Featured Application: A real-time measuring device for contaminated friction of hydraulic spool valve is designed and applied in this paper, which is innovative and practical in the machinery field.Abstract: This paper focuses on the contaminated friction of fit clearance between the spool and valve body to explore the influence principles of clamping stagnation phenomenon. From the perspective of surface morphology and size of particulates in the clearance, designing and manufacturing the valve body, rough spool, conical spool, and standard morphology spool, the test bench was built up and the curves of real-time contaminated friction in the movement of spools were obtained through experiments. The curves show that the contaminated frictions have a feature of pulsation; meanwhile, the stagnation-sensitive size of particulates is between 0.7 and 0.9 times that of clearance. Compared to the ideal morphology spool within the range of sensitive size, the contaminated fiction of rough spool is increased, whereas the lower limit of stagnation-sensitive size range of particulates on conical spool is decreased. The contaminated friction is gradually increased on cis-conical spool but increased first and then decreased on invert cone spool.

The phenomena of concentration and cavitation are identified and analyzed by studying the vanishing pressure limit of solutions to the 3×3 isentropic compressible Euler equations for generalized Chaplygin gas (GCG) with a small parameter. It is rigorously proved that, any Riemann solution containing two shocks and possibly one-contact-discontinuity of the GCG equations converges to a delta-shock solution of the same system as the parameter decreases to a certain critical value. Moreover, as the parameter goes to zero, that is, the pressure vanishes, the limiting solution is just the delta-shock solution of the pressureless gas dynamics (PGD) model, and the intermediate density between the two shocks tends to a weighted δ -measure that forms the delta shock wave; any Riemann solution containing two rarefaction waves and possibly one contact-discontinuity tends to a two-contact-discontinuity solution of the PGD model, and the nonvacuum intermediate state in between tends to a vacuum state. Finally, some numerical results are presented to exhibit the processes of concentration and cavitation as the pressure decreases.

The Riemann problem for the Aw-Rascle (AR) traffic flow model with a double parameter perturbation containing flux and generalized Chaplygin gas is first solved. Then, we show that the delta-shock solution of the perturbed AR model converges to that of the original AR model as the flux perturbation vanishes alone. Particularly, it is proved that as the flux perturbation and pressure decrease, the classical solution of the perturbed system involving a shock wave and a contact discontinuity will first converge to a critical delta shock wave of the perturbed system itself and only later to the delta-shock solution of the pressureless gas dynamics (PGD) model. This formation mechanism is interesting and innovative in the study of the AR model. By contrast, any solution containing a rarefaction wave and a contact discontinuity tends to a two-contact-discontinuity solution of the PGD model, and the nonvacuum intermediate state in between tends to a vacuum state. Finally, some representatively numerical results consistent with the theoretical analysis are presented.

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