|M.Sc Student||Pagi Gilad|
|Subject||An Air-Polymer Analogy for Modeling Air Flow through|
|Department||Department of Mechanical Engineering||Supervisor||Professor Emeritus Eli Altus|
|Full Thesis text|
In this work, we considered a system composed of a metallic cylinder filled with pressured air (up to 5 atm), equipped with metallic lid and a square sectioned rubber ring as a seal. Under a certain pressure difference (internal minus atmosphere pressure) and external sealing force, the rubber seal is compressed and should prevent air leakage. However, experiments show a continuous, nonlinear decrease in the pressure difference as a function of time. The pressure profile was investigated theoretically and experimentally.
A few classical (macro) thermodynamic models for predicting the pressure profile, via describing air flow through cracks, have been suggested before for other applications, but have failed to describe the profile in question due to the coupled constitutive property of rubber and a construction that allows the creation of micro-scale "tunnels" in the rubber-lid interface, through which the air can pass.
A heuristic model is proposed, which assumes a symmetry preserving analogy between the microscale “tunnel like” air streamlines and the rubber polymer strands. Thus, polymer equations based on statistical thermodynamics are applied to the air streamlines. In order to assure the dependence of the streamline topology at the pressure difference, a couple of videotaped experiments were conducted and showed the expected results which support the analogy above.
Using this model, there are four parameters whose values are being set by the experimental profiles, similar to other semi-phenomenological rubber models, such a Moony-Rivlin’s. An excellent correspondence between the model and the experimental data is observed, suggesting that the model captures the physical essence of the phenomenon. The profile wears the form of:
p = (Zt+W)-2L -1(Ce-rt) ; L(x)=-1/x+coth(x).
where the four parameters are: Z,W,C,r. Many standard trendlines have been tried and failed to describe the experimental profile with satisfying accuracy, including 3rd order polynomial which have also four parameters. Moreover, a trendline basing on a sum of two exponents showed good correspondence, but it still cannot top the proposed model results.