A simple closure approximation for slow dynamics of a multiscale system: nonlinear and multiplicative coupling

Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical simulations of such systems often require relatively small time discretization step to resolve fast dynamics, which, in turn, increases computational expense. As a result, it became a popular approach in applications to develop a closed approximate model for slow variables alone, which both effectively reduces the dimension of the phase space of dynamics, as well as allows for a longer time discretization step. In this work we develop a new method for approximate reduced model, based on the linear fluctuation-dissipation theorem applied to statistical states of the fast variables. The method is suitable for situations with quadratically nonlinear and multiplicative coupling. We show that, with complex quadratically nonlinear and multiplicative coupling in both slow and fast variables, this method produces comparable statistics to what is exhibited by an original multiscale model. In contrast, it is observed that the results from the simplified closed model with a constant coupling term parameterization are consistently less precise

Dynamic simulation and exergetic optimization of a Concentrating Photovoltaic/ Thermal (CPVT) system

The development of a dynamic, theoretical model suitable for the prediction of the long-term performance of a parabolic-trough Concentrating Photovoltaic/Thermal CPVT system is discussed in the present study. The formulation of the mathematical model and the considered geometrical and operational parameters of the system, such as the characteristics of the employed PV modules and active cooling system are described in detail. The effect of heat capacity is taken into consideration in the thermal balances and thus the model is able to capture the transient behavior of the system. Besides, the model is validated using available experimental data of a manufactured prototype CPVT system. The daily performance of system is predicted for different values of the cooling fluid flow rate and temperature under various environmental conditions. At a second stage, an exergy analysis is conducted in order to point out the effect of the characteristics of the main system sub-components on the exergetic efficiency and exergy output of the CPVT system. It was established that the system exergetic performance is primarily influenced by the optical quality of the parabolic trough and the electrical efficiency of the PV module. Increasing these two factors to achievable values, e.g. ηopt = 0.75 and ηel = 0.25, can yield an increase of the system exergetic efficiency from 12% to 24%

Robust seismic velocity change estimation using ambient noise recordings

We consider the problem of seismic velocity change estimation using ambient noise recordings. Motivated by [23] we study how the velocity change estimation is affected by seasonal fluctuations in the noise sources. More precisely, we consider a numerical model and introduce spatio-temporal seasonal fluctuations in the noise sources. We show that indeed, as pointed out in [23], the stretching method is affected by these fluctuations and produces misleading apparent velocity variations which reduce dramatically the signal to noise ratio of the method. We also show that these apparent velocity variations can be eliminated by an adequate normalization of the cross-correlation functions. Theoretically we expect our approach to work as long as the seasonal fluctuations in the noise sources are uniform, an assumption which holds for closely located seismic stations. We illustrate with numerical simulations and real measurements that the proposed normalization significantly improves the accuracy of the velocity change estimation

Design and optimization of a micro heat sink for concentrating photovoltaic/thermal (CPVT) systems

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.An optimization methodology for a microchannel heat sink suitable for the cooling of a parabolic trough CPVT system is presented in this study. Two different microchannel configurations are considered, Fixed (FWμ) and stepwise Variable-Width (VWμ) microchannels respectively. The performance evaluation criteria comprise the thermal resistance of the heat sink and the cooling medium pressure drop through the heat sink. Initially, the effect of the geometric parameters on the heat sink thermal and hydrodynamic performance is investigated using a thermal resistance model in order to save computational time. The results of the 1-D model enable the construction of surrogate functions for the thermal resistance and the pressure drop of the heat sink, which are considered as the objective functions for the multiobjective optimization process that leads to the optimal geometric parameters. In a second step, a 3-D numerical model of fluid flow and conjugate heat transfer in the optimized FWμ heat sink is developed in order to investigate in detail the flow and thermal phenomena. The overall analysis demonstrates that microchannel heat sinks achieve very low values of thermal resistance and that the use of variable-width channels can significantly reduce the pressure drop of the cooling fluid. Furthermore, it is proven that the 1-D model is capable of providing a good estimate of the behavior of the heat sink

Homogenization of linear transport equations in a stationary ergodic setting

We study the homogenization of a linear kinetic equation which models the evolution of the density of charged particles submitted to a highly oscillating electric field. The electric field and the initial density are assumed to be random and stationary. We identify the asymptotic microscopic and macroscopic profiles of the density, and we derive formulas for these profiles when the space dimension is equal to one.Comment: 24 page

Multi-objective design optimization of a micro heat sink for Concentrating Photovoltaic/Thermal (CPVT) systems using a genetic algorithm

An optimization methodology for a microchannel, plate-fin heat sink suitable for the cooling of a linear parabolic trough Concentrating Photovoltaic/Thermal (CPVT) system is applied in this study. Two different microchannel configurations are considered, Fixed (FWμ) and stepwise Variable-Width (VWμ) microchannels respectively. The performance evaluation criteria comprise the thermal resistance of the heat sink and the cooling medium pressure drop through the heat sink. Initially, the effect of the geometric parameters on the heat sink thermal and hydrodynamic performance is investigated using a thermal resistance model and analytical correlations, in order to save computational time. The results of the 1-D model enable the construction of surrogate functions for the thermal resistance and the pressure drop of the heat sink, which are considered as the objective functions for the multi-objective optimization through a genetic algorithm that leads to the optimal geometric parameters. In a second step, a 3-D numerical model of fluid flow and conjugate heat transfer for the optimized FWμ heat sink is developed in order to investigate in detail the flow and thermal processes. The overall analysis demonstrates that microchannel heat sinks achieve very low values of thermal resistance and that the use of variable-width channels can significantly reduce the pressure drop of the cooling fluid. Furthermore, it is proven that the 1-D model is capable of providing a good estimate of the behavior of the heat sink

Design and experimental evaluation of a parabolic-trough concentrating photovoltaic/thermal (CPVT) system with high-efficiency cooling

The design and performance evaluation of a novel parabolic-trough concentrating photovoltaic/thermal (CPVT) system are discussed in the present study. Initially, the system design and manufacturing procedures as well as the characteristics of the system sub-components are thoroughly illustrated. At a second stage, the findings in regard to the optical quality of the parabolic trough are presented, as obtained through an experimental procedure that utilizes a custom-made measuring device. The device bears a grid of sensors (photodiodes), so that the irradiation distribution on the receiver surface and the achieved concentration ratio can be determined. Besides, the main factors that have a significant effect on the trough optical quality were identified through ray-tracing simulations. The system electrical and thermal performance was subsequently evaluated in a test rig specially developed for that reason. Three variations of the system receiver incorporating different PV-module and heat-sink designs were evaluated and the prototype CPVT system was found to achieve an overall efficiency approximately equal to 50% (44% thermal and 6% electrical efficiencies, respectively) mainly limited by the trough optical quality, however with a very weak dependency on the operating temperature

Effect of secondary flows due to buoyancy and contraction on heat transfer in a two-section plate-fin heat sink

The effect of buoyancy forces on laminar heat transfer inside a variable width plate-fin heat sink is numerically analyzed: the configuration under investigation comprises an array of rectangular fins, the number of which is doubled at the streamwise middle length of the plate, leading to a stepwise reduction in the respective channel width and hydraulic diameter. The mixed convection problem is thoroughly examined for Archimedes numbers in the range Ar = 1.32-5.82 and Reynolds numbers, based on the channel hydraulic diameter before the stepwise reduction, in the range Re = 559-667, under the thermal boundary condition of axially constant heat flux. It is illustrated that the secondary flow pattern emanating from the flow contraction and manifested through the presence of a pair of counter-rotating horseshoe vortices and a pair of counter-rotating (fin) sidewall vortices interacts with longitudinal rolls created by buoyancy forces. In fact, the lower horseshoe vortices that are co-rotating with the buoyancy-induced rolls are significantly enhanced in magnitude and cause intense fluid mixing in the vicinity of the channel bottom wall, with a substantial distortion of the temperature field. The numerical results indicate that the joint action of the buoyancy-induced rolls and the combined secondary flow pattern has a beneficial impact on the heat sink thermal performance, a fact quantified through the circumferentially-averaged local Nusselt number distributions. The effect of the top lid thermal conductivity on the heat transfer inside the heat sink is also discussed. Finally, a comparative investigation is conducted between the present variable-channel-width configuration and two configurations of fixed-width heat sink designs. The comparative results reveal that the introduction of stepwise channels leads to superior heat transfer performance, i.e. lower values of the total thermal resistance with mitigated pressure drop penalty and increased temperature uniformity on the cooled surface