# Numerical Simulation of Static Seal Contact Mechanics Including Hydrostatic Load at the Contacting Interface

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## Abstract

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## 1. Introduction

## 2. Problem Set-Up

## 3. Results

- $p}_{m$: the maximum contact pressure.
- $x}_{m$: the maximum contact pressure location.
- $l}_{h$: length of contact at the high-pressure side, that is, from the location of the fluid front $x}_{f$ to $x}_{m$.
- $l}_{l$: length of contact at the low-pressure side, that is, from $x}_{m$ to the last contact point.
- $p}_{over$: overshoot pressure, that is, the difference between the maximum contact pressure and the sealed fluid pressure; $p}_{over}={p}_{m}-{p}_{f$. The overshoot pressure ${p}_{over}$ equals to the maximum contact pressure, $p}_{m$, when the sealed fluid pressure, ${p}_{f}$, is 0. As $p}_{f$ increases, $p}_{over$ decreases and when $p}_{over$ reaches to 0, leakage occurs.

## 4. Concluding Remarks

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Details of the problem set-up and FE -model, where $\partial {\mathsf{\Omega}}_{b}$ is the part of the boundary, of the bottom surface, on which the sealed fluid pressure $p}_{f$ acts, $\partial {\mathsf{\Omega}}_{c}$ is the contact zone where the contact pressure $p}_{c$ acts, $x}_{f$ is the location of fluid front, that is, the boundary between the sealed fluid and the solid contact zone, and $x}_{m$ is the location where the maximum contact pressure occurs. The friction coefficient between the seal and the vertical sidewall is $\mu $. The total load at vertical direction is ${P}_{t}$ and sealed fluid pressure ${p}_{f}$ is acting at the left vertical side of the seal.

**Figure 3.**Finite element mesh with 16,467 regular elements and 1210 edge elements at the bottom surface.

**Figure 4.**The stress of the contacting surface and gap height between the contacting surfaces. (

**a**) Normalized y-direction stress at the contacting surfaces as a function of the sealed fluid pressure $p}_{f$. The continuous lines represent y-direction stress ${\sigma}_{y}={\sigma}_{y}\left({p}_{f}\right)$ for the situation when there is fluid inside the interface between sealing surfaces, and the total line load density in the vertical direction is ${P}_{t}\left({p}_{f}\right)={P}_{0}+{p}_{f}\lambda$. The dashed lines represent the y-direction stress for the dry contact case under the total line load density ${P}_{t}\left({p}_{f}\right)$, for which the y-direction stress is ${\sigma}_{y}^{\delta}={\sigma}_{y}^{\delta}\left({p}_{f}\right)$. (

**b**) The gap height between the contacting surfaces. The continuous lines represent the gap height between the contacting surfaces $u=u\left({p}_{f}\right)$ for the situation when there is fluid between the sealing surfaces. The dashed lines represent the gap height between the contacting surfaces for the dry contact case under the total line load density ${P}_{t}\left({p}_{f}\right)={P}_{0}+{p}_{f}\lambda $ along y-direction, for which the gap height between the contacting surfaces is ${u}^{\delta}={u}^{\delta}\left({p}_{f}\right)$.

**Figure 6.**Four of the five normalized performance parameters and their variation with the sealed fluid pressure $p}_{f$ and the sidewall friction coefficient $\mu$. (

**a**) The maximum contact pressure, (

**b**) the maximum contact pressure location, (

**c**) length of the contact at the high-pressure side. The dashed line indicating the position of the maximum ${l}_{h}$ for different friction coefficients, (

**d**) length of the contact at the low-pressure side.

**Figure 8.**Movement of the fluid front from its initial location, as a function of the sealed fluid pressure.

**Figure 9.**The overshoot pressure as a function of the sealed fluid pressure and the sidewall friction coefficient $\mu$.

**Figure 10.**The overshoot pressure and its variation with the sealed fluid pressure and the pre-tension, for the side-wall friction coefficient $\mu =0.4$.

**Figure 11.**Dimensionless overshoot pressure as a function of non-dimensional fluid pressure, for a cosinusoidal (

**blue line**) and a parabolic (

**orange line**) bottom surface profile.

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**MDPI and ACS Style**

Huang, D.; Yan, X.; Larsson, R.; Almqvist, A.
Numerical Simulation of Static Seal Contact Mechanics Including Hydrostatic Load at the Contacting Interface. *Lubricants* **2021**, *9*, 1.
https://doi.org/10.3390/lubricants9010001

**AMA Style**

Huang D, Yan X, Larsson R, Almqvist A.
Numerical Simulation of Static Seal Contact Mechanics Including Hydrostatic Load at the Contacting Interface. *Lubricants*. 2021; 9(1):1.
https://doi.org/10.3390/lubricants9010001

**Chicago/Turabian Style**

Huang, De, Xiang Yan, Roland Larsson, and Andreas Almqvist.
2021. "Numerical Simulation of Static Seal Contact Mechanics Including Hydrostatic Load at the Contacting Interface" *Lubricants* 9, no. 1: 1.
https://doi.org/10.3390/lubricants9010001