## Applied Convective Transfers and Solar Energies

Members of this topic: M. Pons, V. Bourdin, M.-C. Duluc, M. Jarrahi, G. Defresne, M. Firdaouss, E. Tapachès, M. Pavlov, S. Wullens.

Following sub-topics are studied by the group:

### Unsteady laminar free convection around a modulated line heat source

We herein study the unsteady laminar free convective flow created by a linear heat source dissipating a sinusoidal heat flux $$\dot{q}' (t) = \dot{q}'_0[ 1+a sin(2\pi ft) ]$$. An experimental set-up has been constructed: a thin platinum wire, 100 μm in diameter, is immersed in a large pool of water. Once the laminar flow around the wire heated with a constant flux $$\dot{q}'_0$$ is established, an additional sinusoidal heating perturbation is supplied to the wire: $$\dot{q}'_0 a sin(2\pi ft)$$ . The wire temperature is measured over a wide frequency spectrum, showing that the thermal behavior of the solid-fluid system is that of a low-pass-filter (Illustration 1). A  simplified theoretical approximation has been derived yielding trends which are roughly consistent with the experimental data (see Illustration 7).  Although inaccurate, this analytical prediction qualitatively explains why the temperature amplitude vanishes for high frequency heating perturbations.

Moreover, 2D cartesian numerical simulations have been performed with the in-house CFD code Sunfluidh (Y. Fraigneau, P2I). A good match with the experimental results is obtained (Illustration 1).

Such simulations give more insight, for instance on the penetration depth of perturbations, the amplitude of which decreases when the distance from the wire increases. Quantitative laws for correlating these three parameters are currently under identification. In the next future, we will consider more complex configurations, such as two wires close to each other and submitted to independent heating conditions. We expect the possibility to enhance the heat flux around one wire (at least) thanks to a correctly designed heating function inside the second wire.

### Mixing improvement by vortex manipulation

M. Jarrahi’s former laboratory (LTN-UMR 6607, Nantes) studies multifunctional heat exchangers, mixers, or reactors in order to suggest new solutions that would increase their efficiency and reduce their size. He temporarily continued some of his previous studies on chaotic advection and on flow separation and recombination. This also led him to initiate a new collaboration with LIED (UMR 8236, Paris Diderot) on the flow characteristics and mixing quality when the fluid contains autonomously moving particles, e.g. micro-swimmers. Experimental investigation of this emerging issue should develop in the next years.

### Photovoltaic (PV) panels enhanced by fixed planar reflectors - Experiments, simulations and analysis.

Increasing the solar flux received by solar absorbers or PV cells with the help of fixed mirrors is not a new idea (Tabor H. Stationary mirror systems for solar collectors, Solar Energy 2, 27-33 (1958)). In close collaboration with GeePs (ex-LGEP, Orsay) and LMD, we test and simulate such arrangements; this is the ALEPh project. GeePs is expert in PV semiconductor physics and PV cells characterisation; LMD is an expert in theory and measurements of meteorological data, and in solar resource forecasting. This work combines experiments on the SIRTA observatory (Palaiseau, see illustration 3) recording performance of so-enhanced PV panels, and two models developed by M. Pavlov for his PhD thesis. Our experiments demonstrate that daily electricity production can be enhanced by a factor ranging from 5 to 32%, see Illustration 4.

In the models, the optical issues are solved either with the Infinite Row Model (IRM), based on Cartesian optics and analytical solutions, or with the Ray Tracing Model (RTM), developed under the EDStar (RAPSODEE-ENSTIMAC) environment. In addition, the most important physical phenomena, namely electrical and thermal factors, are non-linear and coupled. The aim of the ALEPh project is to build a global model that would optimize geometry and materials for producing electricity in a given location and climate. Beyond reflection, absorption and transmission of visible and near-infrared radiations, calculation of the irradiation, and temperature dependence of cell efficiency, we pay special attention on insolation heterogeneities and on photocurrent mismatches that have not been studied yet. We presently study 1) the spectral composition of solar and diffuse irradiations, and 2) the spectral and angular distributions of the optical properties of reflectors and of panels (strongly dependent on cleanliness) and their influence on the electric producible energy. Besides, the dependence of panel temperature on radiative and convective transfers has recently been addressed (D. Chigara). Calculations based on radiative calculations and phenomenological correlations for convection compare well with temperature measurements done on the back-side of the panels, even under high solar flux. All those results open the way toward simulation of panel temperature in outdoor environment.

### Dynamic simulation of linear Fresnel solar receptors.

Like other solar technologies, Fresnel receptors for concentrated solar power are mainly tested in deserts. However, a significant part of mankind lives in tropical climates, where cloud coverage is frequent and chaotic, like in La Réunion island. Models based on pseudo-stationary states, which are almost the only ones reported in the literature, are no longer valid. This is why our approach, developed in close collaboration with PIMENT (St-Pierre-de-la-Réunion) in the co-supervised PhD thesis of E. Tapachés, integrates the dynamic behavior of the linear receptor. In addition, our model accounts for various non-linear effects, such as temperature-dependent thermophysical properties and heat-transfer-coefficient. As a consequence, oppositely to pseudo-stationary models, our model can simulate the behavior of the Fresnel receptor during and after cloudy events. Indeed, for the sake of material protection special procedures are required in order to maintain the fluid film-temperature under its safety maximum, even in severe situations. We have tested strategies based on feedback control with forward extrapolation and moderated by a time constant related to the current fluid velocity. Although they surely can be improved, some results are yet satisfactory, see Illustration 5. We can thus evaluate the efficiency losses due to control procedures when clouds occur and vanish. As the numerical procedure is efficient enough, operation over two years can be simulated within some hours only. As a result, such solar technology can indeed be of economic interest in isolated places like La Réunion.

Beside the PhD manuscript, some articles are in progress. Lastly, an ANR pre-project was submitted by PIMENT, LIMSI, plus RAPSODEE-ENSTIMAC, PROMES and LSS.

### Use of hydrate slurries with CO2 in secondary refrigeration loops.

This new theme is developing. In order to reduce emissions of refrigerant gases, the global warming potential of which is high, more and more secondary refrigeration loops (filled with a fluid neutral with respect to the environment) replace large scale direct-cooling units e.g. in supermarkets or in hospitals (the smaller the cooling unit itself, the less it leaks). Ice slurries have been used for long a secondary refrigerant in industrial environment because they offer the advantage of large fusion enthalpy over reduced temperature glide. Currently, new types of slurries are under study, clathrate-hydrates, which are ice-like crystalline compounds, mainly made of water molecules that form cages around host molecule(s) thanks to their hydrogen-bonds. Fusion temperature of hydrate slurries lies over zero Celsius (e.g. 7 or 10°C); in addition it can be adjusted to the designed application. In 2013, LIMSI and IRSTEA obtained the PEPS project Formhydable from CNRS-INSIS-Energie. We thus constructed together a first-generation model of a very simple loop, inserted between the evaporator of the cooling unit and just one heat-exchanger where cold is finally used. Our model basically represents all the energy transport and conversion processes from the final use (in the present case, air conditioning) up the heat release to the atmosphere, i.e. including the cooling unit and its consumption of electrical power. This approach is original in the literature. Flow constraints are taken into account in order to avoid both crystal deposition (if the flow is laminar) and too high pressure drops in the loop. As a result, the loop design is adapted to the considered slurry, thus making each simulation self-consistent. Illustration 6 shows comparison of performance of various slurries ranging from glycol-water mixture to clathrate-hydrate of CO2+TBPB; it evidences the energetic advantage of hydrate slurries. In the next future (ANR project Crysalhyd, 42 months, IRSTEA, ENSTA, LIMSI, and two industrial companies), the model will be extended to more realistic configurations, with dynamic behavior and with storage.