Narrow gaps are present in rotating and reciprocating machinery such as turbines, compressors, pistons, and gear pumps. These narrow gaps are often essential for the operation of the machinery, as leakage of the working fluid through the narrow gap provides lubrication between the moving parts, and these narrow gaps frequently are moving.
Narrow gaps can also be used in the computational fluid model although not seen in the physical problem. This occurs in models with solid-to-solid contact. For example, consider the reed valve shown in Figure 1. Reed valves are a type of check valve that restrict flow to a single direction, opening and closing under changing pressure on each face. When the reed valve is open, fluid flows from the inlet port to the top chamber. When the reed valve is closed, solid-to-solid contact between the reed valve and the inlet port seat prevents flow.
Ā
(a)Reed valve is open. Fluid flows from the inlet port to the top chamber.
(b) Reed valve is closed. There is no fluid flow.
Figure 1Ā Ā Fluid flow through a reed valve
In the analysis of a reed valve, see here for an example of aĀ piston with a suction reed valve, fluid elements must be meshed under the reed valve for the flow when the reed valve is open (see Figure 1a). When the reed valve is closed, the fluid elements compress, but they cannot be compressed to zero volume, as the fluid formulation requires a positive element volume for the entire analysis. As a result, the fluid model has a narrow gap when the reed valve is closed that is not present in the physical problem (see Figure 1b). The fluid flow through this narrow gap when the valve is closed must be stopped to accurately simulate the response of the reed valve.
In other problems, the narrow gap continuously moves, for example, in scroll compressors. Scroll compressors are used for compressing air or refrigerant in air conditioners, heat pumps, commercial refrigerators, and automobile superchargers. The scroll compressor has two interleaving scrolls: a fixed scroll and an eccentrically orbiting scroll. As the second scroll orbits, the pockets of gas between the interleaving scrolls compress and are pumped towards the center of the scroll compressor, as shown in Figure 2.
Figure 2Ā Orbiting motion of a scroll compressor to compress fluids
(Click on video to play)
Modelling scroll compressors is challenging, as the narrow gap at the contact point between the scrolls continuously moves as the solution progresses (see Figure 2). The fluid elements cannot be compressed to zero-volume at the contact point. In the actual scroll compressor, the leakage at the contact point between the scrolls is either prevented using tip seals, or the scroll compressor is allowed to have small leakage which is minimized by incorporating a āwear-inā design. Hence, the fluid model must either stop leakage through the narrow gap at the continuously moving contact point, or control the leakage to a specified rate. If the fluid model has more leakage than that observed in reality, the pressure will not build up in the scroll compressor and the model will not give accurate results.
Another challenge in modeling problems with continuously moving narrow gaps is dealing with the large mesh displacements. In these problems, the fluid domain often changes significantly as the solution progresses, and the fluid mesh must remain valid at all solution times. A valid fluid mesh is considered to be one with elements that all have positive volume, without severe distortion.
In this Tech Brief, we discuss how to control fluid flow through narrow gaps that continuously move in time usingĀ ADINA FSI. We illustrate this by analyzing a peristaltic pump using ADINA FSI.
Peristaltic Pumps
Peristaltic pumps are a type of positive displacement pump. The fluid is contained within a flexible tube fitted inside the pump casing. The pumping principle, called peristalsis, is based on alternating compression and relaxation of the tube. A rotating shoe passes outside along the length of the tube creating a temporary seal between the suction and discharge sides of the pump. As the pumpās rotor turns the shoe, this sealing action moves along the tube or hose forcing the fluid to move away from the inlet and towards the discharge. Where the pressure has been released the tube recovers creating a vacuum, which draws the product into the suction side of the pump. This pumping process is shown in Figure 3.
Figure 3Ā Pumping process of peristaltic pumps
(Click on video to play)
As nothing but the pump tube touches the fluid, peristaltic pumps are used in applications where the fluid cannot be contaminated, or for pumping dangerous and abrasive chemicals. Common applications include pumping in the food manufacturing industry (beverage dispensing), chemical handing, pharmaceutical production, waste water and water treatment pumping, and pumping in the biomedical industry and medical field; for example, it is used in heart-lung machines to circulate blood during a bypass surgery.
Modeling Peristaltic Pumps using ADINA FSI
Figure 4 shows a schematic of the fluid-structure interaction model of the peristaltic pump modeled using ADINA FSI.
Figure 4Ā Schematic of the peristaltic pump modeled using ADINA FSI
In the solid model, the rubber tube is modeled using 27-node 3D-solid elements with an eight-chain rubber material model. Contact is modeled between the rubber tube and the roller, between the rubber tube and the pump housing, and self-contact in the inner surface of the rubber tube. A small contact offset is applied to the inner surface of the tube, so that the fluid elements contained within the tube are not compressed to zero-volume. The contact offset determines the thickness of the narrow gap and can be easily adjusted without changing the solid or fluid meshes.
In the first cycle, a prescribed displacement is applied to the two rollers to get the rollers into the correct pumping configuration (see animation in Figure 5). Thereafter, the two rollers are rotated without translation at the operating speed (see animation at the top of the Tech Brief). The rollers continuously squeeze the rubber tube pumping the fluid from the inlet to the outlet, as previously described.
Figure 5Ā Ā Animation of the first pump cycle results
In the fluid model, the fluid is modeled using 4-node 3D-fluid elements. Both the solid model and the fluid model undergo large deformations as the roller rotates, see Figure 6.
(a) Animation of the solid mesh deformations
(b) Animation of the fluid mesh deformations
Figure 6Ā Ā Animation of the mesh deformations of the solid and fluid meshes
The fluid elements deform significantly, depending on the location of the roller, from a circular cross-section to a narrow gap. Steered adaptive meshing (SAM) is used to maintain good element quality in the fluid domain and conditional loading is used to control the leakage through the narrow gap.
Steered Adaptive Meshing (SAM)
The below Tech Briefs demonstrate the powerful steered adaptive meshing (SAM) capabilities supported in ADINA for CFD and FSI solutions.
Steered Adaptive Meshing Applications
Steered Adaptive Meshing in ADINA – for CFD
Steered Adaptive Meshing in ADINA – for FSI
In the peristaltic pump model, SAM is used in automatic mode to automatically repair the mesh as the rollers rotate. The user specifies a preferred element size as the criterion used by SAM. SAM automaticallyĀ re-meshesĀ the fluid region during the complete response to maintain good element quality. Figure 7 shows the automatic re-meshing by SAM.
Figure 7Ā Animation of the automatic re-meshing by SAM
Conditional Loading
In the peristaltic pump model, diffusion loading with a boundary distance condition is applied to the fluid to model flow stoppage due to solid-to-solid contact.
The diffusion loading adds additional viscosity to the originally input fluid viscosity. The amount of viscosity added depends on the distance,Ā d, between two external solid boundaries. The load is fully applied to the element whenĀ dĀ ā¤Ā dclosed, and no load is applied whenĀ dĀ >Ā dopen. WhenĀ dclosedĀ <Ā dĀ <Ā dopen, the load is linearly decreased, whereĀ dopenĀ andĀ dclosedĀ are specified by the user. ADINA FSI automatically calculates the distance,Ā d, for every fluid element at all solution times. This distance can change as the solution progress, for example, in a fluid-structure interaction model. Multiple fluid elements are allowed between the external solid boundaries.
Figure 8 shows the additional viscosity automatically added to the narrow gap by the diffusion loading with a boundary distance condition, and Figure 9 shows the velocity field. These figures show that the added viscosity stops flow through the narrow gap. If leakage is desired through the narrow gap, less viscosity should be added.
Figure 8Ā Additional viscosity added by the diffusion loading with a boundary distance condition
Figure 9Ā Velocity field of the peristaltic pump
Conclusion
This Tech Brief demonstrates how to control fluid flow through narrow gaps using ADINA FSI. The capabilities offered in ADINA FSI can be used to accurately model a wide range of problems with flow stoppage due to solid-to-solid contact, or to model flow leakage due to imperfect solid-to-solid contact. A particularly powerful and unique solution capability of ADINA FSI is the ability to control fluid flow through narrow gaps that continuously move in time.
ADINA also offers special-purpose Reynolds fluid elements to model the flow of thin lubricant films. These fluid elements are formulated using the Reynolds equation for smooth and rough boundaries, and provide more accurate and efficient solutions than Navier-Stokes fluid elements for thin lubricant films.
These powerful capabilities make ADINA FSI the preferred analysis software program for FSI analysis of rotating and reciprocating machinery, pumps, and for modeling thin-film hydrodynamic bearings such as journal bearings and thrust bearings.
Keywords:
Conditional loading, boundary-distance condition, diffusion loading, flow-resistance loading, SAM, scroll compressors, peristaltic pumps, gear pumps, reed valves
