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Register a new userMacroscale boundary conditions for a non-linear heat exchanger
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Multiscale modelling methodologies build macroscale models of materials with complicated fine microscale structure. We propose a methodology to derive boundary conditions for the macroscale model of a prototypical non-linear heat exchanger. The derived macroscale boundary conditions improve the accuracy of macroscale model. We verify the new boundary conditions by numerical methods. The techniques developed here can be adapted to a wide range of multiscale reaction-diffusion-advection systems.
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Multiscale modelling aims to systematically construct macroscale models of materials with fine microscale structure. However, macroscale boundary conditions are typically not systematically derived, but rely on heuristic arguments, potentially resulting in a macroscale model which fails to adequately capture the behaviour of the microscale system. We derive the macroscale boundary conditions of the macroscale model for longitudinal wave propagation on a lattice with periodically varying density and elasticity. We model the macroscale dynamics of the microscale Dirichlet, Robin-like, Cauchy-like and mixed boundary value problem. Numerical experiments test the new methodology. Our method of deriving boundary conditions significantly improves the accuracy of the macroscale models. The methodology developed here can be adapted to a wide range of multiscale wave propagation problems.
Liquid-xenon based particle detectors have been dramatically growing in size during the last years, and are now exceeding the one-ton scale. The required high xenon purity is usually achieved by continuous recirculation of xenon gas through a high-temperature getter. This challenges the traditional way of cooling these large detectors, since in a thermally well insulated detector, most of the cooling power is spent to compensate losses from recirculation. The phase change during recondensing requires five times more cooling power than cooling the gas from ambient temperature to -100C (173 K). Thus, to reduce the cooling power requirements for large detectors, we propose to use the heat from the purified incoming gas to evaporate the outgoing xenon gas, by means of a heat exchanger. Generally, a heat exchanger would appear to be only of very limited use, since evaporation and liquefaction occur at zero temperature difference. However, the use of a recirculation pump reduces the pressure of the extracted liquid, forces it to evaporate, and thus cools it down. We show that this temperature difference can be used for an efficient heat exchange process. We investigate the use of a commercial parallel plate heat exchanger with a small liquid xenon detector. Although we expected to be limited by the available cooling power to flow rates of about 2 SLPM, rates in excess of 12 SLPM can easily be sustained, limited only by the pump speed and the impedance of the flow loop. The heat exchanger operates with an efficiency of (96.8 +/- 0.5)%. This opens the possibility for fast xenon gas recirculation in large-scale experiments, while minimizing thermal losses.
In this paper we analyze a nonlinear parabolic equation characterized by a singular diffusion term describing very fast diffusion effects. The equation is settled in a smooth bounded three-dimensional domain and complemented with a general boundary condition of dynamic type. This type of condition prescribes some kind of mass conservation; hence extinction effects are not expected for solutions that emanate from strictly positive initial data. Our main results regard existence of weak solutions, instantaneous regularization properties, long-time behavior, and, under special conditions, uniqueness.
The LUX (Large Underground Xenon) detector is a two-phase xenon Time Projection Chamber (TPC) designed to search for WIMP-nucleon dark matter interactions. As with all noble element detectors, continuous purification of the detector medium is essential to produce a large ($>$1ms) electron lifetime; this is necessary for efficient measurement of the electron signal which in turn is essential for achieving robust discrimination of signal from background events. In this paper we describe the development of a novel purification system deployed in a prototype detector. The results from the operation of this prototype indicated heat exchange with an efficiency above 94% up to a flow rate of 42 slpm, allowing for an electron drift length greater than 1 meter to be achieved in approximately two days and sustained for the duration of the testing period.
An experimental realization of a heat exchanger with commercial thermoelectric generators (TEGs) is presented. The power producing capabilities as a function of flow rate and temperature span are characterized for two different commercial heat transfer fluids and for three different thermal interface materials. The device is shown to produce 2 W per TEG or 0.22 W cm$^{-2}$ at a fluid temperature difference of 175 $^circ$C and a flow rate per fluid channel of 5 L min$^{-1}$. One experimentally realized design produced 200 W in total from 100 TEGs. For the design considered here, the power production is shown to depend more critically on the fluid temperature span than on the fluid flow rate. Finally, the temperature span across the TEG is shown to be 55% to 75% of the temperature span between the hot and cold fluids.
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