FROM MATHEMATICS
TO REALITY

# Performance of Seals

We built new theory and simulation methods to predict the behavior of sealing solutions before they are manufactured and tested.

Sealing is required wherever a liquid or gas is to be protected from leaking in or out of a container. A popular methodology of sealing is to use gaskets — rings of squishy material that press onto walls of a cavity and prevent liquids or gases from leaking.

The effectiveness of a seal depends on many parameters — the geometries of the seal ring and the cavity, the mechanical pressure on the seal ring, the pressures of the two fluids to be kept separate, the surface properties of the seal and the cavity and the mechanical properties of the material of the seal ring. With so many parameters that can be varied, choosing the optimal design becomes very difficult.

This difficulty is further compounded by the absence of a theory which can predict the performance of a seal given the above parameters. In this project, we created exactly such a theory. This theory can be used to predict the behavior and hence optimize the performance of sealing solutions purely computationally — without any physical trial and error.

## Insight

One of the first insights developed by our team was that any seal is always leaking. The question thus is not whether a particular configuration will or will not successfully seal, but what will the leakage rate be. We built lab instrumentation to characterize leakage rates of various sealing solutions. Data from this instrument has informed our theory development.

## Theory

The multi-physics theory developed by us combines two obvious kinds of physics — solid mechanics and fluid mechanics — to create a theory of seals.

The solid mechanics is used to compute the deformation of the seal given the geometries and the forces. Since one of the forces acting on the seal is fluid pressure, the solid mechanics has to be coupled to the fluid mechanics.

The fluid mechanics of sealing has two aspects. The first aspect is that of leakage mass balance. Given various leakage pathways, and a characterization of each, what is the total leakage rate that can be achieved. This model turns out to be similar to a model from electrical engineering: the discharge of capacitors through a network of resistances. The main mathematical difference is that the resistances in a sealing “network” are non-linear.

The second fluid mechanical aspect is the fluid mechanical computation of the leakage itself. Using believable simplifying assumptions, we created a modified form of the Navier-Stokes equations to model the flow of fluid as it slowly creeps from high pressure to low pressure through the crevices between the seal and cavity surfaces. The flow turns out to depend on the mechanical pressure between the seal and cavity surfaces, and thus, the fluid mechanics has to be coupled to the solid mechanics.

## Computation

We have various computational techniques for calculating seal leakage rates using the above theory. We built a platform using C++ and MATLAB that solves everything from mechanical force balance, to elastomeric deformation, to seal leakage rates. We also built an entire simulation of the above model in COMSOL.

## Conclusion

We get very good agreement between observed and predicted seal performance, and the theory and computational platform can be used to optimize seal designs for various situations.

## Expertise

This project showcases the following expertise of Noumenon Multiphysics:

NOUMENON MULTIPHYSICS PROVIDES MULTI-DISCIPLINARY MODELING AND SIMULATION SERVICES TO THE ENGINEERING INDUSTRY

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