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

Following sub-topics are studied by the group:

- External natural convection around a linear source generated by periodical heating
- Hydrodynamics of microswimmers
- Oblique Darcean flows in anisotropic porous media
- Dynamic simulation of linear Fresnel mirror solar collectors
- Energy efficiency of CO2 hydrate grouts for secondary refrigeration processes
- Photovoltaic Association (PV) + Plane Mirrors - Evaluation of photovoltaic components in outdoor environments - Massive integration of renewable energies into networks - Experiments, simulations and analyses.

### External natural convection around a linear source generated by periodical heating

The impact of periodical heating on external natural convection as induced by a linear source is investigated. The heat flux is modulated around an average value. We study how the thermal disturbance generated at the wall is transmitted to the fluid, where a natural convection flow is already developed. A first study was carried out by considering a pulsed heating system of the "imposed flow" type. A dual approach, experimental and numerical, has been implemented. The configuration studied is a platinum wire immersed in a large volume of liquid water. Numerical simulations are performed with the code SUNFLUIDH.

The frequency response of the "wire-fluid" system to sinusoidal oscillations has been demonstrated. The heat transfer to the wall can thus be represented using a classic Bode diagram showing the amplitude of the yarn temperature oscillations in a frequency range between 0 and 100~Hz. A simplified theoretical model was developed and the comparison with the results showed the interest of this analytical approach but also its limitations [1].

The heat transfer in the median vertical plane above the wire was then studied, only by numerical simulation due to the low overheating involved in the fluid. An appropriate sizing has been proposed in order to be able to compare the temperature and velocity signals recorded at different heights in the frequency range 0-100~Hz. An analysis of the results, obtained in the median vertical plane above the linear source, was conducted by developing a 1D advection-diffusion model. This model allows the comparison of the amplitude of temperature oscillations with the results from numerical simulations. The good agreement observed attests to the relevance of the model. The next step was to highlight the impact of the parameters of the velocity and temperature fields present in the fluid before sinusoidal disturbances were triggered. [2] The impact of forced temperature pulsed heating was also studied, again using numerical simulations. The objective was to test the capabilities of the 1D advection-diffusion model for new heating conditions but also to address the issue of phase shift (temperature oscillations) that could not be addressed in the imposed flow study. The comparison between the model and numerical simulations shows the relevance of the model when the frequency exceeds a critical value, equal here to about 0.8~Hz. Below this frequency, the temperature oscillations have an amplification not represented by the model [3].

[1] M. Jarrahi, M.-C. Duluc, Y. Fraigneau, G. Defresne, Natural convection around a pulsating line heat source, Proc. 15th Int. Heat Transf. Conf. Kyoto, 10-15 aug. 2014.

[2] M.-C. Duluc, Y. Fraigneau, Effect of frequency on natural convection flows induced by a pulsating line-heat source, International Journal of Thermal Sciences, 117, pp.~342-357, 2017.

[3] M.-C. Duluc, Y. Fraigneau,, Convection naturelle externe engendrée par une source linéique soumise à un chauffage pulsé de type température imposée, Congrès Français de Thermique, Marseille, 2017.

### Hydrodynamics of microswimmers

Microorganisms often live in an aquatic environment, and those who are swimmers seek nutrients through their self-propulsion (motility). The hydrodynamics of their environment can play an important role in their motility, growth, and in general their behaviour. As part of a thesis co-supervised at the University of Paris-Diderot (defended in December 2016), we described by a model the effect of hydrodynamic stress present in bioreactors on the motility of microorganisms (Chlamydomonas reinhardtii and Synechocystis) during different phases of their growth cycle. The influence of the same stress on growth was studied using a dynamic systems approach. It has been experimentally demonstrated that the instantaneous growth rate and the per capita growth rate tend towards zero and oscillate around a stable fixed point where the population density reaches the maximum capacity of the system (figure). A logistic model with two growth parameters, exponential growth rate and carrying capacity, is proposed to describe growth over time. Measurements and calculations, made with two types of bioreactors (stirred tank and tubular airlift) show that, in both cases, Synechocystis is very resistant to shear, that the effect of shear on the exponential growth rate is limited to the decomposition of cellular colonies, but that its carrying capacity seems to increase with shear to a maximum value. For its part, Chlamydomonas reinhardtii is more sensitive; its exponential growth rate increases with shear intensity, but its carrying capacity seems less affected. This work is currently continuing with the co-supervision of two theses as part of a collaboration agreement signed in December 2017 between LIMSI and the APC/Paris-Diderot. These theses focus on understanding the interaction between flow and motility of Chlamydomonas reinhardtii in microfluidic systems.

In the same theme, a collaboration with the FAST laboratory began at the end of 2016 to study mixing and transport by microswimmers (biomixing). The swimming of microorganisms creates a mixing zone in their immediate environment. We are studying this mixture as well as the transport of passive tracers by microswimmers. This study requires the development of a micro-scale visualization technique and image processing that will then allow the hydrodynamics of the mixture to be analyzed. Our LaSIPS project entitled " Bio-mix in confined environments (BIOMEMIC) " was accepted in July 2017 to finance the purchase of a fast microscope camera, consumables and two 6-month internships to continue this study until mid-2019 in collaboration with two other laboratories at the Université Paris-Saclay: LGPM and FAST. The goal of this interdisciplinary project is to identify the structures of the mixture and control the chaos created by motile microorganisms in confined environments where the effect of walls can play a decisive role in the dynamics of the system.

### Oblique Darcean flows in anisotropic porous media

The porous medium studied is described by a rectangular periodic base cell of width W, height H and shape ratio A=H/W. In the case of staggered cylinder arrangement, the geometry is isotropic for A=1 (square array) or A=1,732 (hexagonal array). By imposing a macroscopic pressure gradient at the base cell level, Stokes equations are solved at the microscopic scale to determine the velocity and pressure fields. Homogenization techniques are used to characterize the components of the permeability tensor K using Darcy's law that links the macroscopic pressure gradient to the overall velocity. Tensor anisotropy depends on the geometry of the porous medium with a counter-intuitive result: Kyy > Kxx for 1 < A < 1.732, and Kyy < Kxx for 1.732 < A < 2.5. This result was found for different porosities studied: a high (0.8), a medium (0.6) and a low (0.4).

### Dynamic simulation of linear Fresnel mirror solar collectors

Solar test facilities are often located in deserts, when a significant part of humanity lives in humid tropical climates. If pseudo-stationary models are adapted to the former case, only dynamic models can correctly predict operation, and therefore performance, of a solar field locate in a climate with frequent and chaotic cloud passages. In his thesis, that was co-supervised with PIMENT (St-Pierre-de-La-Réunion), E. Tapachès built a dynamic model for linear Fresnel solar collectors, described from the mirrors to the heat transfer fluid. THis model can simulate rapid changes in temperatures and solar flux. In addition, an original control strategy, combining a closed-loop control in normal operation and an open loop one in critical situations, makes it possible to maintain the temperature of the fluid film below its safety limit (600K) everywhere, even in severe situations. The figure here-under shows such a case with highly variable sunlight and a fluid outlet temperature (red curve) correctly regulated at 500K (see the circled area). Such control procedures protect the system from premature degradation, but also reduce performance. By taking them into account, our model gives a good evaluation of the energy actually collected (which would be necessarily overestimated by pseudo-stationary models). The simulation of two years of operation (in only some hours cpu) in the tropical climate of Reunion Island shows that such solar technology can indeed be of economic interest in this isolated context. [Tapachès et al., SFT 2014]

### Energy efficiency of CO2 hydrate slurries for secondary refrigeration processes

The industry of refrigeration faces a new challenge: it must reduce its emissions (due to leaks) of refrigerants, whose GWP is very significant. Secondary refrigeration already offers a solution: first, the volume of the cooling units (and therefore of refrigerant) is limited, while, second, cold distribution is achieved via a loop containing an environmentally fluid, such as a slurry. Like ice, clathrate-hydrates (crystals made of water molecules arranged in cages around host molecules) offer the advantage of large fusion enthalpies. In the ANR project *CRISALHYD*, involving Irstea, ENSTA, LIMSI, Solvay and Lennox, and begun at the end of 2014, LIMSI is mainly interested in the energy efficiency of secondary refrigeration processes, particularly with gas hydrates. An original approach, based on global optimization under constraints, integrates the different couplings for systems designed with various slurries: ice (code IG), CO2- (code CO), TBPB- (code TB) and mixed CO2+TBPB-hydrates (code MH). Among the slurry characteristics, its fusion temperature is the one that ultimately determines the overall energy efficiency of the process (see Fig. here-under).

Correlation between the overall energy consumption of the process (◀)

and the fusion and evaporation temperatures (resp. ▶ and ▷).

Exergy losses in the different components, from HXU to HXC (○ = reversible case).

The global exergy analysis of the process confirms the leading role of that temperature, which determines, on one hand the exergy loss in the user exchanger (cf. HXU in Fig. above), and on the other hand the evaporation temperature of the cooling unit whose COP depends on of the refrigerant[Pons et al., SFT 2015 and 2016, ECOS 2015, IIR-PCM 2016, a first article submitted to Energy]. Phase change kinetics was also introduced into the model (LaSIPS CoolHyd ENSTA-LIMSI project). The results show that, surprisingly, it has only a very small influence on the overall performance of the process (see Fig. MPc)... provided that the heat exchangers are sized accordingly. It is indeed the effective temperatures of the grout in the exchangers, modified by kinetics (cf. Fig. MPd), that will determine the flows, or, once again, the power consumption of the cooling unit[Pons et al., SFT 2017 and a second article submitted to Energy].

A dynamic model of a secondary cold distribution loop is being constructed to simulate the fast transients imposed in the loop by the individual regulations of the different users, and their consequences on the state of the network and the service provided. Control strategies can be studied and possibly optimized. This long-term work is ongoing. Finally, a task of the Crisalhyd project focuses on the industrial consequences of the use of gas hydrates. Indeed, the melting of the crystals releases gaseous CO2, under pressure, which must be stored. Post-doctoral fellow Ziad Youssef first studied a grout/gas separation cyclone at the exit of the "user" exchanger, then built a model to calculate the volumes required to store the released CO2. A process of compressing the gas is thus proposed, reducing volumes and opening the door to a possible contribution to the overall cold production of the process. 1 article submitted to Int. J. Refrigeration].

### Photovoltaic Association (PV) + Plane Mirrors - Evaluation of photovoltaic components in outdoor environments - Massive integration of renewable energies into networks - Experiments, simulations and analyses.

Based on an intensive collaboration with GeePs (CentraleSupélec) and LMD (IPSL-École Polytechnique) and LPICM (CNRS-Total-École Polytechnique), this theme focuses on industrializable solutions to increase PV production by combining mirrors with modules and optimizing their management. It is based on experience and benefits from access to production data from large power plants. This sub-theme has three main axes: (i) characterisation of components (cells, modules, reflectors, electrical converters, etc.) in a real environment - ageing and degradation - diagnosis and prognosis of PV systems, (ii) development of module + mirror solutions to increase production per m² of modules, (iii) integration of renewables in smart-grids (production and consumption forecast and net demand uncertainty, network balancing, storage). Two emerging axes complete it (a) the search for high-performance PV-thermal hybrid systems, (b) the exploration of urban micro-converters for wind and electricity. The ALEPh experiment, initiated in 2010 and built in 2012, combines modules and flat mirrors in an optimized geometry that allow an annual production gain of approximately 20%. Reinstalled on the SIRTA-Palaiseau meteorological site on July 15, 2013, it continues to produce data. This experience was the basis for Marko Pavlov's thesis defended on 25 October 2016, and several M2 and engineering internships. Marko Pavlov continues the development of the concept within a startup. Christine Abdel-Nour's thesis (in progress) concerns the development of a 12kW ALEPh demonstrator to power a microgrid of the future SIRTA building (2019-20 horizon). We operate a "nano-grid" model powered by a Darrieus-Savonius mini-wind turbine and a crystallline silicon module as part of Fausto Calderon-Obaldia's thesis (these two theses are co-directed by A. Migan, J. Badosa and V. Bourdin). We are thus collaborating with the "TREND-X" group at the École Polytechnique. With two startups, we are developing different LCPV (Low Concentration Photovoltaic) systems for applications with power ratings above 300 kW. Since 2016, developments have focused on: (i) better control of the heat exchanges of the modules with a view to (a) improving cooling and as a result of electrical efficiency (figure below), (b) electrical thermal cogeneration (M-C. Duluc, S. Pellerin, B. Antigny, V. Bourdin); (ii) the use of mobile mirrors for better use of reflectors; (iii) the selection of low-cost reflective surfaces; (iv) the development of statistically based algorithms to balance networks by quickly and sustainably offsetting the differences between expected net consumption and actual consumption; (v) the use of vehicle batteries in bidirectional support to the network. The figure below illustrates the results (3D model) obtained during B's internship. Antigny with the NAPEM code developed by S. Pellerin: we focused on the dynamic aspect of the flows generated by the wind around the ALEPh structure. We can see on this section of the flow in the vertical median plane that it is highly turbulent. The analysis of the average velocity field allowed us to highlight recirculations under the module-mirror assembly. This year we are initiating the simulation of the complete system including the energy equation with the SUNFLUIDH Code (Y. Fraigneau).