An optimization-based design approach for a novel self-adjuster using shear thickening fluid

Recently, the increasingly strict safety and emission regulations in the automotive industry drove the interest towards automatic length compensating devices, e.g., hydraulic lash adjusters (lower emission) and slack adjuster in brake systems (faster brake response). These devices have two crucial requirements: (a) be stiff during high load, while (b) be flexible in the released state to compensate for environmental effects such as wear and temperature difference. This study aims to use the advantageous properties of shear thickening fluids to develop a less complicated, cost-efficient design. The proposed design is modeled by a system of ordinary differential equations in which the effect of the non-Newtonian fluid flow is taken into account with a novel, simplified, semi-analytical flow rate-pressure drop relationship suitable for handling arbitrary rheology. The adjuster’s dimensions are determined with a multi-objective genetic algorithm based on the coupled solid-fluid mechanical model for six different shear thickening rheologies. The accuracy of the simplified flow model is verified by means of steady-state and transient CFD simulations for the optimal candidates. We have found that the dominating parameters of such devices are (a) the shear thickening region of the fluid rheology and (b) the gap sizes, while the piston diameters and the zero viscosity or the critical shear rate of the fluid have less effect. Based on the results, we give guidelines to design similar-length compensating devices.

The inviscid limit for the incompressible stationary magnetohydrodynamics equations in three dimensions

This paper is concerned with the zero-viscosity limit of the three-dimensional (3D) incompressible stationary magnetohydrodynamics (MHD) equations in the 3D unbounded domain [Formula: see text]. The main result of this paper establishes that the solution of 3D incompressible stationary MHD equations converges to the solution of the 3D incompressible stationary Euler equations as the viscosity coefficient goes to zero.

Zero viscosity and thermal diffusivity limit of the linearized compressible Navier–Stokes–Fourier equations in the half plane

We study the zero viscosity and thermal diffusivity limit of an initial boundary problem for the linearized Navier–Stokes–Fourier equations of a compressible viscous and heat conducting fluid in the half plane. We consider the case that the viscosity and thermal diffusivity converge to zero at the same order. The approximate solution of the linearized Navier–Stokes–Fourier equations with inner and boundary expansion terms is analyzed formally first by multiscale analysis. Then the pointwise estimates of the error terms of the approximate solution are obtained by energy methods. Thus establish the uniform stability for the linearized Navier–Stokes–Fourier equations in the zero viscosity and heat conductivity limit. This work is based on (Comm. Pure Appl. Math. 52 (1999), 479–541) and generalize their results from isentropic case to the general compressible fluid with thermal diffusive effect. Besides the viscous layer as in (Comm. Pure Appl. Math. 52 (1999), 479–541), the thermal layer appears and couples with the viscous layer linearly.

Conformal Invariance of Characteristic Lines in a Class of Hydrodynamic Models

This paper addresses the problem of the existence of conformal invariance in a class of hydrodynamic models. For this we analyse an underlying transport equation for the one-point probability density function, subject to zero-scalar constraint. We account for the presence of non-zero viscosity and large-scale friction. It is shown analytically, that zero-scalar characteristics of this equation are invariant under conformal transformations in the presence of large-scale friction. However, the non-zero molecular diffusivity breaks the conformal group (CG). This connects our study with previous observations where CG invariance of zero-vorticity isolines of the 2D Navier–Stokes equation was analysed numerically and confirmed only for large scales in the inverse energy cascade. In this paper, an example of CG is analysed and possible interpretations of the analytical results are discussed.