distribution, locate the Distribution section.
4
In the Number of elements text field, type 3.
Convert the mapped mesh to a triangular mesh.
Convert 1
1
In the Mesh toolbar, click  Modify and choose Elements>Convert.
2
In the Model Builder window, right-click Mesh 1 and choose Build All.
Add Study
1
In the Home toolbar, click  Add Study to open the Add Study window.
2
Go to the Add Study window.
3
Find the Studies subsection. In the Select Study tree, select Preset Studies for Selected Physics Interfaces>Frozen Rotor with Initialization.
4
Click Add Study in the window toolbar.
5
In the Home toolbar, click  Add Study to close the Add Study window.
Study 1
Step 2: Frozen Rotor
1
In the Model Builder window, under Study 1 click Step 2: Frozen Rotor.
2
In the Settings window for Frozen Rotor, click to expand the Results While Solving section.
3
From the Probes list, choose None.
4
Click to expand the Study Extensions section. Select the Auxiliary sweep check box.
5
Click  Add.
6
In the table, enter the following settings:
Parameter name
Parameter value list
Parameter unit
p_tot_in (Total pressure at the inlet)
range(-0.05,-0.1/4,-0.15)
bar
The continuation solver works best for models with linear dependence on the parameter. A more robust alternative for nonlinear applications is to start from the solution for the previous parameter value.
7
From the Run continuation for list, choose No parameter.
8
From the Reuse solution from previous step list, choose Yes.
Solution 1 (sol1)
1
In the Study toolbar, click  Show Default Solver.
2
In the Model Builder window, expand the Solution 1 (sol1) node.
3
In the Model Builder window, expand the Study 1>Solver Configurations>Solution 1 (sol1)>Stationary Solver 2 node, then click Segregated 1.
4
In the Settings window for Segregated, click to expand the Results While Solving section.
5
From the Probes list, choose All.
6
In the Study toolbar, click  Compute.
7
In the Settings window for Convergence Plot 2, Click the right end of the Quick Snapshot split button in the window toolbar.
8
From the menu, choose Zoom Extents.
Results
Study 1/Solution 1 (sol1)
In the Model Builder window, expand the Results>Datasets node, then click Study 1/Solution 1 (sol1).
Selection
1
In the Results toolbar, click  Attributes and choose Selection.
2
In the Settings window for Selection, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Domain.
4
Click  Paste Selection.
5
In the Paste Selection dialog box, type 1 3 4 5 6 in the Selection text field.
6
Click OK.
Exterior Walls
1
In the Model Builder window, click Exterior Walls.
2
In the Settings window for Surface, locate the Selection section.
3
From the Selection list, choose Walls.
Surface Average 1
1
In the Model Builder window, expand the Results>Derived Values node.
2
Right-click Derived Values and choose Average>Surface Average.
3
In the Settings window for Surface Average, locate the Selection section.
4
Click  Paste Selection.
5
In the Paste Selection dialog box, type 58 in the Selection text field.
6
Click OK.
7
In the Settings window for Surface Average, locate the Expressions section.
8
In the table, enter the following settings:
Expression
Unit
Description
w
m/s
Velocity field, z component
Surface Average 2
1
In the Results toolbar, click  More Derived Values and choose Average>Surface Average.
2
In the Settings window for Surface Average, locate the Selection section.
3
Click  Paste Selection.
4
In the Paste Selection dialog box, type 58 in the Selection text field.
5
Click OK.
6
In the Settings window for Surface Average, locate the Expressions section.
7
In the table, enter the following settings:
Expression
Unit
Description
p
bar
Pressure
Performance data
1
In the Results toolbar, click  Global Evaluation.
2
In the Settings window for Global Evaluation, type Performance data in the Label text field.
3
Locate the Expressions section. In the table, enter the following settings:
Expression
Unit
Description
delta_p
N/m^2
static pressure increase
delta_p_tot
N/m^2
total pressure increase
Torque
N*m
torque
Power
N*m/s
shaft power consumption
H_power
N*m/s
power given to fluid
eta
1
pump efficiency
H
1
Head
flowrate
l/min
flowrate
4
Clicknext to  Evaluate, then choose New Table.
Performance data
1
In the Model Builder window, expand the Results>Tables node, then click Table 2.
2
In the Settings window for Table, type Performance data in the Label text field.
Pump Curve
1
In the Results toolbar, click  1D Plot Group.
2
In the Settings window for 1D Plot Group, type Pump Curve in the Label text field.
3
Locate the Data section. From the Dataset list, choose None.
4
Click to expand the Title section.
Table Graph 1
1
Right-click Pump Curve and choose Table Graph.
2
In the Settings window for Table Graph, locate the Data section.
3
From the Table list, choose Performance data.
4
From the Plot columns list, choose Manual.
5
In the Columns list, select Head (m).
6
From the x-axis data list, choose flowrate (l/min).
7
Locate the Coloring and Style section. Find the Line markers subsection. From the Marker list, choose Point.
8
From the Positioning list, choose In data points.
9
In the Pump Curve toolbar, click  Plot.
Velocity (spf)
1
In the Model Builder window, expand the Results>Velocity (spf) node, then click Velocity (spf).
2
In the Settings window for 3D Plot Group, locate the Plot Settings section.
3
Clear the Plot dataset edges check box.
4
Locate the Data section. From the Parameter value (p_tot_in (bar)) list, choose -0.075.
5
Click to expand the Title section. From the Title type list, choose None.
Slice
1
In the Model Builder window, click Slice.
2
In the Settings window for Slice, click to expand the Title section.
3
From the Title type list, choose None.
4
Locate the Plane Data section. From the Plane list, choose xy-planes.
5
In the Planes text field, type 1.
6
Select the Interactive check box.
7
In the Shift text field, type -0.04.
8
Locate the Coloring and Style section. Clear the Color legend check box.
Surface 1
1
In the Model Builder window, right-click Velocity (spf) and choose Surface.
2
In the Settings window for Surface, locate the Data section.
3
From the Dataset list, choose Exterior Walls.
4
Locate the Expression section. In the Expression text field, type 1.
5
Click to expand the Title section. From the Title type list, choose None.
6
Locate the Coloring and Style section. From the Coloring list, choose Uniform.
7
From the Color list, choose Gray.
8
In the Velocity (spf) toolbar, click  Plot.
Slice 2
1
Right-click Velocity (spf) and choose Slice.
2
In the Settings window for Slice, locate the Expression section.
3
In the Expression text field, type p.
4
From the Unit list, choose bar.
5
Locate the Title section. From the Title type list, choose Manual.
6
In the Title text area, type Relative pressure (left, Pa) - Velocity (right, m/s).
7
Locate the Plane Data section. From the Plane list, choose xy-planes.
8
In the Planes text field, type 1.
9
Select the Interactive check box.
10
Locate the Coloring and Style section. From the Color table list, choose AuroraAustralis.
11
Locate the Plane Data section. In the Shift text field, type -0.04.
Deformation 1
1
Right-click Slice 2 and choose Deformation.
2
In the Settings window for Deformation, locate the Expression section.
3
In the x component text field, type 8[cm]*sqrt(2).
4
In the y component text field, type -8[cm]*sqrt(2).
5
Locate the Scale section. Select the Scale factor check box.
6
In the associated text field, type 1.
7
In the Velocity (spf) toolbar, click  Plot.
Slice 3
1
In the Model Builder window, right-click Velocity (spf) and choose Slice.
2
In the Settings window for Slice, locate the Title section.
3
From the Title type list, choose None.
4
Locate the Plane Data section. From the Plane list, choose zx-planes.
5
In the Planes text field, type 1.
6
Select the Interactive check box.
7
Click to expand the Inherit Style section. From the Plot list, choose Slice.
8
Locate the Plane Data section. In the Shift text field, type 0.006.
Surface 2
1
Right-click Velocity (spf) and choose Surface.
2
In the Settings window for Surface, locate the Data section.
3
From the Dataset list, choose Exterior Walls.
4
Locate the Expression section. In the Expression text field, type 1.
5
Locate the Title section. From the Title type list, choose Manual.
6
Locate the Coloring and Style section. From the Coloring list, choose Uniform.
7
From the Color list, choose Gray.
Deformation 1
1
Right-click Surface 2 and choose Deformation.
2
In the Settings window for Deformation, locate the Expression section.
3
In the x component text field, type 8[cm]*sqrt(2).
4
In the y component text field, type -8[cm]*sqrt(2).
5
Click to expand the Title section. Locate the Scale section. Select the Scale factor check box.
6
In the associated text field, type 1.
Velocity (spf)
1
In the Model Builder window, click Velocity (spf).
2
In the Settings window for 3D Plot Group, locate the Title section.
3
From the Title type list, choose Automatic.
4
Locate the Color Legend section. From the Position list, choose Alternating.
Slice
1
In the Model Builder window, click Slice.
2
In the Settings window for Slice, locate the Coloring and Style section.
3
Select the Color legend check box.
4
In the Velocity (spf) toolbar, click  Plot.
5
Click the  Zoom Extents button in the Graphics toolbar.
Pressure (spf)
1
In the Model Builder window, click Pressure (spf).
2
In the Settings window for 3D Plot Group, locate the Data section.
3
From the Parameter value (p_tot_in (bar)) list, choose -0.075.
Pressure
1
In the Model Builder window, expand the Pressure (spf) node, then click Pressure.
2
In the Settings window for Contour, locate the Data section.
3
From the Dataset list, choose Exterior Walls.
4
Locate the Expression section. From the Unit list, choose bar.
5
In the Pressure (spf) toolbar, click  Plot.
6
Click the  Zoom Extents button in the Graphics toolbar.
Wall Resolution
1
In the Model Builder window, expand the Wall Resolution (spf) node, then click Wall Resolution.
2
In the Settings window for Surface, locate the Data section.
3
From the Dataset list, choose Exterior Walls.
4
Locate the Expression section. In the Expression text field, type spf.d_w_plus.
5
In the Wall Resolution (spf) toolbar, click  Plot.
Probe Plot Group 4
1
In the Model Builder window, click Probe Plot Group 4.
2
In the Settings window for 1D Plot Group, locate the Plot Settings section.
3
Select the y-axis label check box.
4
In the associated text field, type mass flow (kg/s).
Probe Table Graph 1
1
In the Model Builder window, expand the Probe Plot Group 4 node, then click Probe Table Graph 1.
2
In the Settings window for Table Graph, locate the Coloring and Style section.
3
Find the Line markers subsection. From the Marker list, choose Cycle.
4
From the Positioning list, choose In data points.
5
Click to expand the Legends section. From the Legends list, choose Manual.
6
In the table, enter the following settings:
Legends
m_in (kg/s)
m_out (kg/s)
7
In the Probe Plot Group 4 toolbar, click  Plot.
Exterior Walls 2
1
In the Results toolbar, click  More Datasets and choose Surface.
2
In the Settings window for Surface, type Exterior Walls 2 in the Label text field.
3
Select Boundaries 1–3, 5, 7, 8, 10, 11, 15, 25–38, 40–53, 56, 59–61, 64–78, 82, 85, 87–90, 92–94, 99, and 101–115 only.
Study 1/Solution 1 (4) (sol1)
In the Results toolbar, click  More Datasets and choose Solution.
Cut Plane 1
1
In the Results toolbar, click  Cut Plane.
2
In the Settings window for Cut Plane, locate the Data section.
3
From the Dataset list, choose Study 1/Solution 1 (4) (sol1).
4
Locate the Plane Data section. From the Plane list, choose xy-planes.
5
In the z-coordinate text field, type 0.0125.
3D Plot Group 6
1
In the Results toolbar, click  3D Plot Group.
2
In the Settings window for 3D Plot Group, locate the Data section.
3
From the Dataset list, choose Study 1/Solution 1 (4) (sol1).
4
From the Parameter value (p_tot_in (bar)) list, choose -0.075.
5
Locate the Plot Settings section. Clear the Plot dataset edges check box.
Surface 1
1
Right-click 3D Plot Group 6 and choose Surface.
2
In the Settings window for Surface, locate the Data section.
3
From the Dataset list, choose Exterior Walls  2.
4
From the Parameter value (p_tot_in (bar)) list, choose -0.075.
5
Locate the Coloring and Style section. From the Coloring list, choose Uniform.
6
From the Color list, choose Gray.
Surface 2
1
In the Model Builder window, right-click 3D Plot Group 6 and choose Surface.
2
In the Settings window for Surface, locate the Data section.
3
From the Dataset list, choose Cut Plane 1.
4
From the Parameter value (p_tot_in (bar)) list, choose -0.075.
5
Locate the Coloring and Style section. From the Color table list, choose JupiterAuroraBorealis.
3D Plot Group 6
In the Model Builder window, click 3D Plot Group 6.
Streamline Surface 1
1
In the 3D Plot Group 6 toolbar, click  More Plots and choose Streamline Surface.
2
In the Settings window for Streamline Surface, locate the Data section.
3
From the Dataset list, choose Cut Plane 1.
4
From the Parameter value (p_tot_in (bar)) list, choose -0.075.
5
Locate the Streamline Positioning section. From the Positioning list, choose Uniform density.
6
In the Separating distance text field, type 0.01.
7
Locate the Coloring and Style section. Find the Line style subsection. From the Type list, choose Tube.
8
In the Tube radius expression text field, type 0.05.
9
Select the Radius scale factor check box.
10
In the associated text field, type 0.005.
11
Find the Point style subsection. From the Color list, choose Custom.
12
On Windows, click the colored bar underneath, or — if you are running the cross-platform desktop — the Color button.
13
Click Define custom colors.
14
Set the RGB values to 105, 105, and 105, respectively.
15
Click Add to custom colors.
16
Click Show color palette only or OK on the cross-platform desktop.
Streamline 2
1
Right-click 3D Plot Group 6 and choose Streamline.
2
In the Settings window for Streamline, locate the Streamline Positioning section.
3
In the Number text field, type 14.
4
Select Boundary 58 only.
5
Locate the Coloring and Style section. Find the Line style subsection. From the Type list, choose Tube.
6
In the Tube radius expression text field, type 0.05.
7
Select the Radius scale factor check box.
8
In the associated text field, type 0.005.
9
Find the Point style subsection. From the Color list, choose Custom.
10
On Windows, click the colored bar underneath, or — if you are running the cross-platform desktop — the Color button.
11
Click Define custom colors.
12
Set the RGB values to 105, 105, and 105, respectively.
13
Click Add to custom colors.
14
Click Show color palette only or OK on the cross-platform desktop.
15
In the 3D Plot Group 6 toolbar, click  Plot.
16
Click the  Zoom Extents button in the Graphics toolbar.