Numerical studies on the self-heating phenomenon of elastomers based on finite thermoviscoelasticity

Due to their typical material characteristics, elastomer components are used in almost all areas of engineering. In many cases, these components are subject to large cyclic deformations which result in hysteresis and dissipation-induced self-heating. Further they are exposed to varying ambient temperatures. Increased component temperatures can lead to the loss of a function or to total failure. Therefore, it is important to understand the causes and influences of critical temperatures and to identify them early in the development process under the condition of efficient applicability. In addition to the calculation time and accuracy, this also includes the experimental effort required to identify the material parameters and perform validation measurements. Within this work, the phenomenon of dissipative heating in elastomers is investigated in a numerical study using a modified model of the finite thermoviscoelasticity. For this purpose, a sufficiently simple material model was formulated and implemented under the assumption of the quasi-incompressible material behaviour. Based on this, the type and the characteristic features of the self-heating effect are specifically considered, and its dependence on thermal and mechanical initial and boundary conditions is studied. Thus, a new suitable parameter is introduced, which is particularly useful to identify critical loads. Analogously, the identification of dissipation-sensitive temperature ranges is presented. The utility of the general steadystate equilibrium condition as initial condition is also shown. Furthermore, the influence of the material properties on the steadystate equilibrium is demonstrated for the first time through parameter studies. Based on these findings, recommendations for modelling, calculation and experimental parameterisation are proposed.

Reply to “Comments on ‘An Evaluation of Hurricane Superintensity in Axisymmetric Numerical Models’”

We concur with Makarieva et al. that in our earlier work on the hurricane differential Carnot cycle, we neglected the work done in lifting water and the dissipation of kinetic energy in the outflow (we explicitly acknowledged neglecting these terms). Here, we relax those assumptions, affirm the conclusion of Makarieva et al. that the water lifting term is small, and show that the effect of outflow dissipation is negligible. We remind readers that the differential Carnot theory is not a closed theory for potential intensity as it does not specify the outflow temperature or the boundary layer moist enthalpy at the radius of maximum winds. The addition of enthalpy to the inflow can raise the boundary layer enthalpy, reducing subsequent surface fluxes, regardless of whether that addition comes from surface fluxes themselves or from dissipative heating. We show that while this may indeed reduce the effect of dissipative heating, it does not eliminate it. We disagree with Makarieva et al.’s assertions that dissipative heating does not increase potential intensity and that only latent heat fluxes can drive tropical cyclones when dissipative heating is included.

Dynamical heating of the X-ray emitting intracluster medium: the roles of merger shocks and turbulence dissipation

ABSTRACT The diffuse plasma inside clusters of galaxies has X-ray emitting temperatures of a few keV. The physical mechanisms that heat this intracluster medium (ICM) to such temperatures include the accretion shock at the periphery of a galaxy cluster, the shocks driven by merger events, as well as a somewhat overlooked mechanism – the dissipation of intracluster turbulent motions. We study the relative role of these heating mechanisms using galaxy clusters in Lagrangian tracer particle re-simulations of the Omega500 cosmological simulation. We adopt a novel analysis method of decomposing the temperature increase at each time-step into the contribution from dissipative heating and that from adiabatic heating. In the high-resolution spatial–temporal map of these heating rates, merger tracks are clearly visible, demonstrating the dominant role of merger events in heating the ICM. The dissipative heating contributed by each merger event is extended in time and also occurs in the rarefaction regions, suggesting the importance of heating by the dissipation of merger-induced turbulence. Quantitative analysis shows that turbulence heating, rather than direct heating at merger shocks, dominates the temperature increase of the ICM especially at inner radii r < r500c. In addition, we find that many merger shocks can propagate with almost constant velocity to very large radii r ≫ r500c, some even reach and join with the accretion shock and becoming the outer boundary of the ICM. Altogether, these results suggest that the ICM is heated more in an ‘inside–out’ fashion rather than ‘outside–in’ as depicted in the classical smooth accretion picture.

Characterization of DC Current Sensors With AC Distortion for Railway Applications

<div>To assess the reliability of dc energy measurement equipment on-board trains, a setup was developed to characterize current transducers under realistic operating conditions. The operating principle is based on a current ratio measurement technique. The reference sensor is a high-precision zero-flux current transducer in combination with a broadband high-precision current shunt. The influence of ac distortion on this reference sensor was found to be within a few parts in 10⁶ using an initial version of the setup, in which ac distortion was applied through a separate winding. A revised version of the setup employs a programmable electronic load to apply dynamic currents up to 600 A. The setup was used to characterize a 100 μohm high-current shunt resistor. The effect of dissipative heating on the dc transresistance error was around 0.03 %, with a settling time of about half an hour. The short-term intrinsic current dependence was also around 0.03 %. The effect of ac distortion was within a few parts in 10⁶. The intrinsic current dependence and the onset of the heating effect were also observed when exposing the sensor to a dynamic current profile that was recorded during a trip between two successive underground train stations on Metro de Madrid. These results demonstrate that the setup described in this paper is very effective for characterizing dc current sensors for practical railway applications. Future work will concentrate on even more demanding current signals, such as chopped signals, and on other types of sensors and measurement systems.</div>

Characterization of DC Current Sensors With AC Distortion for Railway Applications

<div>To assess the reliability of dc energy measurement equipment on-board trains, a setup was developed to characterize current transducers under realistic operating conditions. The operating principle is based on a current ratio measurement technique. The reference sensor is a high-precision zero-flux current transducer in combination with a broadband high-precision current shunt. The influence of ac distortion on this reference sensor was found to be within a few parts in 10⁶ using an initial version of the setup, in which ac distortion was applied through a separate winding. A revised version of the setup employs a programmable electronic load to apply dynamic currents up to 600 A. The setup was used to characterize a 100 μohm high-current shunt resistor. The effect of dissipative heating on the dc transresistance error was around 0.03 %, with a settling time of about half an hour. The short-term intrinsic current dependence was also around 0.03 %. The effect of ac distortion was within a few parts in 10⁶. The intrinsic current dependence and the onset of the heating effect were also observed when exposing the sensor to a dynamic current profile that was recorded during a trip between two successive underground train stations on Metro de Madrid. These results demonstrate that the setup described in this paper is very effective for characterizing dc current sensors for practical railway applications. Future work will concentrate on even more demanding current signals, such as chopped signals, and on other types of sensors and measurement systems.</div>