Ball Check Valve

A ball check valve is a special type of valve in which a unidirectional fluid flow is ensured. In this valve, a movable spring-loaded ball controls the flow. When no inlet pressure is applied, the ball is forced into contact with an O-ring through the preload in the spring. For an inlet pressure imposing a flow in the operating direction, the slit between the ball and the O-ring opens when the fluid force acting on the ball becomes larger than the spring force. In the case of a flow in the opposite direction, the slit between the ball and the O-ring remains closed and the fluid is thus prevented from passing through the valve.

Figure 1 illustrates the fluid flow around the ball at the maximum opening position.

Figure 1: 3D view of the velocity field within the valve at the maximum opening position. The flow is directed upward in the figure.

In this example, you will learn how to solve a structural contact problem where a fluid is surrounding and acting on the potentially contacting solid parts.

Model Definition

The valve is 35 mm long with an outer diameter of 10 mm. The ball chamber inner diameter is 8.4 mm, and the ball diameter is 7.2 mm. The tube inner diameter is 5 mm. The ball chamber length is 10 mm.

The model geometry is reduced to a 2D axisymmetric cut as shown in Figure 2.

Figure 2: Geometry and materials.

Material Properties

The ball and the valve body are made of steel, the O-ring is made of nylon. The material properties are given in Table 1.

Table 1: valve Material properties
Properties	Structural steel	Nylon
Density	7850 kg/m3	1150 kg/m3
Young’s modulus	200 GPa	2 GPa
Poisson’s ratio	0.3	0.4

The fluid used in this study is water at room temperature.

Boundary Conditions

Solid Mechanics

The ball is free to move along the symmetry axis and is subjected to both a spring load and to the fluid forces. The fluid forces are automatically applied when using the multiphysics coupling. The nylon O-ring is attached to the valve body which is assumed to be rigid. The rigidity is enforced by applying a to the entire valve body.

Structural contact between the ball and the O-ring is modeled.

The spring that holds the ball against the O-ring is not represented in the geometry, instead a spring foundation is used. The spring constant is 4 N/m, and the spring is under 5 mm predeformation when the ball is at rest in the valve. To ensure consistent initial conditions, the spring predeformation is ramped up using a smooth step function.

Turbulent Flow

To study the functioning of the valve, first a reversed flow and then an operating flow are applied. Upstream (bottom) and downstream (top) boundaries are defined as inlet and outlet conditions, respectively, with a varying pressure. The maximum pressure is 25 mbar.

Moving Mesh

The mesh surrounding the ball is set to deform freely, following a Yeoh mesh smoothing deformation. The mesh displacement is controlled by the structural displacement at the boundaries. At the remaining boundaries, adjacent to the fluid, a fixed boundary is used.

Results and Discussion

Figure 3 shows the fluid velocity at the maximum opening of the valve. The maximum velocity is about 2.5 m/s and the main flow path and the recirculation flow around it are clearly visible.

Figure 3: Fluid velocity at the maximum opening of the valve.

Figure 4 shows the pressure distribution in the fluid and the von Mises stress in the solid at maximum opening of the valve.

Figure 4: Fluid pressure and von Mises stress at maximum opening of the valve.

Figure 5 and Figure 6 show the fluid pressure when the valve is closed and under maximum pressure in the reverse direction.

Figure 5: Fluid pressure and von Mises stress at maximum reversed pressure.

Figure 6: Fluid pressure and von Mises stress at maximum reverse pressure (close-up view of the contact region).

The fluid pressure drop when the flow is blocked in the contact region is clearly visible. The contact is almost localized as a single point contact.

Figure 7 shows the ball displacement as a function of time.

Figure 7: Ball center displacement versus time. The inlet pressures are shown for reference.

The ball moves down slightly as the spring predeformation is applied. As the reverse pressure increases, the displacement of the ball is negligible. After 2 s, the flow in the operating direction is increased until the ball reaches a maximum displacement of about 0.30 mm.

Figure 8 shows the flow in the valve as a function of time.

Figure 8: Fluid flow in the valve versus time.

Up to 1 s, the pressure is imposed in the reversed flow direction. The maximum reverse flow is about 0.3 ml/min. This small value is explained by the clearance between the parts in contact which is necessary to avoid topology changes in the fluid domain (see the section Notes About the COMSOL Implementation for more details). The reversed flow can be decreased even more by reducing the contact offset value, at the price of extra solution time caused by mesh refinement.

Figure 9 shows the operating curve of the valve.

Figure 9: Operating curve of the valve.

From this plot, the opening pressure is seen to be about 9 mbar.

Figure 10 shows the fluid pressure drop in the valve together with the inlet pressure conditions applied during the analysis.

Figure 10: Pressure drop in the valve and inlet pressure condition at top boundary/downstream (dashed green) and bottom/upstream boundary (dashed red).

Notes About the COMSOL Implementation

The main purpose of this model is to show how to solve a fluid structure interaction where two elastic parts separated by a fluid can get in contact with each other. The Arbitrary Lagrangian Eulerian (ALE) formulation used for the discretization of the Navier-Stokes equations in a deforming domain requires that the topology of this domain does not change. In a real contact situation, the topology of the fluid domain changes as the parts get into contact. For a numerical analysis, you need to include an offset in the contact settings to prevent the parts to get into physical contact. In this model, the offset is set to a very small value (5 μm) which is sufficient to preserve the fluid-domain topology while still preventing any significant flow in the reverse direction when the valve is closed.

To obtain a good accuracy of the solution, automatic remeshing is used when the ball is getting into contact with the O-ring or is moving away. Because of boundary layer mesh, it is recommended to use distortion as condition for remeshing, here the geometry is remeshed when the square root of the maximum element distortion exceeds 0.5.Figure 11 shows the different meshes generated by the Automatic Remeshing node during the computation.

Figure 11: Mesh cases used during the computation (from top to bottom, left to right).

In order to ensure proper restart after the automatic remeshing, it is important to well refine the mesh at the fluid-structure interface. Moreover in the solver settings you can enforce consistent initialization.

The Fluid-Solid Interaction multiphysics interface adds a node where you define the fluid domains to be controlled by structural deformation at their boundaries. In this model, the displacement of the ball is confined, and it is a good idea to split the fluid region into three domains. The central fluid domain (the one containing the moving ball) uses a freely moving deformed mesh, while the bottom and top fluid domains use a fixed mesh. This way you restrict the computation of the moving mesh equations to a minimum.

In this particular example, the valve body is actually modeled as rigid, so except for the contact region it could have been removed from the model entirely. Keeping it will, however, allow better visualization of the model and results.

In the Fluid-Structure Interaction multiphysics coupling, all boundaries between fluid and solid are selected as a default. You could choose to remove the boundaries adjacent to the rigid domains. Here the coupling type has instead been changed to to avoid adding the extra degrees of freedoms that would be added for a bidirectional coupling in a fixed geometry case.

Structural_Mechanics_Module/Fluid-Structure_Interaction/ball_check_valve

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

In the text field, type u_fluid.

In the table, enter the following settings:


u_fluid
v_fluid
w_fluid

In the tree, select .

Click .

In the tree, select .

Right-click and choose .

Click

In the tree, select .

Click

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
r1	2.5[mm]	0.0025 m	Inner radius
r2	4.2[mm]	0.0042 m	Ball chamber inner radius
r3	3.6[mm]	0.0036 m	Ball radius
r4	5[mm]	0.005 m	Outer radius
l	12[mm]	0.012 m	Ball chamber length
p0	25[mbar]	2500 Pa	Maximum inlet pressure
k0	4[N/m]	4 N/m	Spring constant
l0	5[mm]	0.005 m	Spring predeformation
offset	5[um]	5E-6 m	Contact offset

Geometry 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Rectangle 1 (r1)

In the toolbar, click

In the window for , locate the section.

In the text field, type r4-r1.

In the text field, type l.

Locate the section. In the text field, type r1.

In the text field, type -l.

Rectangle 2 (r2)

In the toolbar, click

In the window for , locate the section.

In the text field, type r4-r2.

In the text field, type l.

Locate the section. In the text field, type r2.

Rectangle 3 (r3)

In the toolbar, click

In the window for , locate the section.

In the text field, type r4-r1.

In the text field, type 3/2*l.

Locate the section. In the text field, type r1.

In the text field, type l.

Union 1 (uni1)

In the toolbar, click

and choose .

Click in the window and then press Ctrl+A to select all objects.

In the window for , locate the section.

Clear the check box.

Fillet 1 (fil1)

In the toolbar, click

On the object , select Point 6 only.

In the window for , locate the section.

In the text field, type r2-r1.

Fillet 2 (fil2)

In the toolbar, click

On the object , select Point 3 only.

In the window for , locate the section.

In the text field, type r2-r1.

Square 1 (sq1)

In the toolbar, click

In the window for , locate the section.

In the text field, type r2-r1.

Locate the section. In the text field, type r1.

Fillet 3 (fil3)

In the toolbar, click

On the object , select Point 4 only.

In the window for , locate the section.

In the text field, type (r2-r1)/2.

Rectangle 4 (r4)

In the toolbar, click

In the window for , locate the section.

In the text field, type r4.

In the text field, type 7/2*l.

Locate the section. In the text field, type -l.

Circle 1 (c1)

In the toolbar, click

In the window for , locate the section.

In the text field, type r3.

In the text field, type 180.

Locate the section. In the text field, type r3.

Locate the section. In the text field, type -90.

You will now create imprints at the expected contact location.

Partition Domains 1 (pard1)

In the toolbar, click

and choose .

On the object , select Domain 1 only.

In the window for , locate the section.

Find the subsection. Click to select the

toggle button.

From the list, choose .

On the object , select Boundary 1 only.

On the object , select Boundary 5 only.

Move 1 (mov1)

In the toolbar, click

and choose .

Select the object only.

In the window for , locate the section.

In the text field, type 0.19 to ensure a clearance slightly above the contact offset.

Union 2 (uni2)

In the toolbar, click

and choose .

Select the objects and only.

In the window for , locate the section.

Clear the check box.

Rectangle 5 (r5)

In the toolbar, click

In the window for , locate the section.

In the text field, type r2.

In the text field, type 10.

With this fourth rectangle object, you will be able to define where to apply a moving mesh domain.

Form Union (fin)

In the window, click .

In the window for , click

Click the

button in the toolbar.

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select .

Right-click and choose .

In the tree, select .

Right-click and choose .

In the tree, select .

Right-click and choose .

In the toolbar, click

to close the window.

Materials

Water, liquid (mat1)

In the window for , click to expand the section.

Nylon (mat2)

In the window, click .

Select Domain 6 only.

In the window for , click to expand the section.

From the list, choose .

Structural steel (mat3)

In the window, click .

Select Domains 3 and 5 only.

In the window for , click to expand the section.

From the list, choose .

In the window, click .

In the window for , in the window toolbar, click

next to

, then choose .

Moving Mesh

Deforming Domain 1

In the window, under click .

Select Domain 2 only.

Definitions

In the toolbar, click

and choose .

Moving Mesh

Prescribed Normal Mesh Displacement 1

Select Boundaries 3 and 7 only.

Definitions

Piecewise 1 (pw1)

In the toolbar, click

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

Locate the section. From the list, choose .

From the list, choose .

In the text field, type 0.45.

Find the subsection. In the table, enter the following settings:


Start	End	Function
-1	0.5	0
0.5	1.5	p0
1.5	5	0

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

In the text field, type Pa.

Piecewise 2 (pw2)

In the toolbar, click

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

Locate the section. From the list, choose .

From the list, choose .

In the text field, type 1.5.

Find the subsection. In the table, enter the following settings:


Start	End	Function
0	3.5	0
3.5	7	p0

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

In the text field, type Pa.

Step 1 (step1)

In the toolbar, click

and choose .

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

Locate the section. In the text field, type 0.5.

In the text field, type -l0.

Click to expand the section. In the text field, type 1.

Integration 1 (intop1)

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Select Boundary 10 only.

Integration 2 (intop2)

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Select Point 7 only.

Locate the section. Clear the check box.

Variables 1

In the window, right-click and choose .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Unit	Description
flow	intop1(w_fluid)	m³/s	Flow

Turbulent Flow, Algebraic yPlus (spf)

In the window, under click .

Select Domains 1, 2, and 4 only.

In the window for , locate the section.

From the list, choose .

Inlet 1

In the toolbar, click

and choose .

Select Boundary 2 only.

In the window for , locate the section.

From the list, choose .

Locate the section. In the p0 text field, type p_inlet(t).

Clear the check box.

Outlet 1

In the toolbar, click

and choose .

Select Boundary 10 only.

In the window for , locate the section.

In the p0 text field, type p_outlet(t).

Clear the check box.

Solid Mechanics (solid)

In the window, under click .

Select Domains 3, 5, and 6 only.

Fixed Constraint 1

In the toolbar, click

and choose .

Select Domain 5 only.

Spring Foundation 1

In the toolbar, click

and choose .

Select Domain 3 only.

In the window for , locate the section.

From the list, choose .

In the ktot table, enter the following settings:


0	0
0	k0

Predeformation 1

In the toolbar, click

and choose .

In the window for , locate the section.

Specify the u0 vector as


0	r
predef(t)	z

You will now set up the contact condition between the ball and the O-ring.

Definitions

Contact Pair 1 (p1)

In the toolbar, click

and choose .

Select Boundary 29 only.

In the window for , locate the section.

Click to select the

toggle button.

Select Boundary 28 only.

Solid Mechanics (solid)

Contact 1

In the window, under click .

In the window for , click to expand the section.

In the doffset,d text field, type offset to prevent the part from getting physically in contact. This way, the topology of the moving mesh domain is kept.

Multiphysics

Fluid-Structure Interaction 1 (fsi1)